Improved materials and the Kramers-Kronig solver.

dmayerich
1 parent 4198e3be
Showing 28 changed files with 7997 additions and 7851 deletions Show diff stats
CMakeLists.txt
EstimateMaterial.cpp
FileIO.cpp
GAMMA.cpp
PerformanceData.h
SimulateSpectrum.cpp
bessel.h
bessik.CPP
bessjy.cpp
cbessik.cpp
cbessjy.cpp
cudaKK.h
cudaMain.cu
etaToluene.txt
eta_TolueneK.txt
eta_TolueneN.txt
globals.h
interactivemie.cpp
interactivemie.h
interactivemie.ui
@@ -25,6 +25,9 @@ find_package(GLUT REQUIRED)
 #find GLEW
 find_package(GLEW REQUIRED)
+#find Qwt
+find_package(Qwt REQUIRED)
+
 #add Qt OpenGL stuff
 set(QT_USE_QTOPENGL TRUE)
@@ -53,9 +56,10 @@ file(GLOB SRC_CU &quot;*.cu&quot;)
 #set up copying data files
 configure_file(kPMMA.txt ${CMAKE_CURRENT_BINARY_DIR}/kPMMA.txt @ONLY)
 configure_file(eta_polystyreneK.txt ${CMAKE_CURRENT_BINARY_DIR}/eta_polystyreneK.txt @ONLY)
-configure_file(eta_TolueneK.txt ${CMAKE_CURRENT_BINARY_DIR}/eta_TolueneK.txt @ONLY)
-configure_file(eta_TolueneN.txt ${CMAKE_CURRENT_BINARY_DIR}/eta_TolueneN.txt @ONLY)
+configure_file(etaToluene.txt ${CMAKE_CURRENT_BINARY_DIR}/etaToluene.txt @ONLY)
 configure_file(source_midIR.txt ${CMAKE_CURRENT_BINARY_DIR}/source_midIR.txt @ONLY)
+configure_file(kPolyethylene.txt ${CMAKE_CURRENT_BINARY_DIR}/kPolyethylene.txt @ONLY)
+configure_file(kPTFE.txt ${CMAKE_CURRENT_BINARY_DIR}/kPTFE.txt @ONLY)
 #determine which source files have to be moc'd
 Qt4_wrap_cpp(UI_MOC ${SRC_H})
@@ -72,7 +76,4 @@ source_group(QtUI FILES ${SRC_UI})
 cuda_add_executable(IMie ${SRC_CPP} ${SRC_H} ${UI_H} ${UI_MOC} ${ALL_RCC} ${SRC_CU})
 #set the link libraries
-target_link_libraries(IMie ${QT_LIBRARIES} ${QT_QTOPENGL_LIBRARY} ${OPENGL_gl_LIBRARY} ${OPENGL_glu_LIBRARY} ${GLEW_LIBRARY})
-
-
-
+target_link_libraries(IMie ${QT_LIBRARIES} ${QT_QTOPENGL_LIBRARY} ${OPENGL_gl_LIBRARY} ${OPENGL_glu_LIBRARY} ${GLEW_LIBRARY} ${QWT_LIBRARY})
 \ No newline at end of file
-#include "globals.h"
-#include <stdlib.h>
-#define PI 3.14159
-
-double CalculateError(double* E)
-{
-	//Calculate the error between the Reference Spectrum and the Simulated Spectrum
-	double sumE = 0.0;
-	int nVals = RefSpectrum[currentSpec].size();
-	double nu;
-	for(int i=0; i<nVals; i++)
-	{
-		nu = RefSpectrum[currentSpec][i].nu;
-		E[i] = RefSpectrum[currentSpec][i].A + nu * refSlope - SimSpectrum[i].A;
-		sumE += E[i]*E[i];
-	}
-
-	return sumE/nVals;
-}
-
-void EstimateK(double* E)
-{
-	int nVals = RefSpectrum[currentSpec].size();
-	double nuStart = RefSpectrum[currentSpec].front().nu;
-	double nuEnd = RefSpectrum[currentSpec].back().nu;
-
-	double r = radius/10000.0;
-	double nu;
-	double dNu = (nuEnd - nuStart)/(nVals-1);
-	double eScale;
-	for(int i=0; i<nVals; i++)
-	{
-		nu = nuStart + i*2;
-
-		eScale = 1/(8*PI*r*nu);
-		EtaK[i].A = EtaK[i].A + eScale * E[i];
-		if(EtaK[i].A < 0.0) EtaK[i].A = 0.0;
-	}
-}
-
-void EstimateMaterial()
-{
-	/*This function estimates the material properties of a sphere based on the
-	input spectrum RefSpectrum and the optical properties of the system.
-	1) The material properties are stored in EtaK and EtaN
-	2) The best fit is stored in SimSpectrum*/
-
-	//initialize the material index of refraction
-	EtaN.clear();	
-	EtaK.clear();
-
-	//insert the default material properties
-	SpecPair temp;
-	for(int s=0; s<(int)RefSpectrum[currentSpec].size(); s++)
-	{
-		//the real part of the IR is the user-specified baseline IR
-		temp.nu = RefSpectrum[currentSpec][s].nu;
-		temp.A = baseIR;
-		EtaN.push_back(temp);
-		//the imaginary part of the IR is zero absorbance
-		temp.A = 0.0f;
-		EtaK.push_back(temp);
-	}
-
-
-	//allocate space to store the list of error values
-	double* E = (double*)malloc(sizeof(double) * RefSpectrum[currentSpec].size());
-	//copy the absorbance values into a linear array
-	double* k = (double*)malloc(sizeof(double) * EtaK.size());
-	double* n = (double*)malloc(sizeof(double) * EtaN.size());
-
-	//iterate to solve for both n and k
-	double sumE = 99999.9;
-	int j=0;
-	//clear the console
-	system("cls");
-	while(sumE > minMSE && j < maxFitIter)
-	{	
-		//simulate a spectrum based on the current IR		
-		SimulateSpectrum();
-
-		//calculate the error term
-		sumE = CalculateError(E);
-
-		//estimate the new absorbance
-		EstimateK(E);
-
-		//use Kramers-Kronig to compute n
-		
-		for(unsigned int i=0; i<EtaK.size(); i++)
-			k[i] = EtaK[i].A;
-		cudaKramersKronig(n, k, EtaK.size(), EtaK.front().nu, EtaK.back().nu, baseIR);
-
-		//copy the real part of the index of refraction into the vector
-		EtaN.clear();
-		for(int i=0; i<(int)EtaK.size(); i++)
-		{
-			temp.nu =  EtaK[i].nu;
-			temp.A = n[i];
-			EtaN.push_back(temp);
-		}
-
-		cout<<"    E = "<<sumE<<endl;
-		j++;
-		//SaveSpectrum(n, nVals, "simNj.txt");
-		//SaveSpectrum(k, nVals, "simKj.txt");
-		//SaveSpectrum(simSpec, nVals, "simSpec.txt");
-		//exit(1);
-		
-	}
-
-	free(E);
-	free(k);
-	free(n);
-
-
-
-
-}
 \ No newline at end of file
+#include "globals.h"
+#include <stdlib.h>
+#define PI 3.14159
+
+double CalculateError(double* E)
+{
+    //Calculate the error between the Reference Spectrum and the Simulated Spectrum
+    double sumE = 0.0;
+    int nVals = RefSpectrum[currentSpec].size();
+    double nu;
+    for(int i=0; i<nVals; i++)
+    {
+        nu = RefSpectrum[currentSpec][i].nu;
+        E[i] = RefSpectrum[currentSpec][i].A + nu * refSlope - SimSpectrum[i].A;
+        sumE += E[i]*E[i];
+    }
+
+    return sumE/nVals;
+}
+
+void EstimateK(double* E)
+{
+    int nVals = RefSpectrum[currentSpec].size();
+    double nuStart = RefSpectrum[currentSpec].front().nu;
+    double nuEnd = RefSpectrum[currentSpec].back().nu;
+
+    double r = radius/10000.0;
+    double nu;
+    double dNu = (nuEnd - nuStart)/(nVals-1);
+    double eScale;
+    for(int i=0; i<nVals; i++)
+    {
+        nu = nuStart + i*2;
+
+        eScale = 1/(8*PI*r*nu);
+        EtaK[i].A = EtaK[i].A + eScale * E[i];
+        if(EtaK[i].A < 0.0) EtaK[i].A = 0.0;
+    }
+}
+
+void EstimateMaterial()
+{
+    /*This function estimates the material properties of a sphere based on the
+    input spectrum RefSpectrum and the optical properties of the system.
+    1) The material properties are stored in EtaK and EtaN
+    2) The best fit is stored in SimSpectrum*/
+
+    //initialize the material index of refraction
+    EtaN.clear();
+    EtaK.clear();
+
+    //insert the default material properties
+    SpecPair temp;
+    for(int s=0; s<(int)RefSpectrum[currentSpec].size(); s++)
+    {
+        //the real part of the IR is the user-specified baseline IR
+        temp.nu = RefSpectrum[currentSpec][s].nu;
+        temp.A = baseIR;
+        EtaN.push_back(temp);
+        //the imaginary part of the IR is zero absorbance
+        temp.A = 0.0f;
+        EtaK.push_back(temp);
+    }
+
+
+    //allocate space to store the list of error values
+    double* E = (double*)malloc(sizeof(double) * RefSpectrum[currentSpec].size());
+    //copy the absorbance values into a linear array
+    double* k = (double*)malloc(sizeof(double) * EtaK.size());
+    double* n = (double*)malloc(sizeof(double) * EtaN.size());
+
+    //iterate to solve for both n and k
+    double sumE = 99999.9;
+    int j=0;
+    //clear the console
+    system("cls");
+    while(sumE > minMSE && j < maxFitIter)
+    {
+        //simulate a spectrum based on the current IR
+        SimulateSpectrum();
+
+        //calculate the error term
+        sumE = CalculateError(E);
+
+        //estimate the new absorbance
+        EstimateK(E);
+
+        //use Kramers-Kronig to compute n
+
+        for(unsigned int i=0; i<EtaK.size(); i++)
+            k[i] = EtaK[i].A;
+        cudaKramersKronig(n, k, EtaK.size(), EtaK.front().nu, EtaK.back().nu, baseIR);
+
+        //copy the real part of the index of refraction into the vector
+        EtaN.clear();
+        for(int i=0; i<(int)EtaK.size(); i++)
+        {
+            temp.nu =  EtaK[i].nu;
+            temp.A = n[i];
+            EtaN.push_back(temp);
+        }
+
+        cout<<"    E = "<<sumE<<endl;
+        j++;
+        //SaveSpectrum(n, nVals, "simNj.txt");
+        //SaveSpectrum(k, nVals, "simKj.txt");
+        //SaveSpectrum(simSpec, nVals, "simSpec.txt");
+        //exit(1);
+
+    }
+
+    free(E);
+    free(k);
+    free(n);
+
+
+
+
+}
@@ -6,191 +6,198 @@ using namespace std;
 vector<SpecPair> LoadSpectrum(string filename)
 {
-	//load a spectrum from a file and resample to 2wn intervals
-
-	//create the spectrum
-	vector<SpecPair> S;
-
-	//open the file
-	ifstream inFile(filename.c_str());
-
-	//read all elements of the file
-	SpecPair temp;
-	while(!inFile.eof()){
-		inFile>>temp.nu;
-		inFile>>temp.A;
-		S.push_back(temp);
-	}
-
-	//compute the minimum and maximum input wavenumbers
-	double inMin = S.front().nu;
-	double inMax = S.back().nu;
-
-	int nuMin = (int)ceil(inMin);
-	int nuMax = (int)floor(inMax);
-
-	//make sure both are either even or odd
-	if(nuMin % 2 != nuMax % 2)
-		nuMax--;
-
-	//compute the number of values in the resampled spectrum
-	int nVals = (nuMax - nuMin)/2 + 1;
-
-	//allocate space for the spectrum
-	vector<SpecPair> outSpec;
-
-	double nu, highVal, lowVal, a;
-	int j=1;
-	for(int i=0; i<nVals; i++)
-	{
-		nu = nuMin + i * 2;
-		temp.nu = nu;
-
-		//handle the boundary cases
-		if(nu < inMin || nu > inMax)
-			temp.A = 0.0;
-		else
-		{
-			//move to the correct position in the input array
-			while(j < (int)S.size()-1 && S[j].nu <= nu)
-				j++;
-
-
-			lowVal = S[j-1].nu;
-			highVal = S[j].nu;
-			a = (nu - lowVal)/(highVal - lowVal);
-			temp.A = S[j-1].A * (1.0 - a) + S[j].A * a;
-		}
-		outSpec.push_back(temp);
-	}
-
-
-
-	return outSpec;
+    //load a spectrum from a file and resample to 2wn intervals
+
+    //create the spectrum
+    vector<SpecPair> S;
+
+    //open the file
+    ifstream inFile(filename.c_str());
+    if(!inFile)
+    {
+        cout<<"Error loading spectrum: "<<inFile<<endl;
+        return S;
+    }
+
+    //read all elements of the file
+    SpecPair temp;
+    while(!inFile.eof()) {
+        inFile>>temp.nu;
+        inFile>>temp.A;
+        S.push_back(temp);
+    }
+
+    //compute the minimum and maximum input wavenumbers
+    double inMin = S.front().nu;
+    double inMax = S.back().nu;
+
+    int nuMin = (int)ceil(inMin);
+    int nuMax = (int)floor(inMax);
+
+    //make sure both are either even or odd
+    if(nuMin % 2 != nuMax % 2)
+        nuMax--;
+
+    //compute the number of values in the resampled spectrum
+    int nVals = (nuMax - nuMin)/2 + 1;
+
+    //allocate space for the spectrum
+    vector<SpecPair> outSpec;
+
+    double nu, highVal, lowVal, a;
+    int j=1;
+    for(int i=0; i<nVals; i++)
+    {
+        nu = nuMin + i * 2;
+        temp.nu = nu;
+
+        //handle the boundary cases
+        if(nu < inMin || nu > inMax)
+            temp.A = 0.0;
+        else
+        {
+            //move to the correct position in the input array
+            while(j < (int)S.size()-1 && S[j].nu <= nu)
+                j++;
+
+
+            lowVal = S[j-1].nu;
+            highVal = S[j].nu;
+            a = (nu - lowVal)/(highVal - lowVal);
+            temp.A = S[j-1].A * (1.0 - a) + S[j].A * a;
+        }
+        outSpec.push_back(temp);
+    }
+
+
+
+    return outSpec;
 }
 vector<SpecPair> SetReferenceSpectrum(char* text)
 {
-	stringstream inString(text);
+    stringstream inString(text);
-	//create the spectrum
-	vector<SpecPair> S;
+    //create the spectrum
+    vector<SpecPair> S;
-	SpecPair temp;
-	while(!inString.eof()){
-		inString>>temp.nu;
-		inString>>temp.A;
-		S.push_back(temp);
-	}
+    SpecPair temp;
+    while(!inString.eof()) {
+        inString>>temp.nu;
+        inString>>temp.A;
+        S.push_back(temp);
+    }
-	return S;
+    return S;
 }
-void SaveK(string fileName)
+/*void SaveK(string fileName)
 {
-	ofstream outFile(fileName.c_str());
-	for(unsigned int i=0; i<EtaK.size(); i++)
-	{
-		outFile<<EtaK[i].nu<<"          ";
-		outFile<<EtaK[i].A<<endl;
-	}
-	outFile.close();
-}
-
-void SaveN(string fileName)
+    ofstream outFile(fileName.c_str());
+    for(unsigned int i=0; i<EtaK.size(); i++)
+    {
+        outFile<<EtaK[i].nu<<"          ";
+        outFile<<EtaK[i].A<<endl;
+    }
+    outFile.close();
+}*/
+
+void SaveMaterial(string fileName)
 {
-	ofstream outFile(fileName.c_str());
-	for(unsigned int i=0; i<EtaN.size(); i++)
-	{
-		outFile<<EtaN[i].nu<<"          ";
-		outFile<<EtaN[i].A<<endl;
-	}
-	outFile.close();
+    ofstream outFile(fileName.c_str());
+    outFile<<"nu"<<'\t'<<"n"<<'\t'<<"k"<<endl;
+    for(unsigned int i=0; i<EtaN.size(); i++)
+    {
+        outFile<<EtaN[i].nu<<'\t';
+        outFile<<EtaN[i].A<<'\t';
+        outFile<<EtaK[i].A<<endl;
+    }
+    outFile.close();
 }
 void SaveSimulation(string fileName)
 {
-	ofstream outFile(fileName.c_str());
-	outFile.precision(10);
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		outFile<<SimSpectrum[i].nu<<"          ";
-		outFile<<SimSpectrum[i].A<<endl;
-	}
-	outFile.close();
+    ofstream outFile(fileName.c_str());
+    outFile.precision(10);
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        outFile<<SimSpectrum[i].nu<<"          ";
+        outFile<<SimSpectrum[i].A<<endl;
+    }
+    outFile.close();
 }
 void SaveState()
 {
-	ofstream outFile("main.prj");
-	//Window Parameters
-	outFile<<nuMin<<endl;
-	outFile<<nuMax<<endl;
-	outFile<<aMin<<endl;
-	outFile<<aMax<<endl;
-	outFile<<dNu<<endl;
-
-	//material parameters
-	outFile<<radius<<endl;
-	outFile<<baseIR<<endl;
-	outFile<<cA<<endl;
-
-	//optical parameters
-	outFile<<cNAi<<endl;
-	outFile<<cNAo<<endl;
-	outFile<<oNAi<<endl;
-	outFile<<oNAo<<endl;
-
-	outFile.close();
+    ofstream outFile("main.prj");
+    //Window Parameters
+    outFile<<nuMin<<endl;
+    outFile<<nuMax<<endl;
+    outFile<<aMin<<endl;
+    outFile<<aMax<<endl;
+    outFile<<dNu<<endl;
+
+    //material parameters
+    outFile<<radius<<endl;
+    outFile<<baseIR<<endl;
+    outFile<<cA<<endl;
+
+    //optical parameters
+    outFile<<cNAi<<endl;
+    outFile<<cNAo<<endl;
+    outFile<<oNAi<<endl;
+    outFile<<oNAo<<endl;
+
+    outFile.close();
 }
 void LoadState()
 {
-	ifstream inFile("main.prj");
-	//Window Parameters
-	inFile>>nuMin;
-	inFile>>nuMax;
-	inFile>>aMin;
-	inFile>>aMax;
-	inFile>>dNu;
-
-	//material parameters
-	inFile>>radius;
-	inFile>>baseIR;
-	inFile>>cA;
-
-	//optical parameters
-	inFile>>cNAi;
-	inFile>>cNAo;
-	inFile>>oNAi;
-	inFile>>oNAo;
-
-	inFile.close();
+    ifstream inFile("main.prj");
+    //Window Parameters
+    inFile>>nuMin;
+    inFile>>nuMax;
+    inFile>>aMin;
+    inFile>>aMax;
+    inFile>>dNu;
+
+    //material parameters
+    inFile>>radius;
+    inFile>>baseIR;
+    inFile>>cA;
+
+    //optical parameters
+    inFile>>cNAi;
+    inFile>>cNAo;
+    inFile>>oNAi;
+    inFile>>oNAo;
+
+    inFile.close();
 }
 void SetDefaults()
 {
-	nuMin = 800;
-	nuMax = 4000;
-	dNu = 2;
+    nuMin = 800;
+    nuMax = 4000;
+    dNu = 2;
-	aMin = 0;
-	aMax = 1;
+    aMin = 0;
+    aMax = 1;
-	//material parameters
-	radius = 4.0f;
-	baseIR = 1.49f;
-	cA = 1.0;
-	vector<SpecPair> KMaterial;
-	vector<SpecPair> NMaterial;
+    //material parameters
+    radius = 4.0f;
+    baseIR = 1.49f;
+    cA = 1.0;
+    vector<SpecPair> KMaterial;
+    vector<SpecPair> NMaterial;
-	//optical parameters
-	cNAi = 0.0;
-	cNAo = 0.6;
-	oNAi = 0.0;
-	oNAo = 0.6;
-}
 \ No newline at end of file
+    //optical parameters
+    cNAi = 0.0;
+    cNAo = 0.6;
+    oNAi = 0.0;
+    oNAo = 0.6;
+}
-//  gamma.cpp -- computation of gamma function.
-//      Algorithms and coefficient values from "Computation of Special
-//      Functions", Zhang and Jin, John Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-// Returns gamma function of argument 'x'.
-//
-// NOTE: Returns 1e308 if argument is a negative integer or 0,
-//      or if argument exceeds 171.
-//
-#define _USE_MATH_DEFINES
-#include <math.h>
-double gamma(double x)
-{
-    int i,k,m;
-    double ga,gr,r,z;
-
-    static double g[] = {
-        1.0,
-        0.5772156649015329,
-       -0.6558780715202538,
-       -0.420026350340952e-1,
-        0.1665386113822915,
-       -0.421977345555443e-1,
-       -0.9621971527877e-2,
-        0.7218943246663e-2,
-       -0.11651675918591e-2,
-       -0.2152416741149e-3,
-        0.1280502823882e-3,
-       -0.201348547807e-4,
-       -0.12504934821e-5,
-        0.1133027232e-5,
-       -0.2056338417e-6,
-        0.6116095e-8,
-        0.50020075e-8,
-       -0.11812746e-8,
-        0.1043427e-9,
-        0.77823e-11,
-       -0.36968e-11,
-        0.51e-12,
-       -0.206e-13,
-       -0.54e-14,
-        0.14e-14};
-
-    if (x > 171.0) return 1e308;    // This value is an overflow flag.
-    if (x == (int)x) {
-        if (x > 0.0) {
-            ga = 1.0;               // use factorial
-            for (i=2;i<x;i++) {
-               ga *= i;
-            }
-         }
-         else
-            ga = 1e308;
-     }
-     else {
-        if (fabs(x) > 1.0) {
-            z = fabs(x);
-            m = (int)z;
-            r = 1.0;
-            for (k=1;k<=m;k++) {
-                r *= (z-k);
-            }
-            z -= m;
-        }
-        else
-            z = x;
-        gr = g[24];
-        for (k=23;k>=0;k--) {
-            gr = gr*z+g[k];
-        }
-        ga = 1.0/(gr*z);
-        if (fabs(x) > 1.0) {
-            ga *= r;
-            if (x < 0.0) {
-                ga = -M_PI/(x*ga*sin(M_PI*x));
-            }
-        }
-    }
-    return ga;
-}
+//  gamma.cpp -- computation of gamma function.
+//      Algorithms and coefficient values from "Computation of Special
+//      Functions", Zhang and Jin, John Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+// Returns gamma function of argument 'x'.
+//
+// NOTE: Returns 1e308 if argument is a negative integer or 0,
+//      or if argument exceeds 171.
+//
+#define _USE_MATH_DEFINES
+#include <math.h>
+double gamma(double x)
+{
+    int i,k,m;
+    double ga,gr,r,z;
+
+    static double g[] = {
+        1.0,
+        0.5772156649015329,
+        -0.6558780715202538,
+        -0.420026350340952e-1,
+        0.1665386113822915,
+        -0.421977345555443e-1,
+        -0.9621971527877e-2,
+        0.7218943246663e-2,
+        -0.11651675918591e-2,
+        -0.2152416741149e-3,
+        0.1280502823882e-3,
+        -0.201348547807e-4,
+        -0.12504934821e-5,
+        0.1133027232e-5,
+        -0.2056338417e-6,
+        0.6116095e-8,
+        0.50020075e-8,
+        -0.11812746e-8,
+        0.1043427e-9,
+        0.77823e-11,
+        -0.36968e-11,
+        0.51e-12,
+        -0.206e-13,
+        -0.54e-14,
+        0.14e-14
+    };
+
+    if (x > 171.0) return 1e308;    // This value is an overflow flag.
+    if (x == (int)x) {
+        if (x > 0.0) {
+            ga = 1.0;               // use factorial
+            for (i=2; i<x; i++) {
+                ga *= i;
+            }
+        }
+        else
+            ga = 1e308;
+    }
+    else {
+        if (fabs(x) > 1.0) {
+            z = fabs(x);
+            m = (int)z;
+            r = 1.0;
+            for (k=1; k<=m; k++) {
+                r *= (z-k);
+            }
+            z -= m;
+        }
+        else
+            z = x;
+        gr = g[24];
+        for (k=23; k>=0; k--) {
+            gr = gr*z+g[k];
+        }
+        ga = 1.0/(gr*z);
+        if (fabs(x) > 1.0) {
+            ga *= r;
+            if (x < 0.0) {
+                ga = -M_PI/(x*ga*sin(M_PI*x));
+            }
+        }
+    }
+    return ga;
+}
-// add the following to a cpp file:
-// PerformanceData PD;
-
-
-#pragma once
-#include <ostream>
-using namespace std;
-
-enum PerformanceDataType
-{
-	PD_DISPLAY=0,
-	PD_SPS,
-	PD_UNUSED0,
-
-	//my stuff
-	SIMULATE_SPECTRUM,
-	SIMULATE_GPU,
-	KRAMERS_KRONIG,
-
-	
-
-	//end my stuff
-	PERFORMANCE_DATA_TYPE_COUNT
-};
-
-static char PDTypeNames[][255] = {
-		"Display            ",
-		"Simulation Total   ",
-		" ----------------- ",
-		//my stuff
-		"Simulate Spectrum  ",
-		"      GPU Portion  ",
-		"Kramers-Kronig     ",
-
-		//end my stuff
-		
-};
-#ifdef WIN32
-#include <stdio.h>
-#include <windows.h>
-#include <float.h>
-
-#include <iostream>
-#include <iomanip>
-
-//-------------------------------------------------------------------------------
-
-class PerformanceData
-{
-public:
-	PerformanceData() { ClearAll(); QueryPerformanceFrequency(&cps); }
-	~PerformanceData(){}
-
-	void ClearAll()
-	{
-		for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ ) {
-			for ( int j=0; j<256; j++ ) times[i][j] = 0;
-			pos[i] = 0;
-			minTime[i] = 0xFFFFFFFF;
-			maxTime[i] = 0;
-			totalTime[i] = 0;
-			dataReady[i] = false;
-		}
-	}
-
-	void StartTimer( int type ) { QueryPerformanceCounter( &startTime[type] );}
-	void EndTimer( int type ) {
-		LARGE_INTEGER endTime;
-		QueryPerformanceCounter( &endTime );
-		double t = (double)(endTime.QuadPart - startTime[type].QuadPart);
-		//unsigned int t = GetTickCount() - startTime[type];
-		if ( t < minTime[type] ) minTime[type] = t;
-		if ( t > maxTime[type] ) maxTime[type] = t;
-		totalTime[type] -= times[type][ pos[type] ];
-		times[type][ pos[type] ] = t;
-		totalTime[type] += t;
-		pos[type]++;
-		if ( pos[type] == 0 ) dataReady[type] = true;
-	}
-
-	void PrintResult( ostream &os,int i=PERFORMANCE_DATA_TYPE_COUNT)
-	{
-		os.setf(ios::fixed);
-		if ((i<PERFORMANCE_DATA_TYPE_COUNT)&&(i>=0)){
-			double a = GetAvrgTime(i);
-			if ( a ) 
-				os<< PDTypeNames[i]<<" :  avrg="<<setw(8)<<setprecision(3)<<a<<"\tmin="<<setw(8)<<setprecision(3)<< GetMinTime(i) <<"\tmax="<<setw(8)<<setprecision(3)<< GetMaxTime(i) <<endl ;
-			else 
-				os<< PDTypeNames[i]<<" :  avrg=   -----\tmin=   -----\tmax=   -----"<<endl;
-		}
-	}
-
-	void PrintResults( ostream &os)
-	{
-		for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ ) 
-			PrintResult(os,i);
-	}
-
-	double	GetLastTime( int type ) { return times[type][pos[type]]; }
-	double	GetAvrgTime( int type ) { double a = 1000.0 * totalTime[type] / (float)cps.QuadPart / ( (dataReady[type]) ? 256.0 : (double)pos[type] ); return (_finite(a))? a:0; }
-	double	GetMinTime( int type ) { return 1000.0 * minTime[type] / (float)cps.LowPart; }
-	double	GetMaxTime( int type ) { return 1000.0 * maxTime[type] / (float)cps.LowPart; }
-
-private:
-	double times[PERFORMANCE_DATA_TYPE_COUNT][256];
-	unsigned char pos[PERFORMANCE_DATA_TYPE_COUNT];
-	LARGE_INTEGER startTime[PERFORMANCE_DATA_TYPE_COUNT];
-	double minTime[ PERFORMANCE_DATA_TYPE_COUNT ];
-	double maxTime[ PERFORMANCE_DATA_TYPE_COUNT ];
-	double totalTime[ PERFORMANCE_DATA_TYPE_COUNT ];
-	bool dataReady[ PERFORMANCE_DATA_TYPE_COUNT ];
-	LARGE_INTEGER cps;
-};
-
-//-------------------------------------------------------------------------------
-#else	
-
-class PerformanceData{
-public:
-	PerformanceData() {;};
-	~PerformanceData(){;};
-	void ClearAll(){;};
-	void StartTimer( int type ) {;};
-	void EndTimer( int type ) {;};
-	void PrintResults( ostream &os){;};
-	void PrintResult( ostream &os, int i=PERFORMANCE_DATA_TYPE_COUNT){;};
-	double	GetLastTime( int type ) { return 0.0; };
-	double	GetAvrgTime( int type ) { return 0.0; };
-	double	GetMinTime( int type ) { return 0.0; };
-	double	GetMaxTime( int type ) { return 0.0; };
-};
-
-#endif
-//-------------------------------------------------------------------------------
-
-extern PerformanceData PD;
-
-//-------------------------------------------------------------------------------
+// add the following to a cpp file:
+// PerformanceData PD;
+
+
+#pragma once
+#include <ostream>
+using namespace std;
+
+enum PerformanceDataType
+{
+    PD_DISPLAY=0,
+    PD_SPS,
+    PD_UNUSED0,
+
+    //my stuff
+    SIMULATE_SPECTRUM,
+    SIMULATE_GPU,
+    KRAMERS_KRONIG,
+
+
+
+    //end my stuff
+    PERFORMANCE_DATA_TYPE_COUNT
+};
+
+static char PDTypeNames[][255] = {
+    "Display            ",
+    "Simulation Total   ",
+    " ----------------- ",
+    //my stuff
+    "Simulate Spectrum  ",
+    "      GPU Portion  ",
+    "Kramers-Kronig     ",
+
+    //end my stuff
+
+};
+#ifdef WIN32
+#include <stdio.h>
+#include <windows.h>
+#include <float.h>
+
+#include <iostream>
+#include <iomanip>
+
+//-------------------------------------------------------------------------------
+
+class PerformanceData
+{
+public:
+    PerformanceData() {
+        ClearAll();
+        QueryPerformanceFrequency(&cps);
+    }
+    ~PerformanceData() {}
+
+    void ClearAll()
+    {
+        for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ ) {
+            for ( int j=0; j<256; j++ ) times[i][j] = 0;
+            pos[i] = 0;
+            minTime[i] = 0xFFFFFFFF;
+            maxTime[i] = 0;
+            totalTime[i] = 0;
+            dataReady[i] = false;
+        }
+    }
+
+    void StartTimer( int type ) {
+        QueryPerformanceCounter( &startTime[type] );
+    }
+    void EndTimer( int type ) {
+        LARGE_INTEGER endTime;
+        QueryPerformanceCounter( &endTime );
+        double t = (double)(endTime.QuadPart - startTime[type].QuadPart);
+        //unsigned int t = GetTickCount() - startTime[type];
+        if ( t < minTime[type] ) minTime[type] = t;
+        if ( t > maxTime[type] ) maxTime[type] = t;
+        totalTime[type] -= times[type][ pos[type] ];
+        times[type][ pos[type] ] = t;
+        totalTime[type] += t;
+        pos[type]++;
+        if ( pos[type] == 0 ) dataReady[type] = true;
+    }
+
+    void PrintResult( ostream &os,int i=PERFORMANCE_DATA_TYPE_COUNT)
+    {
+        os.setf(ios::fixed);
+        if ((i<PERFORMANCE_DATA_TYPE_COUNT)&&(i>=0)) {
+            double a = GetAvrgTime(i);
+            if ( a )
+                os<< PDTypeNames[i]<<" :  avrg="<<setw(8)<<setprecision(3)<<a<<"\tmin="<<setw(8)<<setprecision(3)<< GetMinTime(i) <<"\tmax="<<setw(8)<<setprecision(3)<< GetMaxTime(i) <<endl ;
+            else
+                os<< PDTypeNames[i]<<" :  avrg=   -----\tmin=   -----\tmax=   -----"<<endl;
+        }
+    }
+
+    void PrintResults( ostream &os)
+    {
+        for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ )
+            PrintResult(os,i);
+    }
+
+    double	GetLastTime( int type ) {
+        return times[type][pos[type]];
+    }
+    double	GetAvrgTime( int type ) {
+        double a = 1000.0 * totalTime[type] / (float)cps.QuadPart / ( (dataReady[type]) ? 256.0 : (double)pos[type] );
+        return (_finite(a))? a:0;
+    }
+    double	GetMinTime( int type ) {
+        return 1000.0 * minTime[type] / (float)cps.LowPart;
+    }
+    double	GetMaxTime( int type ) {
+        return 1000.0 * maxTime[type] / (float)cps.LowPart;
+    }
+
+private:
+    double times[PERFORMANCE_DATA_TYPE_COUNT][256];
+    unsigned char pos[PERFORMANCE_DATA_TYPE_COUNT];
+    LARGE_INTEGER startTime[PERFORMANCE_DATA_TYPE_COUNT];
+    double minTime[ PERFORMANCE_DATA_TYPE_COUNT ];
+    double maxTime[ PERFORMANCE_DATA_TYPE_COUNT ];
+    double totalTime[ PERFORMANCE_DATA_TYPE_COUNT ];
+    bool dataReady[ PERFORMANCE_DATA_TYPE_COUNT ];
+    LARGE_INTEGER cps;
+};
+
+//-------------------------------------------------------------------------------
+#else
+
+class PerformanceData {
+public:
+    PerformanceData() {
+        ;
+    };
+    ~PerformanceData() {
+        ;
+    };
+    void ClearAll() {
+        ;
+    };
+    void StartTimer( int type ) {
+        ;
+    };
+    void EndTimer( int type ) {
+        ;
+    };
+    void PrintResults( ostream &os) {
+        ;
+    };
+    void PrintResult( ostream &os, int i=PERFORMANCE_DATA_TYPE_COUNT) {
+        ;
+    };
+    double	GetLastTime( int type ) {
+        return 0.0;
+    };
+    double	GetAvrgTime( int type ) {
+        return 0.0;
+    };
+    double	GetMinTime( int type ) {
+        return 0.0;
+    };
+    double	GetMaxTime( int type ) {
+        return 0.0;
+    };
+};
+
+#endif
+//-------------------------------------------------------------------------------
+
+extern PerformanceData PD;
+
+//-------------------------------------------------------------------------------
-#include <math.h>
-#include <complex>
-#include <iostream>
-#include <fstream>
-#include "globals.h"
-#include <QProgressDialog>
-#include <stdlib.h>
-//#include "cufft.h"
-using namespace std;
-
-#define pi 3.14159
-
-typedef complex<double> scComplex;
-
-extern int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
-    complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
-extern int bessjyv(double v,double x,double &vm,double *jv,double *yv,
-    double *djv,double *dyv);
-
-complex<double> Jl_neg(complex<double> x)
-{
-	//this function computes the bessel function of the first kind Jl(x) for l = -0.5
-	return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
-}
-
-double Jl_neg(double x)
-{
-	//this function computes the bessel function of the first kind Jl(x) for l = -0.5
-	return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
-}
-
-double Yl_neg(double x)
-{
-	//this function computes the bessel function of the second kind Yl(x) for l = -0.5;
-	return ( sqrt(2.0/pi) * sin(x) )/sqrt(x);
-}
-
-void computeB(complex<double>* B, double radius, complex<double> refIndex, double lambda, int Nl)
-{
-	double k = (2*pi)/lambda;
-	int b = 2;
-
-	//allocate space for the real bessel functions
-	double* jv = (double*)malloc(sizeof(double)*(Nl+b));
-	double* yv = (double*)malloc(sizeof(double)*(Nl+b));
-	double* jvp = (double*)malloc(sizeof(double)*(Nl+b));
-	double* yvp = (double*)malloc(sizeof(double)*(Nl+b));
-
-	//allocate space for the complex bessel functions
-	complex<double>* cjv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-	complex<double>* cyv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-	complex<double>* cjvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-	complex<double>* cyvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-
-	double kr = k*radius;
-	complex<double> knr = k*refIndex*(double)radius;
-	complex<double> n = refIndex;
-
-	//compute the bessel functions for k*r
-	double vm;// = Nl - 1;
-	bessjyv((Nl)+0.5, kr, vm, jv, yv, jvp, yvp);
-	//cout<<"Nl: "<<Nl<<"  vm: "<<vm<<endl;
-	//printf("Nl: %f, vm: %f\n", (float)Nl, (float)vm);
-
-	//compute the bessel functions for k*n*r
-	cbessjyva((Nl)+0.5, knr, vm, cjv, cyv, cjvp, cyvp);
-
-	//scale factor for spherical bessel functions
-	double scale_kr = sqrt(pi/(2.0*kr));
-	complex<double> scale_knr = sqrt(pi/(2.0*knr));
-
-	complex<double> numer, denom;
-	double j_kr;
-	double y_kr;
-	complex<double> j_knr;
-	complex<double> j_d_knr;
-	double j_d_kr;
-	complex<double> h_kr;
-	complex<double> h_d_kr;
-	complex<double> h_neg;
-	complex<double> h_pos;
-
-	//cout<<"B coefficients:"<<endl;
-	for(int l=0; l<Nl; l++)
-	{
-		//compute the spherical bessel functions
-		j_kr = jv[l] * scale_kr;
-		y_kr = yv[l] * scale_kr;
-		j_knr = cjv[l] * scale_knr;
-
-		//compute the Hankel function
-		h_kr = complex<double>(j_kr, y_kr);
-
-		//compute the derivatives
-		if(l == 0)
-		{
-			//spherical bessel functions for l=0
-			j_d_kr = scale_kr * (Jl_neg(kr) - (jv[l] + kr*jv[l+1])/kr )/2.0;
-			j_d_knr = scale_knr * ( Jl_neg(knr) - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
-			h_neg = complex<double>(scale_kr*Jl_neg(kr), scale_kr*Yl_neg(kr));
-			h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
-			h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
-		}
-		else
-		{
-			//spherical bessel functions
-			j_d_kr = scale_kr * (jv[l-1] - (jv[l] + kr*jv[l+1])/kr )/2.0;
-			j_d_knr = scale_knr * ( cjv[l-1] - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
-			h_neg = complex<double>(scale_kr*jv[l-1], scale_kr*yv[l-1]);
-			h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
-			h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
-		}
-
-		numer = j_kr*j_d_knr*n - j_knr*j_d_kr;
-		denom = j_knr*h_d_kr - h_kr*j_d_knr*n;
-		B[l] =  numer/denom;
-
-		//B[l] = scComplex(temp.real(), temp.imag());
-		//cout<<B[l]<<endl;
-	}
-
-	free(jv);
-	free(yv);
-	free(jvp);
-	free(yvp);
-	free(cjv);
-	free(cyv);
-	free(cjvp);
-	free(cyvp);
-}
-
-void Legendre(double* P, double x, int Nl)
-{
-	//computes the legendre polynomials from orders 0 to Nl-1
-	P[0] = 1;
-	if(Nl == 1) return;
-	P[1] = x;
-	for(int l = 2; l < Nl; l++)
-	{
-		P[l] = ((2*l - 1)*x*P[l-1] - (l - 1)*P[l-2])/l;
-	}
-
-}
-
-complex<double> integrateUi(double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
-{
-	/*This function integrates the incident field of magnitude M in the far zone
-	in order to evaluate the field at the central pixel of a detector.
-	cNAi = condenser inner angle
-	cNAo = condenser outer angle
-	oNAi = objective inner angle
-	oNAo = objective outer angle
-	M = field magnitude*/
-
-	double alphaIn = max(cAngleI, oAngleI);
-	double alphaOut = min(cAngleO,oAngleO);
-
-	complex<double> Ui;
-	if(alphaIn > alphaOut)
-		Ui = complex<double>(0.0, 0.0);
-	else
-		Ui = complex<double>(M * 2 * pi * (cos(alphaIn) - cos(alphaOut)), 0.0f);
-
-	return Ui;
-
-}
-
-void computeCondenserAlpha(double* alpha, int Nl, double cAngleI, double cAngleO)
-{
-	/*This function computes the condenser integral in order to build the field of incident light
-	alpha = list of Nl floating point values representing the condenser alpha as a function of l
-	Nl = number of orders in the incident field
-	cAngleI, cAngleO = inner and outer condenser angles (inner and outer NA)*/
-
-	//compute the Legendre polynomials for the condenser aperature
-	double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAo, cos(cAngleO), Nl+1);
-	double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAi, cos(cAngleI), Nl+1);
-
-	for(int l=0; l<Nl; l++)
-	{
-		//integration term
-		if(l == 0)
-			alpha[l] = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
-		else
-			alpha[l] = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
-
-		alpha[l] *= 2 * pi;
-	}
-
-}
-
-complex<double> integrateUs(double r, double lambda, complex<double> eta,
-						   double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
-{
-	/*This function integrates the incident field of magnitude M in the far zone
-	in order to evaluate the field at the central pixel of a detector.
-	r = sphere radius
-	lambda = wavelength
-	eta = index of refraction
-	cNAi = condenser inner NA
-	cNAo = condenser outer NA
-	oNAi = objective inner NA
-	oNAo = objective outer NA
-	M = field magnitude*/
-
-	//compute the required number of orders
-	double k = 2*pi/lambda;
-	int Nl = (int)ceil( k + 4 * exp(log(k*r)/3) + 3 );
-
-	//compute the material coefficients B
-	complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>)*Nl);
-	//compute the Legendre polynomials for the condenser and objective aperatures
-	double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAo, cos(cAngleO), Nl+1);
-	double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAi, cos(cAngleI), Nl+1);
-
-	double* PoNAo = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PoNAo, cos(oAngleO), Nl+1);
-	double* PoNAi = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PoNAi, cos(oAngleI), Nl+1);
-
-	//store the index of refraction;
-	complex<double> IR(eta.real(), eta.imag());
-
-	//compute the scattering coefficients
-	computeB(B, r, IR, lambda, Nl);
-
-	//aperature terms for the condenser (alpha) and objective (beta)
-	double alpha;
-	double beta;
-	double c;
-	complex<double> Us(0.0, 0.0);
-
-	for(int l=0; l<Nl; l++)
-	{
-		//integration term
-		if(l == 0)
-		{
-			alpha = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
-			beta = -PoNAo[l+1] + PoNAo[0] + PoNAi[l+1] - PoNAi[0];
-		}
-		else
-		{
-			alpha = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
-			beta = -PoNAo[l+1] + PoNAo[l-1] + PoNAi[l+1] - PoNAi[l-1];
-		}
-		c = (2*pi)/(2.0 * l + 1.0);
-		Us += c * alpha * beta * B[l] * M;
-
-
-	}
-	free(PcNAo);
-	free(PcNAi);
-	free(PoNAo);
-	free(PoNAi);
-	free(B);
-
-	return Us;
-
-}
-
-void pointSpectrum()
-{
-	PD.StartTimer(SIMULATE_SPECTRUM);
-	//clear the previous spectrum
-	SimSpectrum.clear();
-
-	double dNu = 2.0f;
-	double lambda;
-
-	//compute the angles based on NA
-	double cAngleI = asin(cNAi);
-	double cAngleO = asin(cNAo);
-	double oAngleI = asin(oNAi);
-	double oAngleO = asin(oNAo);
-
-	//implement a reflection-mode system if necessary
-	if(opticsMode == ReflectionOpticsType){
-
-		//set the condenser to match the objective
-		cAngleI = oAngleI;
-		cAngleO = oAngleO;
-
-		//invert the objective
-		oAngleO = pi - cAngleI;
-		oAngleI = pi - cAngleO;
-	}
-
-	//integrate the incident field at the detector position
-	complex<double> Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
-	double I0 = Ui.real() * Ui.real() + Ui.imag() * Ui.imag();
-	I0 *= scaleI0;
-
-
-
-	//double I;
-	SpecPair temp;
-	double nu;
-	complex<double> eta;
-	complex<double> Us, U;
-
-	double vecLen = 0.0;
-	for(unsigned int i=0; i<EtaK.size(); i++)
-	{
-		nu = EtaK[i].nu;
-		lambda = 10000.0f/nu;
-		if(applyMaterial)
-			eta = complex<double>(EtaN[i].A, EtaK[i].A);
-		else
-			eta = complex<double>(baseIR, 0.0);
-
-
-		//integrate the scattered field at the detector position
-		Us = integrateUs(radius, lambda, eta, cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
-		U = Us + Ui;
-		double I = U.real() * U.real() + U.imag() * U.imag();
-
-		temp.nu = nu;
-
-		//set the spectrum value based on the current display type
-		if(dispSimType == AbsorbanceSpecType)
-			temp.A = -log10(I/I0);
-		else
-			temp.A = I;
-
-		if(dispNormalize)
-			vecLen += temp.A * temp.A;
-
-		SimSpectrum.push_back(temp);
-	}
-	vecLen = sqrt(vecLen);
-
-	if(dispNormalize)
-		for(unsigned int i=0; i<SimSpectrum.size(); i++)
-			SimSpectrum[i].A = (SimSpectrum[i].A / vecLen) * dispNormFactor;
-
-	PD.EndTimer(SIMULATE_SPECTRUM);
-}
-
-void updateSpectrum(double* I, double I0, int n)
-{
-	SimSpectrum.clear();
-	SpecPair temp;
-
-	//update the displayed spectrum based on the computed intensity I
-	for(int i=0; i<n; i++)
-	{
-		temp.nu = EtaK[i].nu;
-
-		//set the spectrum value based on the current display type
-		if(dispSimType == AbsorbanceSpecType)
-		{
-			temp.A = -log10(I[i]/I0);
-			//cout<<temp.nu<<"    "<<I[i]<<endl;
-		}
-		else
-		{
-			temp.A = I[i];
-			if(useSourceSpectrum)
-				temp.A *= SourceResampled[i].A;
-		}
-
-		SimSpectrum.push_back(temp);
-	}
-}
-
-void computeCassegrainAngles(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO)
-{
-	//compute the angles based on NA
-	cAngleI = asin(cNAi);
-	cAngleO = asin(cNAo);
-	oAngleI = asin(oNAi);
-	oAngleO = asin(oNAo);
-
-	//implement a reflection-mode system if necessary
-	if(opticsMode == ReflectionOpticsType){
-
-		//set the condenser to match the objective
-		cAngleI = oAngleI;
-		cAngleO = oAngleO;
-
-		//invert the objective
-		oAngleO = pi - cAngleI;
-		oAngleI = pi - cAngleO;
-	}
-
-
-}
-
-int computeNl()
-{
-	double maxNu = EtaK.back().nu;
-	double maxLambda = 10000.0f/maxNu;
-	double k = 2*pi/maxLambda;
-	int Nl = (int)ceil( k + 4 * exp(log(k*radius)/3) + 3 );
-
-	return Nl;
-}
-
-void computeBArray(complex<double>* B, int Nl, int nLambda)
-{
-	double nu;
-	complex<double> eta;
-	double* Lambda = (double*)malloc(sizeof(double) * nLambda);
-
-	//for each wavenumber nu
-	for(unsigned int i=0; i<EtaK.size(); i++)
-	{
-		//compute information based on wavelength and material
-		nu = EtaK[i].nu;
-		Lambda[i] = 10000.0f/nu;
-		if(applyMaterial)
-			eta = complex<double>(EtaN[i].A, EtaK[i].A);
-		else
-			eta = complex<double>(baseIR, 0.0);
-
-		//allocate memory for the scattering coefficients
-		//complex<float>* B = (complex<float>*)malloc(sizeof(complex<float>)*Nl);
-
-		complex<double> IR(eta.real(), eta.imag());
-		computeB(&B[i * Nl], radius, IR, Lambda[i], Nl);
-	}
-}
-
-void computeOpticalParameters(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO, double& I0, double* alpha, int Nl)
-{
-	computeCassegrainAngles(cAngleI, cAngleO, oAngleI, oAngleO);
-
-	//evaluate the incident field intensity
-	I0 = 0.0;
-	complex<double> Ui;
-
-	Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
-	I0 = Ui.real()*2*pi;
-
-	//compute alpha (condenser integral)
-	computeCondenserAlpha(alpha, Nl, cAngleI, cAngleO);
-}
-
-void gpuDetectorSpectrum(int numSamples)
-{
-	//integrate across the objective aperature and calculate the resulting intensity on a detector
-	PD.StartTimer(SIMULATE_SPECTRUM);
-	//clear the previous spectrum
-	SimSpectrum.clear();
-
-	//compute Nl (maximum order of the spectrum)
-	int Nl = computeNl();
-
-	double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
-	double cAngleI, cAngleO, oAngleI, oAngleO, I0;
-	computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
-
-	//allocate space for a list of wavelengths
-	int nLambda = EtaK.size();
-
-	//allocate space for the 2D array (Nl x nu) of scattering coefficients
-	complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
-	computeBArray(B, Nl, nLambda);
-
-
-
-	//allocate temporary space for the spectrum
-	double* I = (double*)malloc(sizeof(double) * EtaK.size());
-
-	//compute the spectrum on the GPU
-	PD.StartTimer(SIMULATE_GPU);
-	cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, numSamples);
-	PD.EndTimer(SIMULATE_GPU);
-
-	updateSpectrum(I, I0, nLambda);
-
-	PD.EndTimer(SIMULATE_SPECTRUM);
-
-}
-
-void SimulateSpectrum()
-{
-	if(pointDetector)
-		pointSpectrum();
-	else
-		gpuDetectorSpectrum(objectiveSamples);
-		//detectorSpectrum(objectiveSamples);
-}
-
-double absorbanceDistortion(){
-
-	//compute the mean of the spectrum
-	double sumSim = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		sumSim += SimSpectrum[i].A;
-	}
-	double meanSim = sumSim/SimSpectrum.size();
-
-	//compute the distortion (MSE from the mean)
-	double sumSE = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		sumSE += pow(SimSpectrum[i].A - meanSim, 2);
-	}
-	double MSE = sumSE / SimSpectrum.size();
-
-	return MSE;
-}
-
-double intensityDistortion(){
-
-	//compute the mean intensity of the spectrum
-	double sumSim = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		sumSim += pow(SimSpectrum[i].A, 2);
-	}
-	double magSim = sqrt(sumSim);
-
-	//compute the distortion (MSE from the mean)
-	double proj = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		proj += (SimSpectrum[i].A/magSim) * (1.0/SimSpectrum.size());
-	}
-	double error = proj;
-
-	return error;
-}
-
-void DistortionMap(float* distortionMap, int nSteps){
-	ofstream outFile("distortion.txt");
-
-	//set the parameters for the distortion simulation
-	double range = 0.4;
-	double step = (range)/(nSteps-1);
-
-	oNAi = 0.2;
-	oNAo = 0.5;
-
-	double startNAi = 0.0;
-	double startNAo = 0.3;
-
-	//compute the optical parameters
-	//compute Nl (maximum order of the spectrum)
-	int Nl = computeNl();
-
-	double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
-	double cAngleI, cAngleO, oAngleI, oAngleO, I0;
-
-	//allocate space for a list of wavelengths
-	int nLambda = EtaK.size();
-
-	//allocate temporary space for the spectrum
-	double* I = (double*)malloc(sizeof(double) * EtaK.size());
-
-	//calculate the material parameters
-	//allocate space for the 2D array (Nl x nu) of scattering coefficients
-	complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
-	computeBArray(B, Nl, nLambda);
-
-    QProgressDialog progress("Computing distortion map...", "Stop", 0, nSteps * nSteps);
-    progress.setWindowModality(Qt::WindowModal);
-
-	double D;
-	double e = 0.001;
-	int i, o;
-	for(i=0; i<nSteps; i++)
-	{
-        for(o=0; o<nSteps; o++)
-		{
-            //update the progress bar and check for an exit
-            progress.setValue(i * nSteps + o);
-            if (progress.wasCanceled())
-                break;
-
-            //set the current optical parameters
-			cNAi = startNAi + i * step;
-			cNAo = startNAo + o * step;
-			//cout<<cNAi<<"   "<<cNAo<<endl;
-
-			//set the current optical parameters
-			//cNAi = i;
-			//cNAo = o;
-
-			//compute the optical parameters
-			computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
-
-			//simulate the spectrum
-			cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, objectiveSamples);
-			updateSpectrum(I, I0, nLambda);
-
-			if(dispSimType == AbsorbanceSpecType)
-			{
-				if(cNAi >= cNAo || cNAi >= oNAo || oNAi >= cNAo || oNAi >= oNAo)
-					D = -1.0;
-				else
-					D = absorbanceDistortion();
-			}
-			else
-			{
-				if(cNAi >= cNAo || oNAi >= oNAo)
-					D = -1.0;
-				else
-					D = intensityDistortion();
-			}
-			distortionMap[o * nSteps + i] = D;
-			outFile<<D<<"       ";
-		}
-		outFile<<endl;
-		//cout<<i<<endl;
-    }
-
-	progress.setValue(nSteps * nSteps);
-
-	outFile.close();
-}
+#include <math.h>
+#include <complex>
+#include <iostream>
+#include <fstream>
+#include "globals.h"
+#include <QProgressDialog>
+#include <stdlib.h>
+//#include "cufft.h"
+using namespace std;
+
+#define pi 3.14159
+
+typedef complex<double> scComplex;
+
+extern int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
+                     complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
+extern int bessjyv(double v,double x,double &vm,double *jv,double *yv,
+                   double *djv,double *dyv);
+
+complex<double> Jl_neg(complex<double> x)
+{
+    //this function computes the bessel function of the first kind Jl(x) for l = -0.5
+    return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
+}
+
+double Jl_neg(double x)
+{
+    //this function computes the bessel function of the first kind Jl(x) for l = -0.5
+    return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
+}
+
+double Yl_neg(double x)
+{
+    //this function computes the bessel function of the second kind Yl(x) for l = -0.5;
+    return ( sqrt(2.0/pi) * sin(x) )/sqrt(x);
+}
+
+void computeB(complex<double>* B, double radius, complex<double> refIndex, double lambda, int Nl)
+{
+    double k = (2*pi)/lambda;
+    int b = 2;
+
+    //allocate space for the real bessel functions
+    double* jv = (double*)malloc(sizeof(double)*(Nl+b));
+    double* yv = (double*)malloc(sizeof(double)*(Nl+b));
+    double* jvp = (double*)malloc(sizeof(double)*(Nl+b));
+    double* yvp = (double*)malloc(sizeof(double)*(Nl+b));
+
+    //allocate space for the complex bessel functions
+    complex<double>* cjv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+    complex<double>* cyv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+    complex<double>* cjvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+    complex<double>* cyvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+
+    double kr = k*radius;
+    complex<double> knr = k*refIndex*(double)radius;
+    complex<double> n = refIndex;
+
+    //compute the bessel functions for k*r
+    double vm;// = Nl - 1;
+    bessjyv((Nl)+0.5, kr, vm, jv, yv, jvp, yvp);
+    //cout<<"Nl: "<<Nl<<"  vm: "<<vm<<endl;
+    //printf("Nl: %f, vm: %f\n", (float)Nl, (float)vm);
+
+    //compute the bessel functions for k*n*r
+    cbessjyva((Nl)+0.5, knr, vm, cjv, cyv, cjvp, cyvp);
+
+    //scale factor for spherical bessel functions
+    double scale_kr = sqrt(pi/(2.0*kr));
+    complex<double> scale_knr = sqrt(pi/(2.0*knr));
+
+    complex<double> numer, denom;
+    double j_kr;
+    double y_kr;
+    complex<double> j_knr;
+    complex<double> j_d_knr;
+    double j_d_kr;
+    complex<double> h_kr;
+    complex<double> h_d_kr;
+    complex<double> h_neg;
+    complex<double> h_pos;
+
+    //cout<<"B coefficients:"<<endl;
+    for(int l=0; l<Nl; l++)
+    {
+        //compute the spherical bessel functions
+        j_kr = jv[l] * scale_kr;
+        y_kr = yv[l] * scale_kr;
+        j_knr = cjv[l] * scale_knr;
+
+        //compute the Hankel function
+        h_kr = complex<double>(j_kr, y_kr);
+
+        //compute the derivatives
+        if(l == 0)
+        {
+            //spherical bessel functions for l=0
+            j_d_kr = scale_kr * (Jl_neg(kr) - (jv[l] + kr*jv[l+1])/kr )/2.0;
+            j_d_knr = scale_knr * ( Jl_neg(knr) - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
+            h_neg = complex<double>(scale_kr*Jl_neg(kr), scale_kr*Yl_neg(kr));
+            h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
+            h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
+        }
+        else
+        {
+            //spherical bessel functions
+            j_d_kr = scale_kr * (jv[l-1] - (jv[l] + kr*jv[l+1])/kr )/2.0;
+            j_d_knr = scale_knr * ( cjv[l-1] - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
+            h_neg = complex<double>(scale_kr*jv[l-1], scale_kr*yv[l-1]);
+            h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
+            h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
+        }
+
+        numer = j_kr*j_d_knr*n - j_knr*j_d_kr;
+        denom = j_knr*h_d_kr - h_kr*j_d_knr*n;
+        B[l] =  numer/denom;
+
+        //B[l] = scComplex(temp.real(), temp.imag());
+        //cout<<B[l]<<endl;
+    }
+
+    free(jv);
+    free(yv);
+    free(jvp);
+    free(yvp);
+    free(cjv);
+    free(cyv);
+    free(cjvp);
+    free(cyvp);
+}
+
+void Legendre(double* P, double x, int Nl)
+{
+    //computes the legendre polynomials from orders 0 to Nl-1
+    P[0] = 1;
+    if(Nl == 1) return;
+    P[1] = x;
+    for(int l = 2; l < Nl; l++)
+    {
+        P[l] = ((2*l - 1)*x*P[l-1] - (l - 1)*P[l-2])/l;
+    }
+
+}
+
+complex<double> integrateUi(double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
+{
+    /*This function integrates the incident field of magnitude M in the far zone
+    in order to evaluate the field at the central pixel of a detector.
+    cNAi = condenser inner angle
+    cNAo = condenser outer angle
+    oNAi = objective inner angle
+    oNAo = objective outer angle
+    M = field magnitude*/
+
+    double alphaIn = max(cAngleI, oAngleI);
+    double alphaOut = min(cAngleO,oAngleO);
+
+    complex<double> Ui;
+    if(alphaIn > alphaOut)
+        Ui = complex<double>(0.0, 0.0);
+    else
+        Ui = complex<double>(M * 2 * pi * (cos(alphaIn) - cos(alphaOut)), 0.0f);
+
+    return Ui;
+
+}
+
+void computeCondenserAlpha(double* alpha, int Nl, double cAngleI, double cAngleO)
+{
+    /*This function computes the condenser integral in order to build the field of incident light
+    alpha = list of Nl floating point values representing the condenser alpha as a function of l
+    Nl = number of orders in the incident field
+    cAngleI, cAngleO = inner and outer condenser angles (inner and outer NA)*/
+
+    //compute the Legendre polynomials for the condenser aperature
+    double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAo, cos(cAngleO), Nl+1);
+    double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAi, cos(cAngleI), Nl+1);
+
+    for(int l=0; l<Nl; l++)
+    {
+        //integration term
+        if(l == 0)
+            alpha[l] = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
+        else
+            alpha[l] = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
+
+        alpha[l] *= 2 * pi;
+    }
+
+}
+
+complex<double> integrateUs(double r, double lambda, complex<double> eta,
+                            double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
+{
+    /*This function integrates the incident field of magnitude M in the far zone
+    in order to evaluate the field at the central pixel of a detector.
+    r = sphere radius
+    lambda = wavelength
+    eta = index of refraction
+    cNAi = condenser inner NA
+    cNAo = condenser outer NA
+    oNAi = objective inner NA
+    oNAo = objective outer NA
+    M = field magnitude*/
+
+    //compute the required number of orders
+    double k = 2*pi/lambda;
+    int Nl = (int)ceil( k + 4 * exp(log(k*r)/3) + 3 );
+
+    //compute the material coefficients B
+    complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>)*Nl);
+    //compute the Legendre polynomials for the condenser and objective aperatures
+    double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAo, cos(cAngleO), Nl+1);
+    double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAi, cos(cAngleI), Nl+1);
+
+    double* PoNAo = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PoNAo, cos(oAngleO), Nl+1);
+    double* PoNAi = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PoNAi, cos(oAngleI), Nl+1);
+
+    //store the index of refraction;
+    complex<double> IR(eta.real(), eta.imag());
+
+    //compute the scattering coefficients
+    computeB(B, r, IR, lambda, Nl);
+
+    //aperature terms for the condenser (alpha) and objective (beta)
+    double alpha;
+    double beta;
+    double c;
+    complex<double> Us(0.0, 0.0);
+
+    for(int l=0; l<Nl; l++)
+    {
+        //integration term
+        if(l == 0)
+        {
+            alpha = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
+            beta = -PoNAo[l+1] + PoNAo[0] + PoNAi[l+1] - PoNAi[0];
+        }
+        else
+        {
+            alpha = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
+            beta = -PoNAo[l+1] + PoNAo[l-1] + PoNAi[l+1] - PoNAi[l-1];
+        }
+        c = (2*pi)/(2.0 * l + 1.0);
+        Us += c * alpha * beta * B[l] * M;
+
+
+    }
+    free(PcNAo);
+    free(PcNAi);
+    free(PoNAo);
+    free(PoNAi);
+    free(B);
+
+    return Us;
+
+}
+
+void pointSpectrum()
+{
+    PD.StartTimer(SIMULATE_SPECTRUM);
+    
+    //if there is no material to simulate
+    if(EtaK.size() == 0)
+	    return;
+    //clear the previous spectrum
+    SimSpectrum.clear();
+
+    double dNu = 2.0f;
+    double lambda;
+
+    //compute the angles based on NA
+    double cAngleI = asin(cNAi);
+    double cAngleO = asin(cNAo);
+    double oAngleI = asin(oNAi);
+    double oAngleO = asin(oNAo);
+
+    //implement a reflection-mode system if necessary
+    if(opticsMode == ReflectionOpticsType) {
+
+        //set the condenser to match the objective
+        cAngleI = oAngleI;
+        cAngleO = oAngleO;
+
+        //invert the objective
+        oAngleO = pi - cAngleI;
+        oAngleI = pi - cAngleO;
+    }
+
+    //integrate the incident field at the detector position
+    complex<double> Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
+    double I0 = Ui.real() * Ui.real() + Ui.imag() * Ui.imag();
+    I0 *= scaleI0;
+
+
+
+    //double I;
+    SpecPair temp;
+    double nu;
+    complex<double> eta;
+    complex<double> Us, U;
+
+    double vecLen = 0.0;
+    for(unsigned int i=0; i<EtaK.size(); i++)
+    {
+        nu = EtaK[i].nu;
+        lambda = 10000.0f/nu;
+        if(applyMaterial)
+            eta = complex<double>(EtaN[i].A, EtaK[i].A);
+        else
+            eta = complex<double>(baseIR, 0.0);
+
+
+        //integrate the scattered field at the detector position
+        Us = integrateUs(radius, lambda, eta, cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
+        U = Us + Ui;
+        double I = U.real() * U.real() + U.imag() * U.imag();
+
+        temp.nu = nu;
+
+        //set the spectrum value based on the current display type
+        if(dispSimType == AbsorbanceSpecType)
+            temp.A = -log10(I/I0);
+        else
+            temp.A = I;
+
+        if(dispNormalize)
+            vecLen += temp.A * temp.A;
+
+        SimSpectrum.push_back(temp);
+    }
+    vecLen = sqrt(vecLen);
+
+    if(dispNormalize)
+        for(unsigned int i=0; i<SimSpectrum.size(); i++)
+            SimSpectrum[i].A = (SimSpectrum[i].A / vecLen) * dispNormFactor;
+
+    PD.EndTimer(SIMULATE_SPECTRUM);
+}
+
+void updateSpectrum(double* I, double I0, int n)
+{
+    SimSpectrum.clear();
+    SpecPair temp;
+
+    //update the displayed spectrum based on the computed intensity I
+    for(int i=0; i<n; i++)
+    {
+        temp.nu = EtaK[i].nu;
+
+        //set the spectrum value based on the current display type
+        if(dispSimType == AbsorbanceSpecType)
+        {
+            temp.A = -log10(I[i]/I0);
+            //cout<<temp.nu<<"    "<<I[i]<<endl;
+        }
+        else
+        {
+            temp.A = I[i];
+            if(useSourceSpectrum)
+                temp.A *= SourceResampled[i].A;
+        }
+
+        SimSpectrum.push_back(temp);
+    }
+}
+
+void computeCassegrainAngles(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO)
+{
+    //compute the angles based on NA
+    cAngleI = asin(cNAi);
+    cAngleO = asin(cNAo);
+    oAngleI = asin(oNAi);
+    oAngleO = asin(oNAo);
+
+    //implement a reflection-mode system if necessary
+    if(opticsMode == ReflectionOpticsType) {
+
+        //set the condenser to match the objective
+        cAngleI = oAngleI;
+        cAngleO = oAngleO;
+
+        //invert the objective
+        oAngleO = pi - cAngleI;
+        oAngleI = pi - cAngleO;
+    }
+
+
+}
+
+int computeNl()
+{
+    double maxNu = EtaK.back().nu;
+    double maxLambda = 10000.0f/maxNu;
+    double k = 2*pi/maxLambda;
+    int Nl = (int)ceil( k + 4 * exp(log(k*radius)/3) + 3 );
+
+    return Nl;
+}
+
+void computeBArray(complex<double>* B, int Nl, int nLambda)
+{
+    double nu;
+    complex<double> eta;
+    double* Lambda = (double*)malloc(sizeof(double) * nLambda);
+
+    //for each wavenumber nu
+    for(unsigned int i=0; i<EtaK.size(); i++)
+    {
+        //compute information based on wavelength and material
+        nu = EtaK[i].nu;
+        Lambda[i] = 10000.0f/nu;
+        if(applyMaterial)
+            eta = complex<double>(EtaN[i].A, EtaK[i].A);
+        else
+            eta = complex<double>(baseIR, 0.0);
+
+        //allocate memory for the scattering coefficients
+        //complex<float>* B = (complex<float>*)malloc(sizeof(complex<float>)*Nl);
+
+        complex<double> IR(eta.real(), eta.imag());
+        computeB(&B[i * Nl], radius, IR, Lambda[i], Nl);
+    }
+}
+
+void computeOpticalParameters(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO, double& I0, double* alpha, int Nl)
+{
+    computeCassegrainAngles(cAngleI, cAngleO, oAngleI, oAngleO);
+
+    //evaluate the incident field intensity
+    I0 = 0.0;
+    complex<double> Ui;
+
+    Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
+    I0 = Ui.real()*2*pi;
+
+    //compute alpha (condenser integral)
+    computeCondenserAlpha(alpha, Nl, cAngleI, cAngleO);
+}
+
+void gpuDetectorSpectrum(int numSamples)
+{
+     //allocate space for a list of wavelengths
+    int nLambda = EtaK.size();
+    if(nLambda == 0)
+	    return;
+    
+    //integrate across the objective aperature and calculate the resulting intensity on a detector
+    PD.StartTimer(SIMULATE_SPECTRUM);
+    //clear the previous spectrum
+    SimSpectrum.clear();
+
+    //compute Nl (maximum order of the spectrum)
+    int Nl = computeNl();
+    
+
+    double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
+    double cAngleI, cAngleO, oAngleI, oAngleO, I0;
+    computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
+    
+
+   
+    
+
+    //allocate space for the 2D array (Nl x nu) of scattering coefficients
+    complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
+    computeBArray(B, Nl, nLambda);
+
+
+
+    //allocate temporary space for the spectrum
+    double* I = (double*)malloc(sizeof(double) * EtaK.size());
+
+    //compute the spectrum on the GPU
+    PD.StartTimer(SIMULATE_GPU);
+    cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, numSamples);
+    PD.EndTimer(SIMULATE_GPU);
+
+    updateSpectrum(I, I0, nLambda);
+
+    PD.EndTimer(SIMULATE_SPECTRUM);
+
+}
+
+void SimulateSpectrum()
+{
+    if(pointDetector)
+        pointSpectrum();
+    else
+        gpuDetectorSpectrum(objectiveSamples);
+	   
+}
+
+double absorbanceDistortion() {
+
+    //compute the mean of the spectrum
+    double sumSim = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        sumSim += SimSpectrum[i].A;
+    }
+    double meanSim = sumSim/SimSpectrum.size();
+
+    //compute the distortion (MSE from the mean)
+    double sumSE = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        sumSE += pow(SimSpectrum[i].A - meanSim, 2);
+    }
+    double MSE = sumSE / SimSpectrum.size();
+
+    return MSE;
+}
+
+double intensityDistortion() {
+
+    //compute the mean intensity of the spectrum
+    double sumSim = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        sumSim += pow(SimSpectrum[i].A, 2);
+    }
+    double magSim = sqrt(sumSim);
+
+    //compute the distortion (MSE from the mean)
+    double proj = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        proj += (SimSpectrum[i].A/magSim) * (1.0/SimSpectrum.size());
+    }
+    double error = proj;
+
+    return error;
+}
+
+void DistortionMap(float* distortionMap, int nSteps) {
+    ofstream outFile("distortion.txt");
+
+    //set the parameters for the distortion simulation
+    double range = 0.4;
+    double step = (range)/(nSteps-1);
+
+    oNAi = 0.2;
+    oNAo = 0.5;
+
+    double startNAi = 0.0;
+    double startNAo = 0.3;
+
+    //compute the optical parameters
+    //compute Nl (maximum order of the spectrum)
+    int Nl = computeNl();
+
+    double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
+    double cAngleI, cAngleO, oAngleI, oAngleO, I0;
+
+    //allocate space for a list of wavelengths
+    int nLambda = EtaK.size();
+
+    //allocate temporary space for the spectrum
+    double* I = (double*)malloc(sizeof(double) * EtaK.size());
+
+    //calculate the material parameters
+    //allocate space for the 2D array (Nl x nu) of scattering coefficients
+    complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
+    computeBArray(B, Nl, nLambda);
+
+    QProgressDialog progress("Computing distortion map...", "Stop", 0, nSteps * nSteps);
+    progress.setWindowModality(Qt::WindowModal);
+
+    double D;
+    double e = 0.001;
+    int i, o;
+    for(i=0; i<nSteps; i++)
+    {
+        for(o=0; o<nSteps; o++)
+        {
+            //update the progress bar and check for an exit
+            progress.setValue(i * nSteps + o);
+            if (progress.wasCanceled())
+                break;
+
+            //set the current optical parameters
+            cNAi = startNAi + i * step;
+            cNAo = startNAo + o * step;
+            //cout<<cNAi<<"   "<<cNAo<<endl;
+
+            //set the current optical parameters
+            //cNAi = i;
+            //cNAo = o;
+
+            //compute the optical parameters
+            computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
+
+            //simulate the spectrum
+            cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, objectiveSamples);
+            updateSpectrum(I, I0, nLambda);
+
+            if(dispSimType == AbsorbanceSpecType)
+            {
+                if(cNAi >= cNAo || cNAi >= oNAo || oNAi >= cNAo || oNAi >= oNAo)
+                    D = -1.0;
+                else
+                    D = absorbanceDistortion();
+            }
+            else
+            {
+                if(cNAi >= cNAo || oNAi >= oNAo)
+                    D = -1.0;
+                else
+                    D = intensityDistortion();
+            }
+            distortionMap[o * nSteps + i] = D;
+            outFile<<D<<"       ";
+        }
+        outFile<<endl;
+        //cout<<i<<endl;
+    }
+
+    progress.setValue(nSteps * nSteps);
+
+    outFile.close();
+}
-#ifndef bessH
-#define bessH
-#define _USE_MATH_DEFINES
-#include <math.h>
-#include <complex>
-using namespace std;
-#define eps 1e-15
-#define el 0.5772156649015329
-
-int msta1(double x,int mp);
-int msta2(double x,int n,int mp);
-int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p);
-int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p);
-int bessjyna(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp);
-int bessjynb(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp);
-int bessjyv(double v,double x,double &vm,double *jv,double *yv,
-    double *jvp,double *yvp);
-int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p);
-int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p);
-int bessikna(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp);
-int bessiknb(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp);
-int bessikv(double v,double x,double &vm,double *iv,double *kv,
-    double *ivp,double *kvp);
-int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
-    complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
-    complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p);
-int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
-int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
-int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
-    complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
-    complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p);
-int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp);
-int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp);
-int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
-    complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
-int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
-    complex<double> *ckv,complex<double> *civp,complex<double> *ckvp);
-
-#endif
+#ifndef bessH
+#define bessH
+#define _USE_MATH_DEFINES
+#include <math.h>
+#include <complex>
+using namespace std;
+#define eps 1e-15
+#define el 0.5772156649015329
+
+int msta1(double x,int mp);
+int msta2(double x,int n,int mp);
+int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p);
+int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p);
+int bessjyna(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp);
+int bessjynb(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp);
+int bessjyv(double v,double x,double &vm,double *jv,double *yv,
+            double *jvp,double *yvp);
+int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p);
+int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p);
+int bessikna(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp);
+int bessiknb(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp);
+int bessikv(double v,double x,double &vm,double *iv,double *kv,
+            double *ivp,double *kvp);
+int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
+              complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
+              complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p);
+int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
+int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
+int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
+              complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
+              complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p);
+int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp);
+int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp);
+int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
+              complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
+int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
+             complex<double> *ckv,complex<double> *civp,complex<double> *ckvp);
+
+#endif
-//  bessik.cpp -- computation of modified Bessel functions In, Kn
-//      and their derivatives. Algorithms and coefficient values from
-//      "Computation of Special Functions", Zhang and Jin, John
-//      Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-#define _USE_MATH_DEFINES
-#include <math.h>
-#include "bessel.h"
-
-double gamma(double x);
-
-int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p)
-{
-    double r,x2,ca,cb,ct,ww,w0,xr,xr2;
-    int k,kz;
-    static double a[] = {
-        0.125,
-        7.03125e-2,
-        7.32421875e-2,
-        1.1215209960938e-1,
-        2.2710800170898e-1,
-        5.7250142097473e-1,
-        1.7277275025845,
-        6.0740420012735,
-        2.4380529699556e1,
-        1.1001714026925e2,
-        5.5133589612202e2,
-        3.0380905109224e3};
-    static double b[] = {
-        -0.375,
-        -1.171875e-1,
-        -1.025390625e-1,
-        -1.4419555664063e-1,
-        -2.7757644653320e-1,
-        -6.7659258842468e-1,
-        -1.9935317337513,
-        -6.8839142681099,
-        -2.7248827311269e1,
-        -1.2159789187654e2,
-        -6.0384407670507e2,
-        -3.3022722944809e3};
-    static double a1[] = {
-        0.125,
-        0.2109375,
-        1.0986328125,
-        1.1775970458984e1,
-        2.1461706161499e2,
-        5.9511522710323e3,
-        2.3347645606175e5,
-        1.2312234987631e7};
-
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        i0 = 1.0;
-        i1 = 0.0;
-        k0 = 1e308;
-        k1 = 1e308;
-        i0p = 0.0;
-        i1p = 0.5;
-        k0p = -1e308;
-        k1p = -1e308;
-        return 0;
-    }
-    x2 = x*x;
-    if (x <= 18.0) {
-        i0 = 1.0;
-        r = 1.0;
-        for (k=1;k<=50;k++) {
-            r *= 0.25*x2/(k*k);
-            i0 += r;
-            if (fabs(r/i0) < eps) break;
-        }
-        i1 = 1.0;
-        r = 1.0;
-        for (k=1;k<=50;k++) {
-            r *= 0.25*x2/(k*(k+1));
-            i1 += r;
-            if (fabs(r/i1) < eps) break;
-        }
-        i1 *= 0.5*x;
-    }
-    else {
-        if (x >= 50.0) kz = 7;
-        else if (x >= 35.0) kz = 9;
-        else kz = 12;
-        ca = exp(x)/sqrt(2.0*M_PI*x);
-        i0 = 1.0;
-        xr = 1.0/x;
-        for (k=0;k<kz;k++) {
-            i0 += a[k]*pow(xr,k+1);
-        }
-        i0 *= ca;
-        i1 = 1.0;
-        for (k=0;k<kz;k++) {
-            i1 += b[k]*pow(xr,k+1);
-        }
-        i1 *= ca;
-    }
-    if (x <= 9.0) {
-        ct = -(log(0.5*x)+el);
-        k0 = 0.0;
-        w0 = 0.0;
-        r = 1.0;
-        ww = 0.0;
-        for (k=1;k<=50;k++) {
-            w0 += 1.0/k;
-            r *= 0.25*x2/(k*k);
-            k0 += r*(w0+ct);
-            if (fabs((k0-ww)/k0) < eps) break;
-            ww = k0;
-        }
-        k0 += ct;
-    }
-    else {
-        cb = 0.5/x;
-        xr2 = 1.0/x2;
-        k0 = 1.0;
-        for (k=0;k<8;k++) {
-            k0 += a1[k]*pow(xr2,k+1);
-        }
-        k0 *= cb/i0;
-    }
-    k1 = (1.0/x - i1*k0)/i0;
-    i0p = i1;
-    i1p = i0-i1/x;
-    k0p = -k1;
-    k1p = -k0-k1/x;
-    return 0;
-}
-
-int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p)
-{
-    double t,t2,dtmp,dtmp1;
-
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        i0 = 1.0;
-        i1 = 0.0;
-        k0 = 1e308;
-        k1 = 1e308;
-        i0p = 0.0;
-        i1p = 0.5;
-        k0p = -1e308;
-        k1p = -1e308;
-        return 0;
-    }
-    if (x < 3.75) {
-        t = x/3.75;
-        t2 = t*t;
-        i0 = (((((0.0045813*t2+0.0360768)*t2+0.2659732)*t2+
-             1.2067492)*t2+3.0899424)*t2+3.5156229)*t2+1.0;
-        i1 = x*(((((0.00032411*t2+0.00301532)*t2+0.02658733*t2+
-             0.15084934)*t2+0.51498869)*t2+0.87890594)*t2+0.5);
-    }
-    else {
-        t = 3.75/x;
-        dtmp1 = exp(x)/sqrt(x);
-        dtmp = (((((((0.00392377*t-0.01647633)*t+0.026355537)*t-0.02057706)*t+
-          0.00916281)*t-0.00157565)*t+0.00225319)*t+0.01328592)*t+0.39894228;
-        i0 = dtmp*dtmp1;
-        dtmp = (((((((-0.00420059*t+0.01787654)*t-0.02895312)*t+0.02282967)*t-
-          0.01031555)*t+0.00163801)*t-0.00362018)*t-0.03988024)*t+0.39894228;
-        i1 = dtmp*dtmp1;
-    }
-    if (x < 2.0) {
-        t = 0.5*x;
-        t2 = t*t;       // already calculated above
-        dtmp = (((((0.0000074*t2+0.0001075)*t2+0.00262698)*t2+0.0348859)*t2+
-          0.23069756)*t2+0.4227842)*t2-0.57721566;
-        k0 = dtmp - i0*log(t);
-        dtmp = (((((-0.00004686*t2-0.00110404)*t2-0.01919402)*t2-
-          0.18156897)*t2-0.67278578)*t2+0.15443144)*t2+1.0;
-        k1 = dtmp/x + i1*log(t);
-    }
-    else {
-        t = 2.0/x;
-        dtmp1 = exp(-x)/sqrt(x);
-        dtmp = (((((0.00053208*t-0.0025154)*t+0.00587872)*t-0.01062446)*t+
-          0.02189568)*t-0.07832358)*t+1.25331414;
-        k0 = dtmp*dtmp1;
-        dtmp = (((((-0.00068245*t+0.00325614)*t-0.00780353)*t+0.01504268)*t-
-          0.0365562)*t+0.23498619)*t+1.25331414;
-        k1 = dtmp*dtmp1;
-    }
-    i0p = i1;
-    i1p = i0 - i1/x;
-    k0p = -k1;
-    k1p = -k0 - k1/x;
-    return 0;
-}
-int bessikna(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp)
-{
-    double bi0,bi1,bk0,bk1,g,g0,g1,f,f0,f1,h,h0,h1,s0;
-    int k,m,ecode;
-
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < eps) {
-        for (k=0;k<=n;k++) {
-            in[k] = 0.0;
-            kn[k] = 1e308;
-            inp[k] = 0.0;
-            knp[k] = -1e308;
-        }
-        in[0] = 1.0;
-        inp[1] = 0.5;
-        return 0;
-    }
-    nm = n;
-    ecode = bessik01a(x,in[0],in[1],kn[0],kn[1],inp[0],inp[1],knp[0],knp[1]);
-    if (n < 2) return 0;
-    bi0 = in[0];
-    bi1 = in[1];
-    bk0 = kn[0];
-    bk1 = kn[1];
-    if ((x > 40.0) && (n < (int)(0.25*x))) {
-        h0 = bi0;
-        h1 = bi1;
-        for (k=2;k<=n;k++) {
-            h = -2.0*(k-1.0)*h1/x+h0;
-            in[k] = h;
-            h0 = h1;
-            h1 = h;
-        }
-    }
-    else {
-        m = msta1(x,200);
-        if (m < n) nm = m;
-        else m = msta2(x,n,15);
-        f0 = 0.0;
-        f1 = 1.0e-100;
-        for (k=m;k>=0;k--) {
-            f = 2.0*(k+1.0)*f1/x+f0;
-            if (x <= nm) in[k] = f;
-            f0 = f1;
-            f1 = f;
-        }
-        s0 = bi0/f;
-        for (k=0;k<=m;k++) {
-            in[k] *= s0;
-        }
-    }
-    g0 = bk0;
-    g1 = bk1;
-    for (k=2;k<=nm;k++) {
-        g = 2.0*(k-1.0)*g1/x+g0;
-        kn[k] = g;
-        g0 = g1;
-        g1 = g;
-    }
-    for (k=2;k<=nm;k++) {
-        inp[k] = in[k-1]-k*in[k]/x;
-        knp[k] = -kn[k-1]-k*kn[k]/x;
-    }
-    return 0;
-}
-int bessiknb(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp)
-{
-    double s0,bs,f,f0,f1,sk0,a0,bkl,vt,r,g,g0,g1;
-    int k,kz,m,l;
-
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < eps) {
-        for (k=0;k<=n;k++) {
-            in[k] = 0.0;
-            kn[k] = 1e308;
-            inp[k] = 0.0;
-            knp[k] = -1e308;
-        }
-        in[0] = 1.0;
-        inp[1] = 0.5;
-        return 0;
-    }
-    nm = n;
-    if (n == 0) nm = 1;
-    m = msta1(x,200);
-    if (m < nm) nm = m;
-    else m = msta2(x,nm,15);
-    bs = 0.0;
-    sk0 = 0.0;
-    f0 = 0.0;
-    f1 = 1.0e-100;
-    for (k=m;k>=0;k--) {
-        f = 2.0*(k+1.0)*f1/x+f0;
-        if (k <= nm) in[k] = f;
-        if ((k != 0) && (k == 2*(int)(k/2))) {
-            sk0 += 4.0*f/k;
-        }
-        bs += 2.0*f;
-        f0 = f1;
-        f1 = f;
-    }
-    s0 = exp(x)/(bs-f);
-    for (k=0;k<=nm;k++) {
-        in[k] *= s0;
-    }
-    if (x <= 8.0) {
-        kn[0] = -(log(0.5*x)+el)*in[0]+s0*sk0;
-        kn[1] = (1.0/x-in[1]*kn[0])/in[0];
-    }
-    else {
-        a0 = sqrt(M_PI_2/x)*exp(-x);
-        if (x >= 200.0) kz = 6;
-        else if (x >= 80.0) kz = 8;
-        else if (x >= 25.0) kz = 10;
-        else kz = 16;
-        for (l=0;l<2;l++) {
-            bkl = 1.0;
-            vt = 4.0*l;
-            r = 1.0;
-            for (k=1;k<=kz;k++) {
-                r *= 0.125*(vt-pow(2.0*k-1.0,2))/(k*x);
-                bkl += r;
-            }
-            kn[l] = a0*bkl;
-        }
-    }
-    g0 = kn[0];
-    g1 = kn[1];
-    for (k=2;k<=nm;k++) {
-        g = 2.0*(k-1.0)*g1/x+g0;
-        kn[k] = g;
-        g0 = g1;
-        g1 = g;
-    }
-    inp[0] = in[1];
-    knp[0] = -kn[1];
-    for (k=1;k<=nm;k++) {
-        inp[k] = in[k-1]-k*in[k]/x;
-        knp[k] = -kn[k-1]-k*kn[k]/x;
-    }
-    return 0;
-}
-
-//  The following program computes the modified Bessel functions
-//  Iv(x) and Kv(x) for arbitrary positive order. For negative
-//  order use:
-//
-//          I-v(x) = Iv(x) + 2/pi sin(v pi) Kv(x)
-//          K-v(x) = Kv(x)
-//
-int bessikv(double v,double x,double &vm,double *iv,double *kv,
-    double *ivp,double *kvp)
-{
-    double x2,v0,piv,vt,a1,v0p,gap,r,bi0,ca,sum;
-    double f,f1,f2,ct,cs,wa,gan,ww,w0,v0n;
-    double r1,r2,bk0,bk1,bk2,a2,cb;
-    int n,k,kz,m;
-
-    if ((v < 0.0) || (x < 0.0)) return 1;
-    x2 = x*x;
-    n = (int)v;
-    v0 = v-n;
-    if (n == 0) n = 1;
-    if (x == 0.0) {
-        for (k=0;k<=n;k++) {
-            iv[k] = 0.0;
-            kv[k] = -1e308;
-            ivp[k] = 0.0;
-            kvp[k] = 1e308;
-        }
-        if (v0 == 0.0) {
-            iv[0] = 1.0;
-            ivp[1] = 0.5;
-        }
-        vm = v;
-        return 0;
-    }
-    piv = M_PI*v0;
-    vt = 4.0*v0*v0;
-    if (v0 == 0.0) {
-        a1 = 1.0;
-    }
-    else {
-        v0p = 1.0+v0;
-        gap = gamma(v0p);
-        a1 = pow(0.5*x,v0)/gap;
-    }
-    if (x >= 50.0) kz = 8;
-    else if (x >= 35.0) kz = 10;
-    else kz = 14;
-    if (x <= 18.0) {
-        bi0 = 1.0;
-        r = 1.0;
-        for (k=1;k<=30;k++) {
-            r *= 0.25*x2/(k*(k+v0));
-            bi0 += r;
-            if (fabs(r/bi0) < eps) break;
-        }
-        bi0 *= a1;
-    }
-    else {
-        ca = exp(x)/sqrt(2.0*M_PI*x);
-        sum = 1.0;
-        r = 1.0;
-        for (k=1;k<=kz;k++) {
-            r *= -0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
-            sum += r;
-        }
-        bi0 = ca*sum;
-    }
-    m = msta1(x,200);
-    if (m < n) n = m;
-    else m = msta2(x,n,15);
-    f2 = 0.0;
-    f1 = 1.0e-100;
-    for (k=m;k>=0;k--) {
-        f = 2.0*(v0+k+1.0)*f1/x+f2;
-        if (k <= n) iv[k] = f;
-        f2 = f1;
-        f1 = f;
-    }
-    cs = bi0/f;
-    for (k=0;k<=n;k++) {
-        iv[k] *= cs;
-    }
-    ivp[0] = v0*iv[0]/x+iv[1];
-    for (k=1;k<=n;k++) {
-        ivp[k] = -(k+v0)*iv[k]/x+iv[k-1];
-    }
-    ww = 0.0;
-    if (x <= 9.0) {
-        if (v0 == 0.0) {
-            ct = -log(0.5*x)-el;
-            cs = 0.0;
-            w0 = 0.0;
-            r = 1.0;
-            for (k=1;k<=50;k++) {
-                w0 += 1.0/k;
-                r *= 0.25*x2/(k*k);
-                cs += r*(w0+ct);
-                wa = fabs(cs);
-                if (fabs((wa-ww)/wa) < eps) break;
-                ww = wa;
-            }
-            bk0 = ct+cs;
-        }
-        else {
-            v0n = 1.0-v0;
-            gan = gamma(v0n);
-            a2 = 1.0/(gan*pow(0.5*x,v0));
-            a1 = pow(0.5*x,v0)/gap;
-            sum = a2-a1;
-            r1 = 1.0;
-            r2 = 1.0;
-            for (k=1;k<=120;k++) {
-                r1 *= 0.25*x2/(k*(k-v0));
-                r2 *= 0.25*x2/(k*(k+v0));
-                sum += a2*r1-a1*r2;
-                wa = fabs(sum);
-                if (fabs((wa-ww)/wa) < eps) break;
-                ww = wa;
-            }
-            bk0 = M_PI_2*sum/sin(piv);
-        }
-    }
-    else {
-        cb = exp(-x)*sqrt(M_PI_2/x);
-        sum = 1.0;
-        r = 1.0;
-        for (k=1;k<=kz;k++) {
-            r *= 0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
-            sum += r;
-        }
-        bk0 = cb*sum;
-    }
-    bk1 = (1.0/x-iv[1]*bk0)/iv[0];
-    kv[0] = bk0;
-    kv[1] = bk1;
-    for (k=2;k<=n;k++) {
-        bk2 = 2.0*(v0+k-1.0)*bk1/x+bk0;
-        kv[k] = bk2;
-        bk0 = bk1;
-        bk1 = bk2;
-    }
-    kvp[0] = v0*kv[0]/x-kv[1];
-    for (k=1;k<=n;k++) {
-        kvp[k] = -(k+v0)*kv[k]/x-kv[k-1];
-    }
-    vm = n+v0;
-    return 0;
-}
+//  bessik.cpp -- computation of modified Bessel functions In, Kn
+//      and their derivatives. Algorithms and coefficient values from
+//      "Computation of Special Functions", Zhang and Jin, John
+//      Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+#define _USE_MATH_DEFINES
+#include <math.h>
+#include "bessel.h"
+
+double gamma(double x);
+
+int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p)
+{
+    double r,x2,ca,cb,ct,ww,w0,xr,xr2;
+    int k,kz;
+    static double a[] = {
+        0.125,
+        7.03125e-2,
+        7.32421875e-2,
+        1.1215209960938e-1,
+        2.2710800170898e-1,
+        5.7250142097473e-1,
+        1.7277275025845,
+        6.0740420012735,
+        2.4380529699556e1,
+        1.1001714026925e2,
+        5.5133589612202e2,
+        3.0380905109224e3
+    };
+    static double b[] = {
+        -0.375,
+        -1.171875e-1,
+        -1.025390625e-1,
+        -1.4419555664063e-1,
+        -2.7757644653320e-1,
+        -6.7659258842468e-1,
+        -1.9935317337513,
+        -6.8839142681099,
+        -2.7248827311269e1,
+        -1.2159789187654e2,
+        -6.0384407670507e2,
+        -3.3022722944809e3
+    };
+    static double a1[] = {
+        0.125,
+        0.2109375,
+        1.0986328125,
+        1.1775970458984e1,
+        2.1461706161499e2,
+        5.9511522710323e3,
+        2.3347645606175e5,
+        1.2312234987631e7
+    };
+
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        i0 = 1.0;
+        i1 = 0.0;
+        k0 = 1e308;
+        k1 = 1e308;
+        i0p = 0.0;
+        i1p = 0.5;
+        k0p = -1e308;
+        k1p = -1e308;
+        return 0;
+    }
+    x2 = x*x;
+    if (x <= 18.0) {
+        i0 = 1.0;
+        r = 1.0;
+        for (k=1; k<=50; k++) {
+            r *= 0.25*x2/(k*k);
+            i0 += r;
+            if (fabs(r/i0) < eps) break;
+        }
+        i1 = 1.0;
+        r = 1.0;
+        for (k=1; k<=50; k++) {
+            r *= 0.25*x2/(k*(k+1));
+            i1 += r;
+            if (fabs(r/i1) < eps) break;
+        }
+        i1 *= 0.5*x;
+    }
+    else {
+        if (x >= 50.0) kz = 7;
+        else if (x >= 35.0) kz = 9;
+        else kz = 12;
+        ca = exp(x)/sqrt(2.0*M_PI*x);
+        i0 = 1.0;
+        xr = 1.0/x;
+        for (k=0; k<kz; k++) {
+            i0 += a[k]*pow(xr,k+1);
+        }
+        i0 *= ca;
+        i1 = 1.0;
+        for (k=0; k<kz; k++) {
+            i1 += b[k]*pow(xr,k+1);
+        }
+        i1 *= ca;
+    }
+    if (x <= 9.0) {
+        ct = -(log(0.5*x)+el);
+        k0 = 0.0;
+        w0 = 0.0;
+        r = 1.0;
+        ww = 0.0;
+        for (k=1; k<=50; k++) {
+            w0 += 1.0/k;
+            r *= 0.25*x2/(k*k);
+            k0 += r*(w0+ct);
+            if (fabs((k0-ww)/k0) < eps) break;
+            ww = k0;
+        }
+        k0 += ct;
+    }
+    else {
+        cb = 0.5/x;
+        xr2 = 1.0/x2;
+        k0 = 1.0;
+        for (k=0; k<8; k++) {
+            k0 += a1[k]*pow(xr2,k+1);
+        }
+        k0 *= cb/i0;
+    }
+    k1 = (1.0/x - i1*k0)/i0;
+    i0p = i1;
+    i1p = i0-i1/x;
+    k0p = -k1;
+    k1p = -k0-k1/x;
+    return 0;
+}
+
+int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p)
+{
+    double t,t2,dtmp,dtmp1;
+
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        i0 = 1.0;
+        i1 = 0.0;
+        k0 = 1e308;
+        k1 = 1e308;
+        i0p = 0.0;
+        i1p = 0.5;
+        k0p = -1e308;
+        k1p = -1e308;
+        return 0;
+    }
+    if (x < 3.75) {
+        t = x/3.75;
+        t2 = t*t;
+        i0 = (((((0.0045813*t2+0.0360768)*t2+0.2659732)*t2+
+                1.2067492)*t2+3.0899424)*t2+3.5156229)*t2+1.0;
+        i1 = x*(((((0.00032411*t2+0.00301532)*t2+0.02658733*t2+
+                   0.15084934)*t2+0.51498869)*t2+0.87890594)*t2+0.5);
+    }
+    else {
+        t = 3.75/x;
+        dtmp1 = exp(x)/sqrt(x);
+        dtmp = (((((((0.00392377*t-0.01647633)*t+0.026355537)*t-0.02057706)*t+
+                   0.00916281)*t-0.00157565)*t+0.00225319)*t+0.01328592)*t+0.39894228;
+        i0 = dtmp*dtmp1;
+        dtmp = (((((((-0.00420059*t+0.01787654)*t-0.02895312)*t+0.02282967)*t-
+                   0.01031555)*t+0.00163801)*t-0.00362018)*t-0.03988024)*t+0.39894228;
+        i1 = dtmp*dtmp1;
+    }
+    if (x < 2.0) {
+        t = 0.5*x;
+        t2 = t*t;       // already calculated above
+        dtmp = (((((0.0000074*t2+0.0001075)*t2+0.00262698)*t2+0.0348859)*t2+
+                 0.23069756)*t2+0.4227842)*t2-0.57721566;
+        k0 = dtmp - i0*log(t);
+        dtmp = (((((-0.00004686*t2-0.00110404)*t2-0.01919402)*t2-
+                  0.18156897)*t2-0.67278578)*t2+0.15443144)*t2+1.0;
+        k1 = dtmp/x + i1*log(t);
+    }
+    else {
+        t = 2.0/x;
+        dtmp1 = exp(-x)/sqrt(x);
+        dtmp = (((((0.00053208*t-0.0025154)*t+0.00587872)*t-0.01062446)*t+
+                 0.02189568)*t-0.07832358)*t+1.25331414;
+        k0 = dtmp*dtmp1;
+        dtmp = (((((-0.00068245*t+0.00325614)*t-0.00780353)*t+0.01504268)*t-
+                 0.0365562)*t+0.23498619)*t+1.25331414;
+        k1 = dtmp*dtmp1;
+    }
+    i0p = i1;
+    i1p = i0 - i1/x;
+    k0p = -k1;
+    k1p = -k0 - k1/x;
+    return 0;
+}
+int bessikna(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp)
+{
+    double bi0,bi1,bk0,bk1,g,g0,g1,f,f0,f1,h,h0,h1,s0;
+    int k,m,ecode;
+
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < eps) {
+        for (k=0; k<=n; k++) {
+            in[k] = 0.0;
+            kn[k] = 1e308;
+            inp[k] = 0.0;
+            knp[k] = -1e308;
+        }
+        in[0] = 1.0;
+        inp[1] = 0.5;
+        return 0;
+    }
+    nm = n;
+    ecode = bessik01a(x,in[0],in[1],kn[0],kn[1],inp[0],inp[1],knp[0],knp[1]);
+    if (n < 2) return 0;
+    bi0 = in[0];
+    bi1 = in[1];
+    bk0 = kn[0];
+    bk1 = kn[1];
+    if ((x > 40.0) && (n < (int)(0.25*x))) {
+        h0 = bi0;
+        h1 = bi1;
+        for (k=2; k<=n; k++) {
+            h = -2.0*(k-1.0)*h1/x+h0;
+            in[k] = h;
+            h0 = h1;
+            h1 = h;
+        }
+    }
+    else {
+        m = msta1(x,200);
+        if (m < n) nm = m;
+        else m = msta2(x,n,15);
+        f0 = 0.0;
+        f1 = 1.0e-100;
+        for (k=m; k>=0; k--) {
+            f = 2.0*(k+1.0)*f1/x+f0;
+            if (x <= nm) in[k] = f;
+            f0 = f1;
+            f1 = f;
+        }
+        s0 = bi0/f;
+        for (k=0; k<=m; k++) {
+            in[k] *= s0;
+        }
+    }
+    g0 = bk0;
+    g1 = bk1;
+    for (k=2; k<=nm; k++) {
+        g = 2.0*(k-1.0)*g1/x+g0;
+        kn[k] = g;
+        g0 = g1;
+        g1 = g;
+    }
+    for (k=2; k<=nm; k++) {
+        inp[k] = in[k-1]-k*in[k]/x;
+        knp[k] = -kn[k-1]-k*kn[k]/x;
+    }
+    return 0;
+}
+int bessiknb(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp)
+{
+    double s0,bs,f,f0,f1,sk0,a0,bkl,vt,r,g,g0,g1;
+    int k,kz,m,l;
+
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < eps) {
+        for (k=0; k<=n; k++) {
+            in[k] = 0.0;
+            kn[k] = 1e308;
+            inp[k] = 0.0;
+            knp[k] = -1e308;
+        }
+        in[0] = 1.0;
+        inp[1] = 0.5;
+        return 0;
+    }
+    nm = n;
+    if (n == 0) nm = 1;
+    m = msta1(x,200);
+    if (m < nm) nm = m;
+    else m = msta2(x,nm,15);
+    bs = 0.0;
+    sk0 = 0.0;
+    f0 = 0.0;
+    f1 = 1.0e-100;
+    for (k=m; k>=0; k--) {
+        f = 2.0*(k+1.0)*f1/x+f0;
+        if (k <= nm) in[k] = f;
+        if ((k != 0) && (k == 2*(int)(k/2))) {
+            sk0 += 4.0*f/k;
+        }
+        bs += 2.0*f;
+        f0 = f1;
+        f1 = f;
+    }
+    s0 = exp(x)/(bs-f);
+    for (k=0; k<=nm; k++) {
+        in[k] *= s0;
+    }
+    if (x <= 8.0) {
+        kn[0] = -(log(0.5*x)+el)*in[0]+s0*sk0;
+        kn[1] = (1.0/x-in[1]*kn[0])/in[0];
+    }
+    else {
+        a0 = sqrt(M_PI_2/x)*exp(-x);
+        if (x >= 200.0) kz = 6;
+        else if (x >= 80.0) kz = 8;
+        else if (x >= 25.0) kz = 10;
+        else kz = 16;
+        for (l=0; l<2; l++) {
+            bkl = 1.0;
+            vt = 4.0*l;
+            r = 1.0;
+            for (k=1; k<=kz; k++) {
+                r *= 0.125*(vt-pow(2.0*k-1.0,2))/(k*x);
+                bkl += r;
+            }
+            kn[l] = a0*bkl;
+        }
+    }
+    g0 = kn[0];
+    g1 = kn[1];
+    for (k=2; k<=nm; k++) {
+        g = 2.0*(k-1.0)*g1/x+g0;
+        kn[k] = g;
+        g0 = g1;
+        g1 = g;
+    }
+    inp[0] = in[1];
+    knp[0] = -kn[1];
+    for (k=1; k<=nm; k++) {
+        inp[k] = in[k-1]-k*in[k]/x;
+        knp[k] = -kn[k-1]-k*kn[k]/x;
+    }
+    return 0;
+}
+
+//  The following program computes the modified Bessel functions
+//  Iv(x) and Kv(x) for arbitrary positive order. For negative
+//  order use:
+//
+//          I-v(x) = Iv(x) + 2/pi sin(v pi) Kv(x)
+//          K-v(x) = Kv(x)
+//
+int bessikv(double v,double x,double &vm,double *iv,double *kv,
+            double *ivp,double *kvp)
+{
+    double x2,v0,piv,vt,a1,v0p,gap,r,bi0,ca,sum;
+    double f,f1,f2,ct,cs,wa,gan,ww,w0,v0n;
+    double r1,r2,bk0,bk1,bk2,a2,cb;
+    int n,k,kz,m;
+
+    if ((v < 0.0) || (x < 0.0)) return 1;
+    x2 = x*x;
+    n = (int)v;
+    v0 = v-n;
+    if (n == 0) n = 1;
+    if (x == 0.0) {
+        for (k=0; k<=n; k++) {
+            iv[k] = 0.0;
+            kv[k] = -1e308;
+            ivp[k] = 0.0;
+            kvp[k] = 1e308;
+        }
+        if (v0 == 0.0) {
+            iv[0] = 1.0;
+            ivp[1] = 0.5;
+        }
+        vm = v;
+        return 0;
+    }
+    piv = M_PI*v0;
+    vt = 4.0*v0*v0;
+    if (v0 == 0.0) {
+        a1 = 1.0;
+    }
+    else {
+        v0p = 1.0+v0;
+        gap = gamma(v0p);
+        a1 = pow(0.5*x,v0)/gap;
+    }
+    if (x >= 50.0) kz = 8;
+    else if (x >= 35.0) kz = 10;
+    else kz = 14;
+    if (x <= 18.0) {
+        bi0 = 1.0;
+        r = 1.0;
+        for (k=1; k<=30; k++) {
+            r *= 0.25*x2/(k*(k+v0));
+            bi0 += r;
+            if (fabs(r/bi0) < eps) break;
+        }
+        bi0 *= a1;
+    }
+    else {
+        ca = exp(x)/sqrt(2.0*M_PI*x);
+        sum = 1.0;
+        r = 1.0;
+        for (k=1; k<=kz; k++) {
+            r *= -0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
+            sum += r;
+        }
+        bi0 = ca*sum;
+    }
+    m = msta1(x,200);
+    if (m < n) n = m;
+    else m = msta2(x,n,15);
+    f2 = 0.0;
+    f1 = 1.0e-100;
+    for (k=m; k>=0; k--) {
+        f = 2.0*(v0+k+1.0)*f1/x+f2;
+        if (k <= n) iv[k] = f;
+        f2 = f1;
+        f1 = f;
+    }
+    cs = bi0/f;
+    for (k=0; k<=n; k++) {
+        iv[k] *= cs;
+    }
+    ivp[0] = v0*iv[0]/x+iv[1];
+    for (k=1; k<=n; k++) {
+        ivp[k] = -(k+v0)*iv[k]/x+iv[k-1];
+    }
+    ww = 0.0;
+    if (x <= 9.0) {
+        if (v0 == 0.0) {
+            ct = -log(0.5*x)-el;
+            cs = 0.0;
+            w0 = 0.0;
+            r = 1.0;
+            for (k=1; k<=50; k++) {
+                w0 += 1.0/k;
+                r *= 0.25*x2/(k*k);
+                cs += r*(w0+ct);
+                wa = fabs(cs);
+                if (fabs((wa-ww)/wa) < eps) break;
+                ww = wa;
+            }
+            bk0 = ct+cs;
+        }
+        else {
+            v0n = 1.0-v0;
+            gan = gamma(v0n);
+            a2 = 1.0/(gan*pow(0.5*x,v0));
+            a1 = pow(0.5*x,v0)/gap;
+            sum = a2-a1;
+            r1 = 1.0;
+            r2 = 1.0;
+            for (k=1; k<=120; k++) {
+                r1 *= 0.25*x2/(k*(k-v0));
+                r2 *= 0.25*x2/(k*(k+v0));
+                sum += a2*r1-a1*r2;
+                wa = fabs(sum);
+                if (fabs((wa-ww)/wa) < eps) break;
+                ww = wa;
+            }
+            bk0 = M_PI_2*sum/sin(piv);
+        }
+    }
+    else {
+        cb = exp(-x)*sqrt(M_PI_2/x);
+        sum = 1.0;
+        r = 1.0;
+        for (k=1; k<=kz; k++) {
+            r *= 0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
+            sum += r;
+        }
+        bk0 = cb*sum;
+    }
+    bk1 = (1.0/x-iv[1]*bk0)/iv[0];
+    kv[0] = bk0;
+    kv[1] = bk1;
+    for (k=2; k<=n; k++) {
+        bk2 = 2.0*(v0+k-1.0)*bk1/x+bk0;
+        kv[k] = bk2;
+        bk0 = bk1;
+        bk1 = bk2;
+    }
+    kvp[0] = v0*kv[0]/x-kv[1];
+    for (k=1; k<=n; k++) {
+        kvp[k] = -(k+v0)*kv[k]/x-kv[k-1];
+    }
+    vm = n+v0;
+    return 0;
+}
-//  bessjy.cpp -- computation of Bessel functions Jn, Yn and their
-//      derivatives. Algorithms and coefficient values from
-//      "Computation of Special Functions", Zhang and Jin, John
-//      Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-// Note that 'math.h' provides (or should provide) values for:
-//      pi      M_PI
-//      2/pi    M_2_PI
-//      pi/4    M_PI_4
-//      pi/2    M_PI_2
-//
-#define _USE_MATH_DEFINES
-#include <math.h>
-#include "bessel.h"
-
-double gamma(double x);
-//
-//  INPUT:
-//      double x    -- argument of Bessel function
-//
-//  OUTPUT (via address pointers):
-//      double j0   -- Bessel function of 1st kind, 0th order
-//      double j1   -- Bessel function of 1st kind, 1st order
-//      double y0   -- Bessel function of 2nd kind, 0th order
-//      double y1   -- Bessel function of 2nd kind, 1st order
-//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
-//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
-//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
-//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
-//
-//  RETURN:
-//      int error code: 0 = OK, 1 = error
-//
-//  This algorithm computes the above functions using series expansions.
-//
-int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p)
-{
-    double x2,r,ec,w0,w1,r0,r1,cs0,cs1;
-    double cu,p0,q0,p1,q1,t1,t2;
-    int k,kz;
-    static double a[] = {
-        -7.03125e-2,
-         0.112152099609375,
-        -0.5725014209747314,
-         6.074042001273483,
-        -1.100171402692467e2,
-         3.038090510922384e3,
-        -1.188384262567832e5,
-         6.252951493434797e6,
-        -4.259392165047669e8,
-         3.646840080706556e10,
-        -3.833534661393944e12,
-         4.854014686852901e14,
-        -7.286857349377656e16,
-         1.279721941975975e19};
-    static double b[] = {
-         7.32421875e-2,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1,
-         5.513358961220206e2,
-        -1.825775547429318e4,
-         8.328593040162893e5,
-        -5.006958953198893e7,
-         3.836255180230433e9,
-        -3.649010818849833e11,
-         4.218971570284096e13,
-        -5.827244631566907e15,
-         9.476288099260110e17,
-        -1.792162323051699e20};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947,
-         1.215978918765359e2,
-        -3.302272294480852e3,
-         1.276412726461746e5,
-        -6.656367718817688e6,
-         4.502786003050393e8,
-        -3.833857520742790e10,
-         4.011838599133198e12,
-        -5.060568503314727e14,
-         7.572616461117958e16,
-        -1.326257285320556e19};
-    static double b1[] = {
-        -0.1025390625,
-         0.2775764465332031,
-        -1.993531733751297,
-         2.724882731126854e1,
-        -6.038440767050702e2,
-         1.971837591223663e4,
-        -8.902978767070678e5,
-         5.310411010968522e7,
-        -4.043620325107754e9,
-         3.827011346598605e11,
-        -4.406481417852278e13,
-         6.065091351222699e15,
-        -9.833883876590679e17,
-         1.855045211579828e20};
-
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        j0 = 1.0;
-        j1 = 0.0;
-        y0 = -1e308;
-        y1 = -1e308;
-        j0p = 0.0;
-        j1p = 0.5;
-        y0p = 1e308;
-        y1p = 1e308;
-        return 0;
-    }
-    x2 = x*x;
-    if (x <= 12.0) {
-        j0 = 1.0;
-        r = 1.0;
-        for (k=1;k<=30;k++) {
-            r *= -0.25*x2/(k*k);
-            j0 += r;
-            if (fabs(r) < fabs(j0)*1e-15) break;
-        }
-        j1 = 1.0;
-        r = 1.0;
-        for (k=1;k<=30;k++) {
-            r *= -0.25*x2/(k*(k+1));
-            j1 += r;
-            if (fabs(r) < fabs(j1)*1e-15) break;
-        }
-        j1 *= 0.5*x;
-        ec = log(0.5*x)+el;
-        cs0 = 0.0;
-        w0 = 0.0;
-        r0 = 1.0;
-        for (k=1;k<=30;k++) {
-            w0 += 1.0/k;
-            r0 *= -0.25*x2/(k*k);
-            r = r0 * w0;
-            cs0 += r;
-            if (fabs(r) < fabs(cs0)*1e-15) break;
-        }
-        y0 = M_2_PI*(ec*j0-cs0);
-        cs1 = 1.0;
-        w1 = 0.0;
-        r1 = 1.0;
-        for (k=1;k<=30;k++) {
-            w1 += 1.0/k;
-            r1 *= -0.25*x2/(k*(k+1));
-            r = r1*(2.0*w1+1.0/(k+1));
-            cs1 += r;
-            if (fabs(r) < fabs(cs1)*1e-15) break;
-        }
-        y1 = M_2_PI * (ec*j1-1.0/x-0.25*x*cs1);
-    }
-    else {
-        if (x >= 50.0) kz = 8;          // Can be changed to 10
-        else if (x >= 35.0) kz = 10;    //  "       "        12
-        else kz = 12;                   //  "       "        14
-        t1 = x-M_PI_4;
-        p0 = 1.0;
-        q0 = -0.125/x;
-        for (k=0;k<kz;k++) {
-            p0 += a[k]*pow(x,-2*k-2);
-            q0 += b[k]*pow(x,-2*k-3);
-        }
-        cu = sqrt(M_2_PI/x);
-        j0 = cu*(p0*cos(t1)-q0*sin(t1));
-        y0 = cu*(p0*sin(t1)+q0*cos(t1));
-        t2 = x-0.75*M_PI;
-        p1 = 1.0;
-        q1 = 0.375/x;
-        for (k=0;k<kz;k++) {
-            p1 += a1[k]*pow(x,-2*k-2);
-            q1 += b1[k]*pow(x,-2*k-3);
-        }
-        j1 = cu*(p1*cos(t2)-q1*sin(t2));
-        y1 = cu*(p1*sin(t2)+q1*cos(t2));
-    }
-    j0p = -j1;
-    j1p = j0-j1/x;
-    y0p = -y1;
-    y1p = y0-y1/x;
-    return 0;
-}
-//
-//  INPUT:
-//      double x    -- argument of Bessel function
-//
-//  OUTPUT:
-//      double j0   -- Bessel function of 1st kind, 0th order
-//      double j1   -- Bessel function of 1st kind, 1st order
-//      double y0   -- Bessel function of 2nd kind, 0th order
-//      double y1   -- Bessel function of 2nd kind, 1st order
-//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
-//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
-//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
-//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
-//
-//  RETURN:
-//      int error code: 0 = OK, 1 = error
-//
-//  This algorithm computes the functions using polynomial approximations.
-//
-int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p)
-{
-    double t,t2,dtmp,a0,p0,q0,p1,q1,ta0,ta1;
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        j0 = 1.0;
-        j1 = 0.0;
-        y0 = -1e308;
-        y1 = -1e308;
-        j0p = 0.0;
-        j1p = 0.5;
-        y0p = 1e308;
-        y1p = 1e308;
-        return 0;
-    }
-    if(x <= 4.0) {
-        t = x/4.0;
-        t2 = t*t;
-        j0 = ((((((-0.5014415e-3*t2+0.76771853e-2)*t2-0.0709253492)*t2+
-            0.4443584263)*t2-1.7777560599)*t2+3.9999973021)*t2
-            -3.9999998721)*t2+1.0;
-        j1 = t*(((((((-0.1289769e-3*t2+0.22069155e-2)*t2-0.0236616773)*t2+
-            0.1777582922)*t2-0.8888839649)*t2+2.6666660544)*t2-
-            3.999999971)*t2+1.9999999998);
-        dtmp = (((((((-0.567433e-4*t2+0.859977e-3)*t2-0.94855882e-2)*t2+
-            0.0772975809)*t2-0.4261737419)*t2+1.4216421221)*t2-
-            2.3498519931)*t2+1.0766115157)*t2+0.3674669052;
-        y0 = M_2_PI*log(0.5*x)*j0+dtmp;
-        dtmp = (((((((0.6535773e-3*t2-0.0108175626)*t2+0.107657607)*t2-
-            0.7268945577)*t2+3.1261399273)*t2-7.3980241381)*t2+
-            6.8529236342)*t2+0.3932562018)*t2-0.6366197726;
-        y1 = M_2_PI*log(0.5*x)*j1+dtmp/x;
-    }
-    else {
-        t = 4.0/x;
-        t2 = t*t;
-        a0 = sqrt(M_2_PI/x);
-        p0 = ((((-0.9285e-5*t2+0.43506e-4)*t2-0.122226e-3)*t2+
-             0.434725e-3)*t2-0.4394275e-2)*t2+0.999999997;
-        q0 = t*(((((0.8099e-5*t2-0.35614e-4)*t2+0.85844e-4)*t2-
-            0.218024e-3)*t2+0.1144106e-2)*t2-0.031249995);
-        ta0 = x-M_PI_4;
-        j0 = a0*(p0*cos(ta0)-q0*sin(ta0));
-        y0 = a0*(p0*sin(ta0)+q0*cos(ta0));
-        p1 = ((((0.10632e-4*t2-0.50363e-4)*t2+0.145575e-3)*t2
-            -0.559487e-3)*t2+0.7323931e-2)*t2+1.000000004;
-        q1 = t*(((((-0.9173e-5*t2+0.40658e-4)*t2-0.99941e-4)*t2
-            +0.266891e-3)*t2-0.1601836e-2)*t2+0.093749994);
-        ta1 = x-0.75*M_PI;
-        j1 = a0*(p1*cos(ta1)-q1*sin(ta1));
-        y1 = a0*(p1*sin(ta1)+q1*cos(ta1));
-    }
-    j0p = -j1;
-    j1p = j0-j1/x;
-    y0p = -y1;
-    y1p = y0-y1/x;
-    return 0;
-}
-int msta1(double x,int mp)
-{
-    double a0,f0,f1,f;
-    int i,n0,n1,nn;
-
-    a0 = fabs(x);
-    n0 = (int)(1.1*a0)+1;
-    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-mp;
-    n1 = n0+5;
-    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-mp;
-    for (i=0;i<20;i++) {
-        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
-        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-mp;
-        if (abs(nn-n1) < 1) break;
-        n0 = n1;
-        f0 = f1;
-        n1 = nn;
-        f1 = f;
-    }
-    return nn;
-}
-int msta2(double x,int n,int mp)
-{
-    double a0,ejn,hmp,f0,f1,f,obj;
-    int i,n0,n1,nn;
-
-    a0 = fabs(x);
-    hmp = 0.5*mp;
-    ejn = 0.5*log10(6.28*n)-n*log10(1.36*a0/n);
-    if (ejn <= hmp) {
-        obj = mp;
-        n0 = (int)(1.1*a0);
-        if (n0 < 1) n0 = 1;
-    }
-    else {
-        obj = hmp+ejn;
-        n0 = n;
-    }
-    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-obj;
-    n1 = n0+5;
-    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-obj;
-    for (i=0;i<20;i++) {
-        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
-        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-obj;
-        if (abs(nn-n1) < 1) break;
-        n0 = n1;
-        f0 = f1;
-        n1 = nn;
-        f1 = f;
-    }
-    return nn+10;
-}
-//
-//  INPUT:
-//  double x    -- argument of Bessel function of 1st and 2nd kind.
-//  int n       -- order
-//
-//  OUPUT:
-//
-//  int nm      -- highest order actually computed (nm <= n)
-//  double jn[] -- Bessel function of 1st kind, orders from 0 to nm
-//  double yn[] -- Bessel function of 2nd kind, orders from 0 to nm
-//  double j'n[]-- derivative of Bessel function of 1st kind,
-//                      orders from 0 to nm
-//  double y'n[]-- derivative of Bessel function of 2nd kind,
-//                      orders from 0 to nm
-//
-//  Computes Bessel functions of all order up to 'n' using recurrence
-//  relations. If 'nm' < 'n' only 'nm' orders are returned.
-//
-int bessjyna(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp)
-{
-    double bj0,bj1,f,f0,f1,f2,cs;
-    int i,k,m,ecode;
-
-    nm = n;
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < 1e-15) {
-        for (i=0;i<=n;i++) {
-            jn[i] = 0.0;
-            yn[i] = -1e308;
-            jnp[i] = 0.0;
-            ynp[i] = 1e308;
-        }
-        jn[0] = 1.0;
-        jnp[1] = 0.5;
-        return 0;
-    }
-    ecode = bessjy01a(x,jn[0],jn[1],yn[0],yn[1],jnp[0],jnp[1],ynp[0],ynp[1]);
-    if (n < 2) return 0;
-    bj0 = jn[0];
-    bj1 = jn[1];
-    if (n < (int)0.9*x) {
-        for (k=2;k<=n;k++) {
-            jn[k] = 2.0*(k-1.0)*bj1/x-bj0;
-            bj0 = bj1;
-            bj1 = jn[k];
-        }
-    }
-    else {
-        m = msta1(x,200);
-        if (m < n) nm = m;
-        else m = msta2(x,n,15);
-        f2 = 0.0;
-        f1 = 1.0e-100;
-        for (k=m;k>=0;k--) {
-            f = 2.0*(k+1.0)/x*f1-f2;
-            if (k <= nm) jn[k] = f;
-            f2 = f1;
-            f1 = f;
-        }
-        if (fabs(bj0) > fabs(bj1)) cs = bj0/f;
-        else cs = bj1/f2;
-        for (k=0;k<=nm;k++) {
-            jn[k] *= cs;
-        }
-    }
-    for (k=2;k<=nm;k++) {
-        jnp[k] = jn[k-1]-k*jn[k]/x;
-    }
-    f0 = yn[0];
-    f1 = yn[1];
-    for (k=2;k<=nm;k++) {
-        f = 2.0*(k-1.0)*f1/x-f0;
-        yn[k] = f;
-        f0 = f1;
-        f1 = f;
-    }
-    for (k=2;k<=nm;k++) {
-        ynp[k] = yn[k-1]-k*yn[k]/x;
-    }
-    return 0;
-}
-//
-//  Same input and output conventions as above. Different recurrence
-//  relations used for 'x' < 300.
-//
-int bessjynb(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp)
-{
-    double t1,t2,f,f1,f2,bj0,bj1,bjk,by0,by1,cu,s0,su,sv;
-    double ec,bs,byk,p0,p1,q0,q1;
-    static double a[] = {
-        -0.7031250000000000e-1,
-         0.1121520996093750,
-        -0.5725014209747314,
-         6.074042001273483};
-    static double b[] = {
-         0.7324218750000000e-1,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947};
-    static double b1[] = {
-       -0.1025390625,
-        0.2775764465332031,
-       -1.993531733751297,
-        2.724882731126854e1};
-        
-    int i,k,m;
-    nm = n;
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < 1e-15) {
-        for (i=0;i<=n;i++) {
-            jn[i] = 0.0;
-            yn[i] = -1e308;
-            jnp[i] = 0.0;
-            ynp[i] = 1e308;
-        }
-        jn[0] = 1.0;
-        jnp[1] = 0.5;
-        return 0;
-    }
-    if (x <= 300.0 || n > (int)(0.9*x)) {
-        if (n == 0) nm = 1;
-        m = msta1(x,200);
-        if (m < nm) nm = m;
-        else m = msta2(x,nm,15);
-        bs = 0.0;
-        su = 0.0;
-        sv = 0.0;
-        f2 = 0.0;
-        f1 = 1.0e-100;
-        for (k = m;k>=0;k--) {
-            f = 2.0*(k+1.0)/x*f1 - f2;
-            if (k <= nm) jn[k] = f;
-            if ((k == 2*(int)(k/2)) && (k != 0)) {
-                bs += 2.0*f;
-//                su += pow(-1,k>>1)*f/(double)k;
-                su += (-1)*((k & 2)-1)*f/(double)k;
-            }
-            else if (k > 1) {
-//                sv += pow(-1,k>>1)*k*f/(k*k-1.0);
-                sv += (-1)*((k & 2)-1)*(double)k*f/(k*k-1.0);
-            }
-            f2 = f1;
-            f1 = f;
-        }
-        s0 = bs+f;
-        for (k=0;k<=nm;k++) {
-            jn[k] /= s0;
-        }
-        ec = log(0.5*x) +0.5772156649015329;
-        by0 = M_2_PI*(ec*jn[0]-4.0*su/s0);
-        yn[0] = by0;
-        by1 = M_2_PI*((ec-1.0)*jn[1]-jn[0]/x-4.0*sv/s0);
-        yn[1] = by1;
-    }
-    else {
-        t1 = x-M_PI_4;
-        p0 = 1.0;
-        q0 = -0.125/x;
-        for (k=0;k<4;k++) {
-            p0 += a[k]*pow(x,-2*k-2);
-            q0 += b[k]*pow(x,-2*k-3);
-        }
-        cu = sqrt(M_2_PI/x);
-        bj0 = cu*(p0*cos(t1)-q0*sin(t1));
-        by0 = cu*(p0*sin(t1)+q0*cos(t1));
-        jn[0] = bj0;
-        yn[0] = by0;
-        t2 = x-0.75*M_PI;
-        p1 = 1.0;
-        q1 = 0.375/x;
-        for (k=0;k<4;k++) {
-            p1 += a1[k]*pow(x,-2*k-2);
-            q1 += b1[k]*pow(x,-2*k-3);
-        }
-        bj1 = cu*(p1*cos(t2)-q1*sin(t2));
-        by1 = cu*(p1*sin(t2)+q1*cos(t2));
-        jn[1] = bj1;
-        yn[1] = by1;
-        for (k=2;k<=nm;k++) {
-            bjk = 2.0*(k-1.0)*bj1/x-bj0;
-            jn[k] = bjk;
-            bj0 = bj1;
-            bj1 = bjk;
-        }
-    }
-    jnp[0] = -jn[1];
-    for (k=1;k<=nm;k++) {
-        jnp[k] = jn[k-1]-k*jn[k]/x;
-    }
-    for (k=2;k<=nm;k++) {
-        byk = 2.0*(k-1.0)*by1/x-by0;
-        yn[k] = byk;
-        by0 = by1;
-        by1 = byk;
-    }
-    ynp[0] = -yn[1];
-    for (k=1;k<=nm;k++) {
-        ynp[k] = yn[k-1]-k*yn[k]/x;
-    }
-    return 0;
-
-}
-
-//  The following routine computes Bessel Jv(x) and Yv(x) for
-//  arbitrary positive order (v). For negative order, use:
-//
-//      J-v(x) = Jv(x)cos(v pi) - Yv(x)sin(v pi)
-//      Y-v(x) = Jv(x)sin(v pi) + Yv(x)cos(v pi)
-//
-int bessjyv(double v,double x,double &vm,double *jv,double *yv,
-    double *djv,double *dyv)
-{
-    double v0,vl,vg,vv,a,a0,r,x2,bjv0,bjv1,bjvl,f,f0,f1,f2;
-    double r0,r1,ck,cs,cs0,cs1,sk,qx,px,byv0,byv1,rp,xk,rq;
-    double b,ec,w0,w1,bju0,bju1,pv0,pv1,byvk;
-    int j,k,l,m,n,kz;
-
-    x2 = x*x;
-    n = (int)v;
-    v0 = v-n;
-    if ((x < 0.0) || (v < 0.0)) return 1;
-    if (x < 1e-15) {
-        for (k=0;k<=n;k++) {
-            jv[k] = 0.0;
-            yv[k] = -1e308;
-            djv[k] = 0.0;
-            dyv[k] = 1e308;
-            if (v0 == 0.0) {
-                jv[0] = 1.0;
-                djv[1] = 0.5;
-            }
-            else djv[0] = 1e308;
-        }
-        vm = v;
-        return 0;
-    }
-    if (x <= 12.0) {
-        for (l=0;l<2;l++) {
-            vl = v0 + l;
-            bjvl = 1.0;
-            r = 1.0;
-            for (k=1;k<=40;k++) {
-                r *= -0.25*x2/(k*(k+vl));
-                bjvl += r;
-                if (fabs(r) < fabs(bjvl)*1e-15) break;
-            }
-            vg = 1.0 + vl;
-            a = pow(0.5*x,vl)/gamma(vg);
-            if (l == 0) bjv0 = bjvl*a;
-            else bjv1 = bjvl*a;
-        }
-    }
-    else {
-        if (x >= 50.0) kz = 8;
-        else if (x >= 35.0) kz = 10;
-        else kz = 11;
-        for (j=0;j<2;j++) {
-            vv = 4.0*(j+v0)*(j+v0);
-            px = 1.0;
-            rp = 1.0;
-            for (k=1;k<=kz;k++) {
-                rp *= (-0.78125e-2)*(vv-pow(4.0*k-3.0,2.0))*
-                    (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*x2);
-                px += rp;
-            }
-            qx = 1.0;
-            rq = 1.0;
-            for (k=1;k<=kz;k++) {
-                rq *= (-0.78125e-2)*(vv-pow(4.0*k-1.0,2.0))*
-                    (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*x2);
-                qx += rq;
-            }
-            qx *= 0.125*(vv-1.0)/x;
-            xk = x-(0.5*(j+v0)+0.25)*M_PI;
-            a0 = sqrt(M_2_PI/x);
-            ck = cos(xk);
-            sk = sin(xk);
-
-            if (j == 0) {
-                bjv0 = a0*(px*ck-qx*sk);
-                byv0 = a0*(px*sk+qx*ck);
-            }
-            else if (j == 1) {
-                bjv1 = a0*(px*ck-qx*sk);
-                byv1 = a0*(px*sk+qx*ck);
-            }
-        }
-    }
-    jv[0] = bjv0;
-    jv[1] = bjv1;
-    djv[0] = v0*jv[0]/x-jv[1];
-    djv[1] = -(1.0+v0)*jv[1]/x+jv[0];
-    if ((n >= 2) && (n <= (int)(0.9*x))) {
-        f0 = bjv0;
-        f1 = bjv1;
-        for (k=2;k<=n;k++) {
-            f = 2.0*(k+v0-1.0)*f1/x-f0;
-            jv[k] = f;
-            f0 = f1;
-            f1 = f;
-        }
-    }
-    else if (n >= 2) {
-        m = msta1(x,200);
-        if (m < n) n = m;
-        else m = msta2(x,n,15);
-        f2 = 0.0;
-        f1 = 1.0e-100;
-        for (k=m;k>=0;k--) {
-            f = 2.0*(v0+k+1.0)*f1/x-f2;
-            if (k <= n) jv[k] = f;
-            f2 = f1;
-            f1 = f;
-        }
-        if (fabs(bjv0) > fabs(bjv1)) cs = bjv0/f;
-        else cs = bjv1/f2;
-        for (k=0;k<=n;k++) {
-            jv[k] *= cs;
-        }
-    }
-    for (k=2;k<=n;k++) {
-        djv[k] = -(k+v0)*jv[k]/x+jv[k-1];
-    }
-    if (x <= 12.0) {
-        if (v0 != 0.0) {
-            for (l=0;l<2;l++) {
-                vl = v0 +l;
-                bjvl = 1.0;
-                r = 1.0;
-                for (k=1;k<=40;k++) {
-                    r *= -0.25*x2/(k*(k-vl));
-                    bjvl += r;
-                    if (fabs(r) < fabs(bjvl)*1e-15) break;
-                }
-                vg = 1.0-vl;
-                b = pow(2.0/x,vl)/gamma(vg);
-                if (l == 0) bju0 = bjvl*b;
-                else bju1 = bjvl*b;
-            }
-            pv0 = M_PI*v0;
-            pv1 = M_PI*(1.0+v0);
-            byv0 = (bjv0*cos(pv0)-bju0)/sin(pv0);
-            byv1 = (bjv1*cos(pv1)-bju1)/sin(pv1);
-        }
-        else {
-            ec = log(0.5*x)+el;
-            cs0 = 0.0;
-            w0 = 0.0;
-            r0 = 1.0;
-            for (k=1;k<=30;k++) {
-                w0 += 1.0/k;
-                r0 *= -0.25*x2/(k*k);
-                cs0 += r0*w0;
-            }
-            byv0 = M_2_PI*(ec*bjv0-cs0);
-            cs1 = 1.0;
-            w1 = 0.0;
-            r1 = 1.0;
-            for (k=1;k<=30;k++) {
-                w1 += 1.0/k;
-                r1 *= -0.25*x2/(k*(k+1));
-                cs1 += r1*(2.0*w1+1.0/(k+1.0));
-            }
-            byv1 = M_2_PI*(ec*bjv1-1.0/x-0.25*x*cs1);
-        }
-    }
-    yv[0] = byv0;
-    yv[1] = byv1;
-    for (k=2;k<=n;k++) {
-        byvk = 2.0*(v0+k-1.0)*byv1/x-byv0;
-        yv[k] = byvk;
-        byv0 = byv1;
-        byv1 = byvk;
-    }
-    dyv[0] = v0*yv[0]/x-yv[1];
-    for (k=1;k<=n;k++) {
-        dyv[k] = -(k+v0)*yv[k]/x+yv[k-1];
-    }
-    vm = n + v0;
-    return 0;
-}
- 
+//  bessjy.cpp -- computation of Bessel functions Jn, Yn and their
+//      derivatives. Algorithms and coefficient values from
+//      "Computation of Special Functions", Zhang and Jin, John
+//      Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+// Note that 'math.h' provides (or should provide) values for:
+//      pi      M_PI
+//      2/pi    M_2_PI
+//      pi/4    M_PI_4
+//      pi/2    M_PI_2
+//
+#define _USE_MATH_DEFINES
+#include <math.h>
+#include "bessel.h"
+
+double gamma(double x);
+//
+//  INPUT:
+//      double x    -- argument of Bessel function
+//
+//  OUTPUT (via address pointers):
+//      double j0   -- Bessel function of 1st kind, 0th order
+//      double j1   -- Bessel function of 1st kind, 1st order
+//      double y0   -- Bessel function of 2nd kind, 0th order
+//      double y1   -- Bessel function of 2nd kind, 1st order
+//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
+//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
+//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
+//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
+//
+//  RETURN:
+//      int error code: 0 = OK, 1 = error
+//
+//  This algorithm computes the above functions using series expansions.
+//
+int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p)
+{
+    double x2,r,ec,w0,w1,r0,r1,cs0,cs1;
+    double cu,p0,q0,p1,q1,t1,t2;
+    int k,kz;
+    static double a[] = {
+        -7.03125e-2,
+        0.112152099609375,
+        -0.5725014209747314,
+        6.074042001273483,
+        -1.100171402692467e2,
+        3.038090510922384e3,
+        -1.188384262567832e5,
+        6.252951493434797e6,
+        -4.259392165047669e8,
+        3.646840080706556e10,
+        -3.833534661393944e12,
+        4.854014686852901e14,
+        -7.286857349377656e16,
+        1.279721941975975e19
+    };
+    static double b[] = {
+        7.32421875e-2,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1,
+        5.513358961220206e2,
+        -1.825775547429318e4,
+        8.328593040162893e5,
+        -5.006958953198893e7,
+        3.836255180230433e9,
+        -3.649010818849833e11,
+        4.218971570284096e13,
+        -5.827244631566907e15,
+        9.476288099260110e17,
+        -1.792162323051699e20
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947,
+        1.215978918765359e2,
+        -3.302272294480852e3,
+        1.276412726461746e5,
+        -6.656367718817688e6,
+        4.502786003050393e8,
+        -3.833857520742790e10,
+        4.011838599133198e12,
+        -5.060568503314727e14,
+        7.572616461117958e16,
+        -1.326257285320556e19
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1,
+        -6.038440767050702e2,
+        1.971837591223663e4,
+        -8.902978767070678e5,
+        5.310411010968522e7,
+        -4.043620325107754e9,
+        3.827011346598605e11,
+        -4.406481417852278e13,
+        6.065091351222699e15,
+        -9.833883876590679e17,
+        1.855045211579828e20
+    };
+
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        j0 = 1.0;
+        j1 = 0.0;
+        y0 = -1e308;
+        y1 = -1e308;
+        j0p = 0.0;
+        j1p = 0.5;
+        y0p = 1e308;
+        y1p = 1e308;
+        return 0;
+    }
+    x2 = x*x;
+    if (x <= 12.0) {
+        j0 = 1.0;
+        r = 1.0;
+        for (k=1; k<=30; k++) {
+            r *= -0.25*x2/(k*k);
+            j0 += r;
+            if (fabs(r) < fabs(j0)*1e-15) break;
+        }
+        j1 = 1.0;
+        r = 1.0;
+        for (k=1; k<=30; k++) {
+            r *= -0.25*x2/(k*(k+1));
+            j1 += r;
+            if (fabs(r) < fabs(j1)*1e-15) break;
+        }
+        j1 *= 0.5*x;
+        ec = log(0.5*x)+el;
+        cs0 = 0.0;
+        w0 = 0.0;
+        r0 = 1.0;
+        for (k=1; k<=30; k++) {
+            w0 += 1.0/k;
+            r0 *= -0.25*x2/(k*k);
+            r = r0 * w0;
+            cs0 += r;
+            if (fabs(r) < fabs(cs0)*1e-15) break;
+        }
+        y0 = M_2_PI*(ec*j0-cs0);
+        cs1 = 1.0;
+        w1 = 0.0;
+        r1 = 1.0;
+        for (k=1; k<=30; k++) {
+            w1 += 1.0/k;
+            r1 *= -0.25*x2/(k*(k+1));
+            r = r1*(2.0*w1+1.0/(k+1));
+            cs1 += r;
+            if (fabs(r) < fabs(cs1)*1e-15) break;
+        }
+        y1 = M_2_PI * (ec*j1-1.0/x-0.25*x*cs1);
+    }
+    else {
+        if (x >= 50.0) kz = 8;          // Can be changed to 10
+        else if (x >= 35.0) kz = 10;    //  "       "        12
+        else kz = 12;                   //  "       "        14
+        t1 = x-M_PI_4;
+        p0 = 1.0;
+        q0 = -0.125/x;
+        for (k=0; k<kz; k++) {
+            p0 += a[k]*pow(x,-2*k-2);
+            q0 += b[k]*pow(x,-2*k-3);
+        }
+        cu = sqrt(M_2_PI/x);
+        j0 = cu*(p0*cos(t1)-q0*sin(t1));
+        y0 = cu*(p0*sin(t1)+q0*cos(t1));
+        t2 = x-0.75*M_PI;
+        p1 = 1.0;
+        q1 = 0.375/x;
+        for (k=0; k<kz; k++) {
+            p1 += a1[k]*pow(x,-2*k-2);
+            q1 += b1[k]*pow(x,-2*k-3);
+        }
+        j1 = cu*(p1*cos(t2)-q1*sin(t2));
+        y1 = cu*(p1*sin(t2)+q1*cos(t2));
+    }
+    j0p = -j1;
+    j1p = j0-j1/x;
+    y0p = -y1;
+    y1p = y0-y1/x;
+    return 0;
+}
+//
+//  INPUT:
+//      double x    -- argument of Bessel function
+//
+//  OUTPUT:
+//      double j0   -- Bessel function of 1st kind, 0th order
+//      double j1   -- Bessel function of 1st kind, 1st order
+//      double y0   -- Bessel function of 2nd kind, 0th order
+//      double y1   -- Bessel function of 2nd kind, 1st order
+//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
+//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
+//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
+//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
+//
+//  RETURN:
+//      int error code: 0 = OK, 1 = error
+//
+//  This algorithm computes the functions using polynomial approximations.
+//
+int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p)
+{
+    double t,t2,dtmp,a0,p0,q0,p1,q1,ta0,ta1;
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        j0 = 1.0;
+        j1 = 0.0;
+        y0 = -1e308;
+        y1 = -1e308;
+        j0p = 0.0;
+        j1p = 0.5;
+        y0p = 1e308;
+        y1p = 1e308;
+        return 0;
+    }
+    if(x <= 4.0) {
+        t = x/4.0;
+        t2 = t*t;
+        j0 = ((((((-0.5014415e-3*t2+0.76771853e-2)*t2-0.0709253492)*t2+
+                 0.4443584263)*t2-1.7777560599)*t2+3.9999973021)*t2
+              -3.9999998721)*t2+1.0;
+        j1 = t*(((((((-0.1289769e-3*t2+0.22069155e-2)*t2-0.0236616773)*t2+
+                    0.1777582922)*t2-0.8888839649)*t2+2.6666660544)*t2-
+                 3.999999971)*t2+1.9999999998);
+        dtmp = (((((((-0.567433e-4*t2+0.859977e-3)*t2-0.94855882e-2)*t2+
+                    0.0772975809)*t2-0.4261737419)*t2+1.4216421221)*t2-
+                 2.3498519931)*t2+1.0766115157)*t2+0.3674669052;
+        y0 = M_2_PI*log(0.5*x)*j0+dtmp;
+        dtmp = (((((((0.6535773e-3*t2-0.0108175626)*t2+0.107657607)*t2-
+                    0.7268945577)*t2+3.1261399273)*t2-7.3980241381)*t2+
+                 6.8529236342)*t2+0.3932562018)*t2-0.6366197726;
+        y1 = M_2_PI*log(0.5*x)*j1+dtmp/x;
+    }
+    else {
+        t = 4.0/x;
+        t2 = t*t;
+        a0 = sqrt(M_2_PI/x);
+        p0 = ((((-0.9285e-5*t2+0.43506e-4)*t2-0.122226e-3)*t2+
+               0.434725e-3)*t2-0.4394275e-2)*t2+0.999999997;
+        q0 = t*(((((0.8099e-5*t2-0.35614e-4)*t2+0.85844e-4)*t2-
+                  0.218024e-3)*t2+0.1144106e-2)*t2-0.031249995);
+        ta0 = x-M_PI_4;
+        j0 = a0*(p0*cos(ta0)-q0*sin(ta0));
+        y0 = a0*(p0*sin(ta0)+q0*cos(ta0));
+        p1 = ((((0.10632e-4*t2-0.50363e-4)*t2+0.145575e-3)*t2
+               -0.559487e-3)*t2+0.7323931e-2)*t2+1.000000004;
+        q1 = t*(((((-0.9173e-5*t2+0.40658e-4)*t2-0.99941e-4)*t2
+                  +0.266891e-3)*t2-0.1601836e-2)*t2+0.093749994);
+        ta1 = x-0.75*M_PI;
+        j1 = a0*(p1*cos(ta1)-q1*sin(ta1));
+        y1 = a0*(p1*sin(ta1)+q1*cos(ta1));
+    }
+    j0p = -j1;
+    j1p = j0-j1/x;
+    y0p = -y1;
+    y1p = y0-y1/x;
+    return 0;
+}
+int msta1(double x,int mp)
+{
+    double a0,f0,f1,f;
+    int i,n0,n1,nn;
+
+    a0 = fabs(x);
+    n0 = (int)(1.1*a0)+1;
+    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-mp;
+    n1 = n0+5;
+    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-mp;
+    for (i=0; i<20; i++) {
+        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
+        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-mp;
+        if (abs(nn-n1) < 1) break;
+        n0 = n1;
+        f0 = f1;
+        n1 = nn;
+        f1 = f;
+    }
+    return nn;
+}
+int msta2(double x,int n,int mp)
+{
+    double a0,ejn,hmp,f0,f1,f,obj;
+    int i,n0,n1,nn;
+
+    a0 = fabs(x);
+    hmp = 0.5*mp;
+    ejn = 0.5*log10(6.28*n)-n*log10(1.36*a0/n);
+    if (ejn <= hmp) {
+        obj = mp;
+        n0 = (int)(1.1*a0);
+        if (n0 < 1) n0 = 1;
+    }
+    else {
+        obj = hmp+ejn;
+        n0 = n;
+    }
+    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-obj;
+    n1 = n0+5;
+    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-obj;
+    for (i=0; i<20; i++) {
+        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
+        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-obj;
+        if (abs(nn-n1) < 1) break;
+        n0 = n1;
+        f0 = f1;
+        n1 = nn;
+        f1 = f;
+    }
+    return nn+10;
+}
+//
+//  INPUT:
+//  double x    -- argument of Bessel function of 1st and 2nd kind.
+//  int n       -- order
+//
+//  OUPUT:
+//
+//  int nm      -- highest order actually computed (nm <= n)
+//  double jn[] -- Bessel function of 1st kind, orders from 0 to nm
+//  double yn[] -- Bessel function of 2nd kind, orders from 0 to nm
+//  double j'n[]-- derivative of Bessel function of 1st kind,
+//                      orders from 0 to nm
+//  double y'n[]-- derivative of Bessel function of 2nd kind,
+//                      orders from 0 to nm
+//
+//  Computes Bessel functions of all order up to 'n' using recurrence
+//  relations. If 'nm' < 'n' only 'nm' orders are returned.
+//
+int bessjyna(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp)
+{
+    double bj0,bj1,f,f0,f1,f2,cs;
+    int i,k,m,ecode;
+
+    nm = n;
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < 1e-15) {
+        for (i=0; i<=n; i++) {
+            jn[i] = 0.0;
+            yn[i] = -1e308;
+            jnp[i] = 0.0;
+            ynp[i] = 1e308;
+        }
+        jn[0] = 1.0;
+        jnp[1] = 0.5;
+        return 0;
+    }
+    ecode = bessjy01a(x,jn[0],jn[1],yn[0],yn[1],jnp[0],jnp[1],ynp[0],ynp[1]);
+    if (n < 2) return 0;
+    bj0 = jn[0];
+    bj1 = jn[1];
+    if (n < (int)0.9*x) {
+        for (k=2; k<=n; k++) {
+            jn[k] = 2.0*(k-1.0)*bj1/x-bj0;
+            bj0 = bj1;
+            bj1 = jn[k];
+        }
+    }
+    else {
+        m = msta1(x,200);
+        if (m < n) nm = m;
+        else m = msta2(x,n,15);
+        f2 = 0.0;
+        f1 = 1.0e-100;
+        for (k=m; k>=0; k--) {
+            f = 2.0*(k+1.0)/x*f1-f2;
+            if (k <= nm) jn[k] = f;
+            f2 = f1;
+            f1 = f;
+        }
+        if (fabs(bj0) > fabs(bj1)) cs = bj0/f;
+        else cs = bj1/f2;
+        for (k=0; k<=nm; k++) {
+            jn[k] *= cs;
+        }
+    }
+    for (k=2; k<=nm; k++) {
+        jnp[k] = jn[k-1]-k*jn[k]/x;
+    }
+    f0 = yn[0];
+    f1 = yn[1];
+    for (k=2; k<=nm; k++) {
+        f = 2.0*(k-1.0)*f1/x-f0;
+        yn[k] = f;
+        f0 = f1;
+        f1 = f;
+    }
+    for (k=2; k<=nm; k++) {
+        ynp[k] = yn[k-1]-k*yn[k]/x;
+    }
+    return 0;
+}
+//
+//  Same input and output conventions as above. Different recurrence
+//  relations used for 'x' < 300.
+//
+int bessjynb(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp)
+{
+    double t1,t2,f,f1,f2,bj0,bj1,bjk,by0,by1,cu,s0,su,sv;
+    double ec,bs,byk,p0,p1,q0,q1;
+    static double a[] = {
+        -0.7031250000000000e-1,
+        0.1121520996093750,
+        -0.5725014209747314,
+        6.074042001273483
+    };
+    static double b[] = {
+        0.7324218750000000e-1,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1
+    };
+
+    int i,k,m;
+    nm = n;
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < 1e-15) {
+        for (i=0; i<=n; i++) {
+            jn[i] = 0.0;
+            yn[i] = -1e308;
+            jnp[i] = 0.0;
+            ynp[i] = 1e308;
+        }
+        jn[0] = 1.0;
+        jnp[1] = 0.5;
+        return 0;
+    }
+    if (x <= 300.0 || n > (int)(0.9*x)) {
+        if (n == 0) nm = 1;
+        m = msta1(x,200);
+        if (m < nm) nm = m;
+        else m = msta2(x,nm,15);
+        bs = 0.0;
+        su = 0.0;
+        sv = 0.0;
+        f2 = 0.0;
+        f1 = 1.0e-100;
+        for (k = m; k>=0; k--) {
+            f = 2.0*(k+1.0)/x*f1 - f2;
+            if (k <= nm) jn[k] = f;
+            if ((k == 2*(int)(k/2)) && (k != 0)) {
+                bs += 2.0*f;
+//                su += pow(-1,k>>1)*f/(double)k;
+                su += (-1)*((k & 2)-1)*f/(double)k;
+            }
+            else if (k > 1) {
+//                sv += pow(-1,k>>1)*k*f/(k*k-1.0);
+                sv += (-1)*((k & 2)-1)*(double)k*f/(k*k-1.0);
+            }
+            f2 = f1;
+            f1 = f;
+        }
+        s0 = bs+f;
+        for (k=0; k<=nm; k++) {
+            jn[k] /= s0;
+        }
+        ec = log(0.5*x) +0.5772156649015329;
+        by0 = M_2_PI*(ec*jn[0]-4.0*su/s0);
+        yn[0] = by0;
+        by1 = M_2_PI*((ec-1.0)*jn[1]-jn[0]/x-4.0*sv/s0);
+        yn[1] = by1;
+    }
+    else {
+        t1 = x-M_PI_4;
+        p0 = 1.0;
+        q0 = -0.125/x;
+        for (k=0; k<4; k++) {
+            p0 += a[k]*pow(x,-2*k-2);
+            q0 += b[k]*pow(x,-2*k-3);
+        }
+        cu = sqrt(M_2_PI/x);
+        bj0 = cu*(p0*cos(t1)-q0*sin(t1));
+        by0 = cu*(p0*sin(t1)+q0*cos(t1));
+        jn[0] = bj0;
+        yn[0] = by0;
+        t2 = x-0.75*M_PI;
+        p1 = 1.0;
+        q1 = 0.375/x;
+        for (k=0; k<4; k++) {
+            p1 += a1[k]*pow(x,-2*k-2);
+            q1 += b1[k]*pow(x,-2*k-3);
+        }
+        bj1 = cu*(p1*cos(t2)-q1*sin(t2));
+        by1 = cu*(p1*sin(t2)+q1*cos(t2));
+        jn[1] = bj1;
+        yn[1] = by1;
+        for (k=2; k<=nm; k++) {
+            bjk = 2.0*(k-1.0)*bj1/x-bj0;
+            jn[k] = bjk;
+            bj0 = bj1;
+            bj1 = bjk;
+        }
+    }
+    jnp[0] = -jn[1];
+    for (k=1; k<=nm; k++) {
+        jnp[k] = jn[k-1]-k*jn[k]/x;
+    }
+    for (k=2; k<=nm; k++) {
+        byk = 2.0*(k-1.0)*by1/x-by0;
+        yn[k] = byk;
+        by0 = by1;
+        by1 = byk;
+    }
+    ynp[0] = -yn[1];
+    for (k=1; k<=nm; k++) {
+        ynp[k] = yn[k-1]-k*yn[k]/x;
+    }
+    return 0;
+
+}
+
+//  The following routine computes Bessel Jv(x) and Yv(x) for
+//  arbitrary positive order (v). For negative order, use:
+//
+//      J-v(x) = Jv(x)cos(v pi) - Yv(x)sin(v pi)
+//      Y-v(x) = Jv(x)sin(v pi) + Yv(x)cos(v pi)
+//
+int bessjyv(double v,double x,double &vm,double *jv,double *yv,
+            double *djv,double *dyv)
+{
+    double v0,vl,vg,vv,a,a0,r,x2,bjv0,bjv1,bjvl,f,f0,f1,f2;
+    double r0,r1,ck,cs,cs0,cs1,sk,qx,px,byv0,byv1,rp,xk,rq;
+    double b,ec,w0,w1,bju0,bju1,pv0,pv1,byvk;
+    int j,k,l,m,n,kz;
+
+    x2 = x*x;
+    n = (int)v;
+    v0 = v-n;
+    if ((x < 0.0) || (v < 0.0)) return 1;
+    if (x < 1e-15) {
+        for (k=0; k<=n; k++) {
+            jv[k] = 0.0;
+            yv[k] = -1e308;
+            djv[k] = 0.0;
+            dyv[k] = 1e308;
+            if (v0 == 0.0) {
+                jv[0] = 1.0;
+                djv[1] = 0.5;
+            }
+            else djv[0] = 1e308;
+        }
+        vm = v;
+        return 0;
+    }
+    if (x <= 12.0) {
+        for (l=0; l<2; l++) {
+            vl = v0 + l;
+            bjvl = 1.0;
+            r = 1.0;
+            for (k=1; k<=40; k++) {
+                r *= -0.25*x2/(k*(k+vl));
+                bjvl += r;
+                if (fabs(r) < fabs(bjvl)*1e-15) break;
+            }
+            vg = 1.0 + vl;
+            a = pow(0.5*x,vl)/gamma(vg);
+            if (l == 0) bjv0 = bjvl*a;
+            else bjv1 = bjvl*a;
+        }
+    }
+    else {
+        if (x >= 50.0) kz = 8;
+        else if (x >= 35.0) kz = 10;
+        else kz = 11;
+        for (j=0; j<2; j++) {
+            vv = 4.0*(j+v0)*(j+v0);
+            px = 1.0;
+            rp = 1.0;
+            for (k=1; k<=kz; k++) {
+                rp *= (-0.78125e-2)*(vv-pow(4.0*k-3.0,2.0))*
+                      (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*x2);
+                px += rp;
+            }
+            qx = 1.0;
+            rq = 1.0;
+            for (k=1; k<=kz; k++) {
+                rq *= (-0.78125e-2)*(vv-pow(4.0*k-1.0,2.0))*
+                      (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*x2);
+                qx += rq;
+            }
+            qx *= 0.125*(vv-1.0)/x;
+            xk = x-(0.5*(j+v0)+0.25)*M_PI;
+            a0 = sqrt(M_2_PI/x);
+            ck = cos(xk);
+            sk = sin(xk);
+
+            if (j == 0) {
+                bjv0 = a0*(px*ck-qx*sk);
+                byv0 = a0*(px*sk+qx*ck);
+            }
+            else if (j == 1) {
+                bjv1 = a0*(px*ck-qx*sk);
+                byv1 = a0*(px*sk+qx*ck);
+            }
+        }
+    }
+    jv[0] = bjv0;
+    jv[1] = bjv1;
+    djv[0] = v0*jv[0]/x-jv[1];
+    djv[1] = -(1.0+v0)*jv[1]/x+jv[0];
+    if ((n >= 2) && (n <= (int)(0.9*x))) {
+        f0 = bjv0;
+        f1 = bjv1;
+        for (k=2; k<=n; k++) {
+            f = 2.0*(k+v0-1.0)*f1/x-f0;
+            jv[k] = f;
+            f0 = f1;
+            f1 = f;
+        }
+    }
+    else if (n >= 2) {
+        m = msta1(x,200);
+        if (m < n) n = m;
+        else m = msta2(x,n,15);
+        f2 = 0.0;
+        f1 = 1.0e-100;
+        for (k=m; k>=0; k--) {
+            f = 2.0*(v0+k+1.0)*f1/x-f2;
+            if (k <= n) jv[k] = f;
+            f2 = f1;
+            f1 = f;
+        }
+        if (fabs(bjv0) > fabs(bjv1)) cs = bjv0/f;
+        else cs = bjv1/f2;
+        for (k=0; k<=n; k++) {
+            jv[k] *= cs;
+        }
+    }
+    for (k=2; k<=n; k++) {
+        djv[k] = -(k+v0)*jv[k]/x+jv[k-1];
+    }
+    if (x <= 12.0) {
+        if (v0 != 0.0) {
+            for (l=0; l<2; l++) {
+                vl = v0 +l;
+                bjvl = 1.0;
+                r = 1.0;
+                for (k=1; k<=40; k++) {
+                    r *= -0.25*x2/(k*(k-vl));
+                    bjvl += r;
+                    if (fabs(r) < fabs(bjvl)*1e-15) break;
+                }
+                vg = 1.0-vl;
+                b = pow(2.0/x,vl)/gamma(vg);
+                if (l == 0) bju0 = bjvl*b;
+                else bju1 = bjvl*b;
+            }
+            pv0 = M_PI*v0;
+            pv1 = M_PI*(1.0+v0);
+            byv0 = (bjv0*cos(pv0)-bju0)/sin(pv0);
+            byv1 = (bjv1*cos(pv1)-bju1)/sin(pv1);
+        }
+        else {
+            ec = log(0.5*x)+el;
+            cs0 = 0.0;
+            w0 = 0.0;
+            r0 = 1.0;
+            for (k=1; k<=30; k++) {
+                w0 += 1.0/k;
+                r0 *= -0.25*x2/(k*k);
+                cs0 += r0*w0;
+            }
+            byv0 = M_2_PI*(ec*bjv0-cs0);
+            cs1 = 1.0;
+            w1 = 0.0;
+            r1 = 1.0;
+            for (k=1; k<=30; k++) {
+                w1 += 1.0/k;
+                r1 *= -0.25*x2/(k*(k+1));
+                cs1 += r1*(2.0*w1+1.0/(k+1.0));
+            }
+            byv1 = M_2_PI*(ec*bjv1-1.0/x-0.25*x*cs1);
+        }
+    }
+    yv[0] = byv0;
+    yv[1] = byv1;
+    for (k=2; k<=n; k++) {
+        byvk = 2.0*(v0+k-1.0)*byv1/x-byv0;
+        yv[k] = byvk;
+        byv0 = byv1;
+        byv1 = byvk;
+    }
+    dyv[0] = v0*yv[0]/x-yv[1];
+    for (k=1; k<=n; k++) {
+        dyv[k] = -(k+v0)*yv[k]/x+yv[k-1];
+    }
+    vm = n + v0;
+    return 0;
+}
+
-//  cbessik.cpp -- complex modified Bessel functions.
-//  Algorithms and coefficient values from "Computation of Special
-//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-#include <complex>
-using namespace std;
-#include "bessel.h"
-
-static complex<double> cii(0.0,1.0);
-static complex<double> czero(0.0,0.0);
-static complex<double> cone(1.0,0.0);
-
-double gamma(double x);
-
-int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
-    complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
-    complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p)
-{
-    complex<double> z1,z2,zr,zr2,cr,ca,cb,cs,ct,cw;
-    double a0,w0;
-    int k,kz;
-    static double a[] = {
-        0.125,
-        7.03125e-2,
-        7.32421875e-2,
-        1.1215209960938e-1,
-        2.2710800170898e-1,
-        5.7250142097473e-1,
-        1.7277275025845,
-        6.0740420012735,
-        2.4380529699556e1,
-        1.1001714026925e2,
-        5.5133589612202e2,
-        3.0380905109224e3};
-    static double b[] = {
-        -0.375,
-        -1.171875e-1,
-        -1.025390625e-1,
-        -1.4419555664063e-1,
-        -2.7757644653320e-1,
-        -6.7659258842468e-1,
-        -1.9935317337513,
-        -6.8839142681099,
-        -2.7248827311269e1,
-        -1.2159789187654e2,
-        -6.0384407670507e2,
-        -3.3022722944809e3};
-    static double a1[] = {
-        0.125,
-        0.2109375,
-        1.0986328125,
-        1.1775970458984e1,
-        2.1461706161499e2,
-        5.9511522710323e3,
-        2.3347645606175e5,
-        1.2312234987631e7,
-        8.401390346421e08,
-        7.2031420482627e10};
-
-    a0 = abs(z);
-    z2 = z*z;
-    z1 = z;
-    if (a0 == 0.0) {
-        ci0 = cone;
-        ci1 = czero;
-        ck0 = complex<double> (1e308,0);
-        ck1 = complex<double> (1e308,0);
-        ci0p = czero;
-        ci1p = complex<double>(0.5,0.0);
-        ck0p = complex<double>(-1e308,0);
-        ck1p = complex<double>(-1e308,0);
-        return 0;
-    }
-    if (real(z) < 0.0) z1 = -z;
-    if (a0 <= 18.0) {
-        ci0 = cone;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            cr *= 0.25*z2/(double)(k*k);
-            ci0 += cr;
-            if (abs(cr/ci0) < eps) break;
-        }
-        ci1 = cone;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            cr *= 0.25*z2/(double)(k*(k+1.0));
-            ci1 += cr;
-            if (abs(cr/ci1) < eps) break;
-        }
-        ci1 *= 0.5*z1;
-    }
-    else {
-        if (a0 >= 50.0) kz = 7;
-        else if (a0 >= 35.0) kz = 9;
-        else kz = 12;
-        ca = exp(z1)/sqrt(2.0*M_PI*z1);
-        ci0 = cone;
-        zr = 1.0/z1;
-        for (k=0;k<kz;k++) {
-            ci0 += a[k]*pow(zr,k+1.0);
-        }
-        ci0 *= ca;
-        ci1 = cone;
-        for (k=0;k<kz;k++) {
-            ci1 += b[k]*pow(zr,k+1.0);
-        }
-        ci1 *= ca;
-    }
-    if (a0 <= 9.0) {
-        cs = czero;
-        ct = -log(0.5*z1)-el;
-        w0 = 0.0;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            w0 += 1.0/k;
-            cr *= 0.25*z2/(double)(k*k);
-            cs += cr*(w0+ct);
-            if (abs((cs-cw)/cs) < eps) break;
-            cw = cs;
-        }
-        ck0 = ct+cs;
-    }
-    else {
-        cb = 0.5/z1;
-        zr2 = 1.0/z2;
-        ck0 = cone;
-        for (k=0;k<10;k++) {
-            ck0 += a1[k]*pow(zr2,k+1.0);
-        }
-        ck0 *= cb/ci0;
-    }
-    ck1 = (1.0/z1 - ci1*ck0)/ci0;
-    if (real(z) < 0.0) {
-        if (imag(z) < 0.0) {
-            ck0 += cii*M_PI*ci0;
-            ck1 = -ck1+cii*M_PI*ci1;
-        }
-        else if (imag(z) > 0.0) {
-            ck0 -= cii*M_PI*ci0;
-            ck1 = -ck1-cii*M_PI*ci1;
-        }
-        ci1 = -ci1;
-    }
-    ci0p = ci1;
-    ci1p = ci0-1.0*ci1/z;
-    ck0p = -ck1;
-    ck1p = -ck0-1.0*ck1/z;
-    return 0;
-}
-int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp)
-{
-    complex<double> ci0,ci1,ck0,ck1,ckk,cf,cf1,cf2,cs;
-    double a0;
-    int k,m,ecode;
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            ci[k] = czero;
-            ck[k] = complex<double>(-1e308,0);
-            cip[k] = czero;
-            ckp[k] = complex<double>(1e308,0);
-        }
-        ci[0] = cone;
-        cip[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    ecode = cbessik01(z,ci[0],ci[1],ck[0],ck[1],cip[0],cip[1],ckp[0],ckp[1]);
-    if (n < 2) return 0;
-    ci0 = ci[0];
-    ci1 = ci[1];
-    ck0 = ck[0];
-    ck1 = ck[1];
-    m = msta1(a0,200);
-    if (m < n) nm = m;
-    else m = msta2(a0,n,15);
-    cf2 = czero;
-    cf1 = complex<double>(1.0e-100,0.0);
-    for (k=m;k>=0;k--) {
-        cf = 2.0*(k+1.0)*cf1/z+cf2;
-        if (k <= nm) ci[k] = cf;
-        cf2 = cf1;
-        cf1 = cf;
-    }
-    cs = ci0/cf;
-    for (k=0;k<=nm;k++) {
-        ci[k] *= cs;
-    }
-    for (k=2;k<=nm;k++) {
-        if (abs(ci[k-1]) > abs(ci[k-2])) {
-            ckk = (1.0/z-ci[k]*ck[k-1])/ci[k-1];
-        }
-        else {
-            ckk = (ci[k]*ck[k-2]+2.0*(k-1.0)/(z*z))/ci[k-2];
-        }
-        ck[k] = ckk;
-    }
-    for (k=2;k<=nm;k++) {
-        cip[k] = ci[k-1]-(double)k*ci[k]/z;
-        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
-    }
-    return 0;
-}
-int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp)
-{
-    complex<double> z1,cbs,csk0,cf,cf0,cf1,ca0,cbkl;
-    complex<double> cg,cg0,cg1,cs0,cs,cr;
-    double a0,vt,fac;
-    int k,kz,l,m;
-
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            ci[k] = czero;
-            ck[k] = complex<double>(1e308,0);
-            cip[k] = czero;
-            ckp[k] = complex<double>(-1e308,0);
-        }
-        ci[0] = complex<double>(1.0,0.0);
-        cip[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    z1 = z;
-    if (real(z) < 0.0) z1 = -z;
-    if (n == 0) nm = 1;
-    m = msta1(a0,200);
-    if (m < nm) nm = m;
-    else m = msta2(a0,nm,15);
-    cbs = czero;
-    csk0 = czero;
-    cf0 = czero;
-    cf1 = complex<double>(1.0e-100,0.0);
-    for (k=m;k>=0;k--) {
-        cf = 2.0*(k+1.0)*cf1/z1+cf0;
-        if (k <=nm) ci[k] = cf;
-        if ((k != 0) && (k == 2*(k>>1)))  csk0 += 4.0*cf/(double)k;
-        cbs += 2.0*cf;
-        cf0 = cf1;
-        cf1 = cf;
-    }
-    cs0 = exp(z1)/(cbs-cf);
-    for (k=0;k<=nm;k++) {
-        ci[k] *= cs0;
-    }
-    if (a0 <= 9.0) {
-        ck[0] = -(log(0.5*z1)+el)*ci[0]+cs0*csk0;
-        ck[1] = (1.0/z1-ci[1]*ck[0])/ci[0];
-    }
-    else {
-        ca0 = sqrt(M_PI_2/z1)*exp(-z1);
-        if (a0 >= 200.0) kz = 6;
-        else if (a0 >= 80.0) kz = 8;
-        else if (a0 >= 25.0) kz = 10;
-        else kz = 16;
-        for (l=0;l<2;l++) {
-            cbkl = cone;
-            vt = 4.0*l;
-            cr = cone;
-            for (k=1;k<=kz;k++) {
-                cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
-                cbkl += cr;
-            }
-            ck[l] = ca0*cbkl;
-        }
-    }
-    cg0 = ck[0];    
-    cg1 = ck[1];
-    for (k=2;k<=nm;k++) {
-        cg = 2.0*(k-1.0)*cg1/z1+cg0;
-        ck[k] = cg;
-        cg0 = cg1;
-        cg1 = cg;
-    }
-    if (real(z) < 0.0) {
-        fac = 1.0;
-        for (k=0;k<=nm;k++) {
-            if (imag(z) < 0.0) {
-                ck[k] = fac*ck[k]+cii*M_PI*ci[k];
-            }
-            else {
-                ck[k] = fac*ck[k]-cii*M_PI*ci[k];
-            }
-            ci[k] *= fac;
-            fac = -fac;
-        }
-    }
-    cip[0] = ci[1];
-    ckp[0] = -ck[1];
-    for (k=1;k<=nm;k++) {
-        cip[k] = ci[k-1]-(double)k*ci[k]/z;
-        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
-    }
-    return 0;
-}
-int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
-    complex<double> *ckv,complex<double> *civp,complex<double> *ckvp)
-{
-    complex<double> z1,z2,ca1,ca,cs,cr,ci0,cbi0,cf,cf1,cf2;
-    complex<double> ct,cp,cbk0,ca2,cr1,cr2,csu,cws,cb;
-    complex<double> cg0,cg1,cgk,cbk1,cvk;
-    double a0,v0,v0p,v0n,vt,w0,piv,gap,gan;
-    int m,n,k,kz;
-
-    a0 = abs(z);
-    z1 = z;
-    z2 = z*z;
-    n = (int)v;
-    v0 = v-n;
-    piv = M_PI*v0;
-    vt = 4.0*v0*v0;
-    if (n == 0) n = 1;
-    if (a0 < 1e-100) {
-        for (k=0;k<=n;k++) {
-            civ[k] = czero;
-            ckv[k] = complex<double>(-1e308,0);
-            civp[k] = czero;
-            ckvp[k] = complex<double>(1e308,0);
-        }
-        if (v0 == 0.0) {
-            civ[0] = cone;
-            civp[1] = complex<double> (0.5,0.0);
-        }
-        vm = v;
-        return 0;
-    }
-    if (a0 >= 50.0) kz = 8;
-    else if (a0 >= 35.0) kz = 10;
-    else kz = 14;
-    if (real(z) <= 0.0) z1 = -z;
-    if (a0 < 18.0) {
-        if (v0 == 0.0) {
-            ca1 = cone;
-        }
-        else {
-            v0p = 1.0+v0;
-            gap = gamma(v0p);
-            ca1 = pow(0.5*z1,v0)/gap;
-        }
-        ci0 = cone;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            cr *= 0.25*z2/(k*(k+v0));
-            ci0 += cr;
-            if (abs(cr/ci0) < eps) break;
-        }
-        cbi0 = ci0*ca1;
-    }
-    else {
-        ca = exp(z1)/sqrt(2.0*M_PI*z1);
-        cs = cone;
-        cr = cone;
-        for (k=1;k<=kz;k++) {
-            cr *= -0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
-            cs += cr;
-        }
-        cbi0 = ca*cs;
-    }
-    m = msta1(a0,200);
-    if (m < n) n = m;
-    else m = msta2(a0,n,15);
-    cf2 = czero;
-    cf1 = complex<double>(1.0e-100,0.0);
-    for (k=m;k>=0;k--) {
-        cf = 2.0*(v0+k+1.0)*cf1/z1+cf2;
-        if (k <= n) civ[k] = cf;
-        cf2 = cf1;
-        cf1 = cf;
-    }
-    cs = cbi0/cf;
-    for (k=0;k<=n;k++) {
-        civ[k] *= cs;
-    }
-    if (a0 <= 9.0) {
-        if (v0 == 0.0) {
-            ct = -log(0.5*z1)-el;
-            cs = czero;
-            w0 = 0.0;
-            cr = cone;
-            for (k=1;k<=50;k++) {
-                w0 += 1.0/k;
-                cr *= 0.25*z2/(double)(k*k);
-                cp = cr*(w0+ct);
-                cs += cp;
-                if ((k >= 10) && (abs(cp/cs) < eps)) break;
-            }
-            cbk0 = ct+cs;
-        }
-        else {
-            v0n = 1.0-v0;
-            gan = gamma(v0n);
-            ca2 = 1.0/(gan*pow(0.5*z1,v0));
-            ca1 = pow(0.5*z1,v0)/gap;
-            csu = ca2-ca1;
-            cr1 = cone;
-            cr2 = cone;
-            cws = czero;
-            for (k=1;k<=50;k++) {
-                cr1 *= 0.25*z2/(k*(k-v0));
-                cr2 *= 0.25*z2/(k*(k+v0));
-                csu += ca2*cr1-ca1*cr2;
-                if ((k >= 10) && (abs((cws-csu)/csu) < eps)) break;
-                cws = csu;
-            }
-            cbk0 = csu*M_PI_2/sin(piv);
-        }
-    }
-    else {
-        cb = exp(-z1)*sqrt(M_PI_2/z1);
-        cs = cone;
-        cr = cone;
-        for (k=1;k<=kz;k++) {
-            cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
-            cs += cr;
-        }
-        cbk0 = cb*cs;
-    }
-    cbk1 = (1.0/z1-civ[1]*cbk0)/civ[0];
-    ckv[0] = cbk0;
-    ckv[1] = cbk1;
-    cg0 = cbk0;
-    cg1 = cbk1;
-    for (k=2;k<=n;k++) {
-        cgk = 2.0*(v0+k-1.0)*cg1/z1+cg0;
-        ckv[k] = cgk;
-        cg0 = cg1;
-        cg1 = cgk;
-    }
-    if (real(z) < 0.0) {
-        for (k=0;k<=n;k++) {
-            cvk = exp((k+v0)*M_PI*cii);
-            if (imag(z) < 0.0) {
-                ckv[k] = cvk*ckv[k]+M_PI*cii*civ[k];
-                civ[k] /= cvk;
-            }
-            else if (imag(z) > 0.0) {
-                ckv[k] = ckv[k]/cvk-M_PI*cii*civ[k];
-                civ[k] *= cvk;
-            }
-        }
-    }
-    civp[0] = v0*civ[0]/z+civ[1];
-    ckvp[0] = v0*ckv[0]/z-ckv[1];
-    for (k=1;k<=n;k++) {
-        civp[k] = -(k+v0)*civ[k]/z+civ[k-1];
-        ckvp[k] = -(k+v0)*ckv[k]/z-ckv[k-1];
-    }
-    vm = n+v0;
-    return 0;
-}
+//  cbessik.cpp -- complex modified Bessel functions.
+//  Algorithms and coefficient values from "Computation of Special
+//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+#include <complex>
+using namespace std;
+#include "bessel.h"
+
+static complex<double> cii(0.0,1.0);
+static complex<double> czero(0.0,0.0);
+static complex<double> cone(1.0,0.0);
+
+double gamma(double x);
+
+int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
+              complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
+              complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p)
+{
+    complex<double> z1,z2,zr,zr2,cr,ca,cb,cs,ct,cw;
+    double a0,w0;
+    int k,kz;
+    static double a[] = {
+        0.125,
+        7.03125e-2,
+        7.32421875e-2,
+        1.1215209960938e-1,
+        2.2710800170898e-1,
+        5.7250142097473e-1,
+        1.7277275025845,
+        6.0740420012735,
+        2.4380529699556e1,
+        1.1001714026925e2,
+        5.5133589612202e2,
+        3.0380905109224e3
+    };
+    static double b[] = {
+        -0.375,
+        -1.171875e-1,
+        -1.025390625e-1,
+        -1.4419555664063e-1,
+        -2.7757644653320e-1,
+        -6.7659258842468e-1,
+        -1.9935317337513,
+        -6.8839142681099,
+        -2.7248827311269e1,
+        -1.2159789187654e2,
+        -6.0384407670507e2,
+        -3.3022722944809e3
+    };
+    static double a1[] = {
+        0.125,
+        0.2109375,
+        1.0986328125,
+        1.1775970458984e1,
+        2.1461706161499e2,
+        5.9511522710323e3,
+        2.3347645606175e5,
+        1.2312234987631e7,
+        8.401390346421e08,
+        7.2031420482627e10
+    };
+
+    a0 = abs(z);
+    z2 = z*z;
+    z1 = z;
+    if (a0 == 0.0) {
+        ci0 = cone;
+        ci1 = czero;
+        ck0 = complex<double> (1e308,0);
+        ck1 = complex<double> (1e308,0);
+        ci0p = czero;
+        ci1p = complex<double>(0.5,0.0);
+        ck0p = complex<double>(-1e308,0);
+        ck1p = complex<double>(-1e308,0);
+        return 0;
+    }
+    if (real(z) < 0.0) z1 = -z;
+    if (a0 <= 18.0) {
+        ci0 = cone;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            cr *= 0.25*z2/(double)(k*k);
+            ci0 += cr;
+            if (abs(cr/ci0) < eps) break;
+        }
+        ci1 = cone;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            cr *= 0.25*z2/(double)(k*(k+1.0));
+            ci1 += cr;
+            if (abs(cr/ci1) < eps) break;
+        }
+        ci1 *= 0.5*z1;
+    }
+    else {
+        if (a0 >= 50.0) kz = 7;
+        else if (a0 >= 35.0) kz = 9;
+        else kz = 12;
+        ca = exp(z1)/sqrt(2.0*M_PI*z1);
+        ci0 = cone;
+        zr = 1.0/z1;
+        for (k=0; k<kz; k++) {
+            ci0 += a[k]*pow(zr,k+1.0);
+        }
+        ci0 *= ca;
+        ci1 = cone;
+        for (k=0; k<kz; k++) {
+            ci1 += b[k]*pow(zr,k+1.0);
+        }
+        ci1 *= ca;
+    }
+    if (a0 <= 9.0) {
+        cs = czero;
+        ct = -log(0.5*z1)-el;
+        w0 = 0.0;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            w0 += 1.0/k;
+            cr *= 0.25*z2/(double)(k*k);
+            cs += cr*(w0+ct);
+            if (abs((cs-cw)/cs) < eps) break;
+            cw = cs;
+        }
+        ck0 = ct+cs;
+    }
+    else {
+        cb = 0.5/z1;
+        zr2 = 1.0/z2;
+        ck0 = cone;
+        for (k=0; k<10; k++) {
+            ck0 += a1[k]*pow(zr2,k+1.0);
+        }
+        ck0 *= cb/ci0;
+    }
+    ck1 = (1.0/z1 - ci1*ck0)/ci0;
+    if (real(z) < 0.0) {
+        if (imag(z) < 0.0) {
+            ck0 += cii*M_PI*ci0;
+            ck1 = -ck1+cii*M_PI*ci1;
+        }
+        else if (imag(z) > 0.0) {
+            ck0 -= cii*M_PI*ci0;
+            ck1 = -ck1-cii*M_PI*ci1;
+        }
+        ci1 = -ci1;
+    }
+    ci0p = ci1;
+    ci1p = ci0-1.0*ci1/z;
+    ck0p = -ck1;
+    ck1p = -ck0-1.0*ck1/z;
+    return 0;
+}
+int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp)
+{
+    complex<double> ci0,ci1,ck0,ck1,ckk,cf,cf1,cf2,cs;
+    double a0;
+    int k,m,ecode;
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            ci[k] = czero;
+            ck[k] = complex<double>(-1e308,0);
+            cip[k] = czero;
+            ckp[k] = complex<double>(1e308,0);
+        }
+        ci[0] = cone;
+        cip[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    ecode = cbessik01(z,ci[0],ci[1],ck[0],ck[1],cip[0],cip[1],ckp[0],ckp[1]);
+    if (n < 2) return 0;
+    ci0 = ci[0];
+    ci1 = ci[1];
+    ck0 = ck[0];
+    ck1 = ck[1];
+    m = msta1(a0,200);
+    if (m < n) nm = m;
+    else m = msta2(a0,n,15);
+    cf2 = czero;
+    cf1 = complex<double>(1.0e-100,0.0);
+    for (k=m; k>=0; k--) {
+        cf = 2.0*(k+1.0)*cf1/z+cf2;
+        if (k <= nm) ci[k] = cf;
+        cf2 = cf1;
+        cf1 = cf;
+    }
+    cs = ci0/cf;
+    for (k=0; k<=nm; k++) {
+        ci[k] *= cs;
+    }
+    for (k=2; k<=nm; k++) {
+        if (abs(ci[k-1]) > abs(ci[k-2])) {
+            ckk = (1.0/z-ci[k]*ck[k-1])/ci[k-1];
+        }
+        else {
+            ckk = (ci[k]*ck[k-2]+2.0*(k-1.0)/(z*z))/ci[k-2];
+        }
+        ck[k] = ckk;
+    }
+    for (k=2; k<=nm; k++) {
+        cip[k] = ci[k-1]-(double)k*ci[k]/z;
+        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
+    }
+    return 0;
+}
+int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp)
+{
+    complex<double> z1,cbs,csk0,cf,cf0,cf1,ca0,cbkl;
+    complex<double> cg,cg0,cg1,cs0,cs,cr;
+    double a0,vt,fac;
+    int k,kz,l,m;
+
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            ci[k] = czero;
+            ck[k] = complex<double>(1e308,0);
+            cip[k] = czero;
+            ckp[k] = complex<double>(-1e308,0);
+        }
+        ci[0] = complex<double>(1.0,0.0);
+        cip[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    z1 = z;
+    if (real(z) < 0.0) z1 = -z;
+    if (n == 0) nm = 1;
+    m = msta1(a0,200);
+    if (m < nm) nm = m;
+    else m = msta2(a0,nm,15);
+    cbs = czero;
+    csk0 = czero;
+    cf0 = czero;
+    cf1 = complex<double>(1.0e-100,0.0);
+    for (k=m; k>=0; k--) {
+        cf = 2.0*(k+1.0)*cf1/z1+cf0;
+        if (k <=nm) ci[k] = cf;
+        if ((k != 0) && (k == 2*(k>>1)))  csk0 += 4.0*cf/(double)k;
+        cbs += 2.0*cf;
+        cf0 = cf1;
+        cf1 = cf;
+    }
+    cs0 = exp(z1)/(cbs-cf);
+    for (k=0; k<=nm; k++) {
+        ci[k] *= cs0;
+    }
+    if (a0 <= 9.0) {
+        ck[0] = -(log(0.5*z1)+el)*ci[0]+cs0*csk0;
+        ck[1] = (1.0/z1-ci[1]*ck[0])/ci[0];
+    }
+    else {
+        ca0 = sqrt(M_PI_2/z1)*exp(-z1);
+        if (a0 >= 200.0) kz = 6;
+        else if (a0 >= 80.0) kz = 8;
+        else if (a0 >= 25.0) kz = 10;
+        else kz = 16;
+        for (l=0; l<2; l++) {
+            cbkl = cone;
+            vt = 4.0*l;
+            cr = cone;
+            for (k=1; k<=kz; k++) {
+                cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
+                cbkl += cr;
+            }
+            ck[l] = ca0*cbkl;
+        }
+    }
+    cg0 = ck[0];
+    cg1 = ck[1];
+    for (k=2; k<=nm; k++) {
+        cg = 2.0*(k-1.0)*cg1/z1+cg0;
+        ck[k] = cg;
+        cg0 = cg1;
+        cg1 = cg;
+    }
+    if (real(z) < 0.0) {
+        fac = 1.0;
+        for (k=0; k<=nm; k++) {
+            if (imag(z) < 0.0) {
+                ck[k] = fac*ck[k]+cii*M_PI*ci[k];
+            }
+            else {
+                ck[k] = fac*ck[k]-cii*M_PI*ci[k];
+            }
+            ci[k] *= fac;
+            fac = -fac;
+        }
+    }
+    cip[0] = ci[1];
+    ckp[0] = -ck[1];
+    for (k=1; k<=nm; k++) {
+        cip[k] = ci[k-1]-(double)k*ci[k]/z;
+        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
+    }
+    return 0;
+}
+int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
+             complex<double> *ckv,complex<double> *civp,complex<double> *ckvp)
+{
+    complex<double> z1,z2,ca1,ca,cs,cr,ci0,cbi0,cf,cf1,cf2;
+    complex<double> ct,cp,cbk0,ca2,cr1,cr2,csu,cws,cb;
+    complex<double> cg0,cg1,cgk,cbk1,cvk;
+    double a0,v0,v0p,v0n,vt,w0,piv,gap,gan;
+    int m,n,k,kz;
+
+    a0 = abs(z);
+    z1 = z;
+    z2 = z*z;
+    n = (int)v;
+    v0 = v-n;
+    piv = M_PI*v0;
+    vt = 4.0*v0*v0;
+    if (n == 0) n = 1;
+    if (a0 < 1e-100) {
+        for (k=0; k<=n; k++) {
+            civ[k] = czero;
+            ckv[k] = complex<double>(-1e308,0);
+            civp[k] = czero;
+            ckvp[k] = complex<double>(1e308,0);
+        }
+        if (v0 == 0.0) {
+            civ[0] = cone;
+            civp[1] = complex<double> (0.5,0.0);
+        }
+        vm = v;
+        return 0;
+    }
+    if (a0 >= 50.0) kz = 8;
+    else if (a0 >= 35.0) kz = 10;
+    else kz = 14;
+    if (real(z) <= 0.0) z1 = -z;
+    if (a0 < 18.0) {
+        if (v0 == 0.0) {
+            ca1 = cone;
+        }
+        else {
+            v0p = 1.0+v0;
+            gap = gamma(v0p);
+            ca1 = pow(0.5*z1,v0)/gap;
+        }
+        ci0 = cone;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            cr *= 0.25*z2/(k*(k+v0));
+            ci0 += cr;
+            if (abs(cr/ci0) < eps) break;
+        }
+        cbi0 = ci0*ca1;
+    }
+    else {
+        ca = exp(z1)/sqrt(2.0*M_PI*z1);
+        cs = cone;
+        cr = cone;
+        for (k=1; k<=kz; k++) {
+            cr *= -0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
+            cs += cr;
+        }
+        cbi0 = ca*cs;
+    }
+    m = msta1(a0,200);
+    if (m < n) n = m;
+    else m = msta2(a0,n,15);
+    cf2 = czero;
+    cf1 = complex<double>(1.0e-100,0.0);
+    for (k=m; k>=0; k--) {
+        cf = 2.0*(v0+k+1.0)*cf1/z1+cf2;
+        if (k <= n) civ[k] = cf;
+        cf2 = cf1;
+        cf1 = cf;
+    }
+    cs = cbi0/cf;
+    for (k=0; k<=n; k++) {
+        civ[k] *= cs;
+    }
+    if (a0 <= 9.0) {
+        if (v0 == 0.0) {
+            ct = -log(0.5*z1)-el;
+            cs = czero;
+            w0 = 0.0;
+            cr = cone;
+            for (k=1; k<=50; k++) {
+                w0 += 1.0/k;
+                cr *= 0.25*z2/(double)(k*k);
+                cp = cr*(w0+ct);
+                cs += cp;
+                if ((k >= 10) && (abs(cp/cs) < eps)) break;
+            }
+            cbk0 = ct+cs;
+        }
+        else {
+            v0n = 1.0-v0;
+            gan = gamma(v0n);
+            ca2 = 1.0/(gan*pow(0.5*z1,v0));
+            ca1 = pow(0.5*z1,v0)/gap;
+            csu = ca2-ca1;
+            cr1 = cone;
+            cr2 = cone;
+            cws = czero;
+            for (k=1; k<=50; k++) {
+                cr1 *= 0.25*z2/(k*(k-v0));
+                cr2 *= 0.25*z2/(k*(k+v0));
+                csu += ca2*cr1-ca1*cr2;
+                if ((k >= 10) && (abs((cws-csu)/csu) < eps)) break;
+                cws = csu;
+            }
+            cbk0 = csu*M_PI_2/sin(piv);
+        }
+    }
+    else {
+        cb = exp(-z1)*sqrt(M_PI_2/z1);
+        cs = cone;
+        cr = cone;
+        for (k=1; k<=kz; k++) {
+            cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
+            cs += cr;
+        }
+        cbk0 = cb*cs;
+    }
+    cbk1 = (1.0/z1-civ[1]*cbk0)/civ[0];
+    ckv[0] = cbk0;
+    ckv[1] = cbk1;
+    cg0 = cbk0;
+    cg1 = cbk1;
+    for (k=2; k<=n; k++) {
+        cgk = 2.0*(v0+k-1.0)*cg1/z1+cg0;
+        ckv[k] = cgk;
+        cg0 = cg1;
+        cg1 = cgk;
+    }
+    if (real(z) < 0.0) {
+        for (k=0; k<=n; k++) {
+            cvk = exp((k+v0)*M_PI*cii);
+            if (imag(z) < 0.0) {
+                ckv[k] = cvk*ckv[k]+M_PI*cii*civ[k];
+                civ[k] /= cvk;
+            }
+            else if (imag(z) > 0.0) {
+                ckv[k] = ckv[k]/cvk-M_PI*cii*civ[k];
+                civ[k] *= cvk;
+            }
+        }
+    }
+    civp[0] = v0*civ[0]/z+civ[1];
+    ckvp[0] = v0*ckv[0]/z-ckv[1];
+    for (k=1; k<=n; k++) {
+        civp[k] = -(k+v0)*civ[k]/z+civ[k-1];
+        ckvp[k] = -(k+v0)*ckv[k]/z-ckv[k-1];
+    }
+    vm = n+v0;
+    return 0;
+}
-//  cbessjy.cpp -- complex Bessel functions.
-//  Algorithms and coefficient values from "Computation of Special
-//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-#include <complex>
-using namespace std;
-#include "bessel.h"
-double gamma(double);
-
-static complex<double> cii(0.0,1.0);
-static complex<double> cone(1.0,0.0);
-static complex<double> czero(0.0,0.0);
-
-int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
-    complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
-    complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p)
-{
-    complex<double> z1,z2,cr,cp,cs,cp0,cq0,cp1,cq1,ct1,ct2,cu;
-    double a0,w0,w1;
-    int k,kz;
-
-    static double a[] = {
-        -7.03125e-2,
-         0.112152099609375,
-        -0.5725014209747314,
-         6.074042001273483,
-        -1.100171402692467e2,
-         3.038090510922384e3,
-        -1.188384262567832e5,
-         6.252951493434797e6,
-        -4.259392165047669e8,
-         3.646840080706556e10,
-        -3.833534661393944e12,
-         4.854014686852901e14,
-        -7.286857349377656e16,
-         1.279721941975975e19};
-    static double b[] = {
-         7.32421875e-2,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1,
-         5.513358961220206e2,
-        -1.825775547429318e4,
-         8.328593040162893e5,
-        -5.006958953198893e7,
-         3.836255180230433e9,
-        -3.649010818849833e11,
-         4.218971570284096e13,
-        -5.827244631566907e15,
-         9.476288099260110e17,
-        -1.792162323051699e20};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947,
-         1.215978918765359e2,
-        -3.302272294480852e3,
-         1.276412726461746e5,
-        -6.656367718817688e6,
-         4.502786003050393e8,
-        -3.833857520742790e10,
-         4.011838599133198e12,
-        -5.060568503314727e14,
-         7.572616461117958e16,
-        -1.326257285320556e19};
-    static double b1[] = {
-        -0.1025390625,
-         0.2775764465332031,
-        -1.993531733751297,
-         2.724882731126854e1,
-        -6.038440767050702e2,
-         1.971837591223663e4,
-        -8.902978767070678e5,
-         5.310411010968522e7,
-        -4.043620325107754e9,
-         3.827011346598605e11,
-        -4.406481417852278e13,
-         6.065091351222699e15,
-        -9.833883876590679e17,
-         1.855045211579828e20};
-
-    a0 = abs(z);
-    z2 = z*z;
-    z1 = z;
-    if (a0 == 0.0) {
-        cj0 = cone;
-        cj1 = czero;
-        cy0 = complex<double>(-1e308,0);
-        cy1 = complex<double>(-1e308,0);
-        cj0p = czero;
-        cj1p = complex<double>(0.5,0.0);
-        cy0p = complex<double>(1e308,0);
-        cy1p = complex<double>(1e308,0);
-        return 0;
-    }
-    if (real(z) < 0.0) z1 = -z;
-    if (a0 <= 12.0) {
-        cj0 = cone;
-        cr = cone;
-        for (k=1;k<=40;k++) {
-            cr *= -0.25*z2/(double)(k*k);
-            cj0 += cr;
-            if (abs(cr) < abs(cj0)*eps) break;
-        }
-        cj1 = cone;
-        cr = cone;
-        for (k=1;k<=40;k++) {
-            cr *= -0.25*z2/(k*(k+1.0));
-            cj1 += cr;
-            if (abs(cr) < abs(cj1)*eps) break;
-        }
-        cj1 *= 0.5*z1;
-        w0 = 0.0;
-        cr = cone;
-        cs = czero;
-        for (k=1;k<=40;k++) {
-            w0 += 1.0/k;
-            cr *= -0.25*z2/(double)(k*k);
-            cp = cr*w0;
-            cs += cp;
-            if (abs(cp) < abs(cs)*eps) break;
-        }
-        cy0 = M_2_PI*((log(0.5*z1)+el)*cj0-cs);
-        w1 = 0.0;
-        cr = cone;
-        cs = cone;
-        for (k=1;k<=40;k++) {
-            w1 += 1.0/k;
-            cr *= -0.25*z2/(k*(k+1.0));
-            cp = cr*(2.0*w1+1.0/(k+1.0));
-            cs += cp;
-            if (abs(cp) < abs(cs)*eps) break;
-        }
-        cy1 = M_2_PI*((log(0.5*z1)+el)*cj1-1.0/z1-0.25*z1*cs);
-    }
-    else {
-        if (a0 >= 50.0) kz = 8;         // can be changed to 10
-        else if (a0 >= 35.0) kz = 10;   //   "      "     "  12
-        else kz = 12;                   //   "      "     "  14
-        ct1 = z1 - M_PI_4;
-        cp0 = cone;
-        for (k=0;k<kz;k++) {
-            cp0 += a[k]*pow(z1,-2.0*k-2.0);
-        }
-        cq0 = -0.125/z1;
-        for (k=0;k<kz;k++) {
-            cq0 += b[k]*pow(z1,-2.0*k-3.0);
-        }
-        cu = sqrt(M_2_PI/z1);
-        cj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
-        cy0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
-        ct2 = z1 - 0.75*M_PI;
-        cp1 = cone;
-        for (k=0;k<kz;k++) {
-            cp1 += a1[k]*pow(z1,-2.0*k-2.0);
-        }
-        cq1 = 0.375/z1;
-        for (k=0;k<kz;k++) {
-            cq1 += b1[k]*pow(z1,-2.0*k-3.0);
-        }
-        cj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
-        cy1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
-    }
-    if (real(z) < 0.0) {
-        if (imag(z) < 0.0) {
-            cy0 -= 2.0*cii*cj0;
-            cy1 = -(cy1-2.0*cii*cj1);
-        }
-        else if (imag(z) > 0.0) {
-            cy0 += 2.0*cii*cj0;
-            cy1 = -(cy1+2.0*cii*cj1);
-        }
-        cj1 = -cj1;
-    }
-    cj0p = -cj1;
-    cj1p = cj0-cj1/z;
-    cy0p = -cy1;
-    cy1p = cy0-cy1/z;
-    return 0;
-}
-
-int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
-{
-    complex<double> cbj0,cbj1,cby0,cby1,cj0,cjk,cj1,cf,cf1,cf2;
-    complex<double> cs,cg0,cg1,cyk,cyl1,cyl2,cylk,cp11,cp12,cp21,cp22;
-    complex<double> ch0,ch1,ch2;
-    double a0,yak,ya1,ya0,wa;
-    int m,k,lb,lb0;
-
-    if (n < 0) return 1;
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            cj[k] = czero;
-            cy[k] = complex<double> (-1e308,0);
-            cjp[k] = czero;
-            cyp[k] = complex<double>(1e308,0);
-        }
-        cj[0] = cone;
-        cjp[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    cbessjy01(z,cj[0],cj[1],cy[0],cy[1],cjp[0],cjp[1],cyp[0],cyp[1]);
-    cbj0 = cj[0];
-    cbj1 = cj[1];
-    cby0 = cy[0];
-    cby1 = cy[1];
-    if (n <= 1) return 0;
-    if (n < (int)0.25*a0) {
-        cj0 = cbj0;
-        cj1 = cbj1;
-        for (k=2;k<=n;k++) {
-            cjk = 2.0*(k-1.0)*cj1/z-cj0;
-            cj[k] = cjk;
-            cj0 = cj1;
-            cj1 = cjk;
-        }
-    }
-    else {
-        m = msta1(a0,200);
-        if (m < n) nm = m;
-        else m = msta2(a0,n,15);
-        cf2 = czero;
-        cf1 = complex<double> (1.0e-100,0.0);
-        for (k=m;k>=0;k--) {
-            cf = 2.0*(k+1.0)*cf1/z-cf2;
-            if (k <=nm) cj[k] = cf;
-            cf2 = cf1;
-            cf1 = cf;
-        }
-        if (abs(cbj0) > abs(cbj1)) cs = cbj0/cf;
-        else cs = cbj1/cf2;
-        for (k=0;k<=nm;k++) {
-            cj[k] *= cs;
-        }
-    }
-    for (k=2;k<=nm;k++) {
-        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
-    }
-    ya0 = abs(cby0);
-    lb = 0;
-    cg0 = cby0;
-    cg1 = cby1;
-    for (k=2;k<=nm;k++) {
-        cyk = 2.0*(k-1.0)*cg1/z-cg0;
-        yak = abs(cyk);
-        ya1 = abs(cg0);
-        if ((yak < ya0) && (yak < ya1)) lb = k;
-        cy[k] = cyk;
-        cg0 = cg1;
-        cg1 = cyk;
-    }
-    lb0 = 0;
-    if ((lb > 4) && (imag(z) != 0.0)) {
-        while (lb != lb0) {
-            ch2 = cone;
-            ch1 = czero;
-            lb0 = lb;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*k*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp12 = ch0;
-            cp22 = ch2;
-            ch2 = czero;
-            ch1 = cone;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*k*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp11 = ch0;
-            cp21 = ch2;
-            if (lb == nm)
-                cj[lb+1] = 2.0*lb*cj[lb]/z-cj[lb-1];
-            if (abs(cj[0]) > abs(cj[1])) {
-                cy[lb+1] = (cj[lb+1]*cby0-2.0*cp11/(M_PI*z))/cj[0];
-                cy[lb] = (cj[lb]*cby0+2.0*cp12/(M_PI*z))/cj[0];
-            }
-            else {
-                cy[lb+1] = (cj[lb+1]*cby1-2.0*cp21/(M_PI*z))/cj[1];
-                cy[lb] = (cj[lb]*cby1+2.0*cp22/(M_PI*z))/cj[1];
-            }
-            cyl2 = cy[lb+1];
-            cyl1 = cy[lb];
-            for (k=lb-1;k>=0;k--) {
-                cylk = 2.0*(k+1.0)*cyl1/z-cyl2;
-                cy[k] = cylk;
-                cyl2 = cyl1;
-                cyl1 = cylk;
-            }
-            cyl1 = cy[lb];
-            cyl2 = cy[lb+1];
-            for (k=lb+1;k<n;k++) {
-                cylk = 2.0*k*cyl2/z-cyl1;
-                cy[k+1] = cylk;
-                cyl1 = cyl2;
-                cyl2 = cylk;
-            }
-            for (k=2;k<=nm;k++) {
-                wa = abs(cy[k]);
-                if (wa < abs(cy[k-1])) lb = k;
-            }
-        }
-    }
-    for (k=2;k<=nm;k++) {
-        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
-    }
-    return 0;
-}
-
-int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
-{
-    complex<double> cf,cf0,cf1,cf2,cbs,csu,csv,cs0,ce;
-    complex<double> ct1,cp0,cq0,cp1,cq1,cu,cbj0,cby0,cbj1,cby1;
-    complex<double> cyy,cbjk,ct2;
-    double a0,y0;
-    int k,m;
-    static double a[] = {
-        -0.7031250000000000e-1,
-         0.1121520996093750,
-        -0.5725014209747314,
-         6.074042001273483};
-    static double b[] = {
-         0.7324218750000000e-1,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947};
-    static double b1[] = {
-       -0.1025390625,
-        0.2775764465332031,
-       -1.993531733751297,
-        2.724882731126854e1};
-
-    y0 = abs(imag(z));
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            cj[k] = czero;
-            cy[k] = complex<double> (-1e308,0);
-            cjp[k] = czero;
-            cyp[k] = complex<double>(1e308,0);
-        }
-        cj[0] = cone;
-        cjp[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    if ((a0 <= 300.0) || (n > (int)(0.25*a0))) {
-        if (n == 0) nm = 1;
-        m = msta1(a0,200);
-        if (m < nm) nm = m;
-        else m = msta2(a0,nm,15);
-        cbs = czero;
-        csu = czero;
-        csv = czero;
-        cf2 = czero;
-        cf1 = complex<double> (1.0e-100,0.0);
-        for (k=m;k>=0;k--) {
-            cf = 2.0*(k+1.0)*cf1/z-cf2;
-            if (k <= nm) cj[k] = cf;
-            if (((k & 1) == 0) && (k != 0)) {
-                if (y0 <= 1.0) {
-                    cbs += 2.0*cf;
-                }
-                else {
-                    cbs += (-1)*((k & 2)-1)*2.0*cf;
-                }
-                csu += (double)((-1)*((k & 2)-1))*cf/(double)k;
-            }
-            else if (k > 1) {
-                csv += (double)((-1)*((k & 2)-1)*k)*cf/(double)(k*k-1.0);    
-            }
-            cf2 = cf1;
-            cf1 = cf;
-        }
-        if (y0 <= 1.0) cs0 = cbs+cf;
-        else cs0 = (cbs+cf)/cos(z);
-        for (k=0;k<=nm;k++) {
-            cj[k] /= cs0;
-        }
-        ce = log(0.5*z)+el;
-        cy[0] = M_2_PI*(ce*cj[0]-4.0*csu/cs0);
-        cy[1] = M_2_PI*(-cj[0]/z+(ce-1.0)*cj[1]-4.0*csv/cs0);
-    }
-    else {
-        ct1 = z-M_PI_4;
-        cp0 = cone;
-        for (k=0;k<4;k++) {
-            cp0 += a[k]*pow(z,-2.0*k-2.0);
-        }
-        cq0 = -0.125/z;
-        for (k=0;k<4;k++) {
-            cq0 += b[k] *pow(z,-2.0*k-3.0);
-        }
-        cu = sqrt(M_2_PI/z);
-        cbj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
-        cby0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
-        cj[0] = cbj0;
-        cy[0] = cby0;
-        ct2 = z-0.75*M_PI;
-        cp1 = cone;
-        for (k=0;k<4;k++) {
-            cp1 += a1[k]*pow(z,-2.0*k-2.0);
-        }
-        cq1 = 0.375/z;
-        for (k=0;k<4;k++) {
-            cq1 += b1[k]*pow(z,-2.0*k-3.0);
-        }
-        cbj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
-        cby1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
-        cj[1] = cbj1;
-        cy[1] = cby1;
-        for (k=2;k<=n;k++) {
-            cbjk = 2.0*(k-1.0)*cbj1/z-cbj0;
-            cj[k] = cbjk;
-            cbj0 = cbj1;
-            cbj1 = cbjk;
-        }
-    }
-    cjp[0] = -cj[1];
-    for (k=1;k<=nm;k++) {
-        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
-    }
-    if (abs(cj[0]) > 1.0)
-        cy[1] = (cj[1]*cy[0]-2.0/(M_PI*z))/cj[0];
-    for (k=2;k<=nm;k++) {
-        if (abs(cj[k-1]) >= abs(cj[k-2]))
-            cyy = (cj[k]*cy[k-1]-2.0/(M_PI*z))/cj[k-1];
-        else
-            cyy = (cj[k]*cy[k-2]-4.0*(k-1.0)/(M_PI*z*z))/cj[k-2];
-        cy[k] = cyy;
-    }
-    cyp[0] = -cy[1];
-    for (k=1;k<=nm;k++) {
-        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
-    }
-
-    return 0;
-}
-
-int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
-    complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp)
-{
-    complex<double> z1,z2,zk,cjvl,cr,ca,cjv0,cjv1,cpz,crp;
-    complex<double> cqz,crq,ca0,cck,csk,cyv0,cyv1,cju0,cju1,cb;
-    complex<double> cs,cs0,cr0,cs1,cr1,cec,cf,cf0,cf1,cf2;
-    complex<double> cfac0,cfac1,cg0,cg1,cyk,cp11,cp12,cp21,cp22;
-    complex<double> ch0,ch1,ch2,cyl1,cyl2,cylk;
-
-    double a0,v0,pv0,pv1,vl,ga,gb,vg,vv,w0,w1,ya0,yak,ya1,wa;
-    int j,n,k,kz,l,lb,lb0,m;
-
-    a0 = abs(z);
-    z1 = z;
-    z2 = z*z;
-    n = (int)v;
-
-
-    v0 = v-n;
-
-    pv0 = M_PI*v0;
-    pv1 = M_PI*(1.0+v0);
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            cjv[k] = czero;
-            cyv[k] = complex<double> (-1e308,0);
-            cjvp[k] = czero;
-            cyvp[k] = complex<double> (1e308,0);
-
-        }
-        if (v0 == 0.0) {
-            cjv[0] = cone;
-            cjvp[1] = complex<double> (0.5,0.0);
-        }
-        else {
-            cjvp[0] = complex<double> (1e308,0);
-        }
-        vm = v;
-        return 0;
-    }
-    if (real(z1) < 0.0) z1 = -z;
-    if (a0 <= 12.0) {
-        for (l=0;l<2;l++) {
-            vl = v0+l;
-            cjvl = cone;
-            cr = cone;
-            for (k=1;k<=40;k++) {
-                cr *= -0.25*z2/(k*(k+vl));
-                cjvl += cr;
-                if (abs(cr) < abs(cjvl)*eps) break;
-            }
-           vg = 1.0 + vl;
-           ga = gamma(vg);
-           ca = pow(0.5*z1,vl)/ga;
-           if (l == 0) cjv0 = cjvl*ca;
-           else cjv1 = cjvl*ca;
-        }
-    }
-    else {
-        if (a0 >= 50.0) kz = 8;
-        else if (a0 >= 35.0) kz = 10;
-        else kz = 11;
-        for (j=0;j<2;j++) {
-            vv = 4.0*(j+v0)*(j+v0);
-            cpz = cone;
-            crp = cone;
-            for (k=1;k<=kz;k++) {
-                crp = -0.78125e-2*crp*(vv-pow(4.0*k-3.0,2.0))*
-                    (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*z2);
-                cpz += crp;
-            }
-            cqz = cone;
-            crq = cone;
-            for (k=1;k<=kz;k++) {
-                crq = -0.78125e-2*crq*(vv-pow(4.0*k-1.0,2.0))*
-                    (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*z2);
-                cqz += crq;
-            }
-            cqz *= 0.125*(vv-1.0)/z1;
-            zk = z1-(0.5*(j+v0)+0.25)*M_PI;
-            ca0 = sqrt(M_2_PI/z1);
-            cck = cos(zk);
-            csk = sin(zk);
-            if (j == 0) {
-                cjv0 = ca0*(cpz*cck-cqz*csk);
-                cyv0 = ca0*(cpz*csk+cqz+cck);
-            }
-            else {
-                cjv1 = ca0*(cpz*cck-cqz*csk);
-                cyv1 = ca0*(cpz*csk+cqz*cck);
-            }
-        }
-    }
-    if (a0 <= 12.0) {
-        if (v0 != 0.0) {
-            for (l=0;l<2;l++) {
-                vl = v0+l;
-                cjvl = cone;
-                cr = cone;
-                for (k=1;k<=40;k++) {
-                    cr *= -0.25*z2/(k*(k-vl));
-                    cjvl += cr;
-                    if (abs(cr) < abs(cjvl)*eps) break;
-                }
-                vg = 1.0-vl;
-                gb = gamma(vg);
-                cb = pow(2.0/z1,vl)/gb;
-                if (l == 0) cju0 = cjvl*cb;
-                else cju1 = cjvl*cb;
-            }
-            cyv0 = (cjv0*cos(pv0)-cju0)/sin(pv0);
-            cyv1 = (cjv1*cos(pv1)-cju1)/sin(pv1);
-        }
-        else {
-            cec = log(0.5*z1)+el;
-            cs0 = czero;
-            w0 = 0.0;
-            cr0 = cone;
-            for (k=1;k<=30;k++) {
-                w0 += 1.0/k;
-                cr0 *= -0.25*z2/(double)(k*k);
-                cs0 += cr0*w0;
-            }
-            cyv0 = M_2_PI*(cec*cjv0-cs0);
-            cs1 = cone;
-            w1 = 0.0;
-            cr1 = cone;
-            for (k=1;k<=30;k++) {
-                w1 += 1.0/k;
-                cr1 *= -0.25*z2/(k*(k+1.0));
-                cs1 += cr1*(2.0*w1+1.0/(k+1.0));
-            }
-            cyv1 = M_2_PI*(cec*cjv1-1.0/z1-0.25*z1*cs1);
-        }
-    }
-    if (real(z) < 0.0) {
-        cfac0 = exp(pv0*cii);
-        cfac1 = exp(pv1*cii);
-        if (imag(z) < 0.0) {
-            cyv0 = cfac0*cyv0-2.0*cii*cos(pv0)*cjv0;
-            cyv1 = cfac1*cyv1-2.0*cii*cos(pv1)*cjv1;
-            cjv0 /= cfac0;
-            cjv1 /= cfac1;
-        }
-        else if (imag(z) > 0.0) {
-            cyv0 = cyv0/cfac0+2.0*cii*cos(pv0)*cjv0;
-            cyv1 = cyv1/cfac1+2.0*cii*cos(pv1)*cjv1;
-            cjv0 *= cfac0;
-            cjv1 *= cfac1;
-        }
-    }
-    cjv[0] = cjv0;
-    cjv[1] = cjv1;
-    if ((n >= 2) && (n <= (int)(0.25*a0))) {
-        cf0 = cjv0;
-        cf1 = cjv1;
-        for (k=2;k<= n;k++) {
-            cf = 2.0*(k+v0-1.0)*cf1/z-cf0;
-            cjv[k] = cf;
-            cf0 = cf1;
-            cf1 = cf;
-        }
-    }
-    else if (n >= 2) {
-        m = msta1(a0,200);
-        if (m < n) n = m;
-        else  m = msta2(a0,n,15);
-        cf2 = czero;
-        cf1 = complex<double>(1.0e-100,0.0);
-        for (k=m;k>=0;k--) {
-            cf = 2.0*(v0+k+1.0)*cf1/z-cf2;
-            if (k <= n) cjv[k] = cf;
-            cf2 = cf1;
-            cf1 = cf;
-        }
-        if (abs(cjv0) > abs(cjv1)) cs = cjv0/cf;
-        else cs = cjv1/cf2;
-        for (k=0;k<=n;k++) {
-            cjv[k] *= cs;
-        }
-    }
-    cjvp[0] = v0*cjv[0]/z-cjv[1];
-    for (k=1;k<=n;k++) {
-        cjvp[k] = -(k+v0)*cjv[k]/z+cjv[k-1];
-    }
-    cyv[0] = cyv0;
-    cyv[1] = cyv1;
-    ya0 = abs(cyv0);
-    lb = 0;
-    cg0 = cyv0;
-    cg1 = cyv1;
-    for (k=2;k<=n;k++) {
-        cyk = 2.0*(v0+k-1.0)*cg1/z-cg0;
-        yak = abs(cyk);
-        ya1 = abs(cg0);
-        if ((yak < ya0) && (yak< ya1)) lb = k;
-        cyv[k] = cyk;
-        cg0 = cg1;
-        cg1 = cyk;
-    }
-    lb0 = 0;
-    if ((lb > 4) && (imag(z) != 0.0)) {
-        while(lb != lb0) {
-            ch2 = cone;
-            ch1 = czero;
-            lb0 = lb;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*(k+v0)*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp12 = ch0;
-            cp22 = ch2;
-            ch2 = czero;
-            ch1 = cone;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*(k+v0)*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp11 = ch0;
-            cp21 = ch2;
-            if (lb == n)
-                cjv[lb+1] = 2.0*(lb+v0)*cjv[lb]/z-cjv[lb-1];
-            if (abs(cjv[0]) > abs(cjv[1])) {
-                cyv[lb+1] = (cjv[lb+1]*cyv0-2.0*cp11/(M_PI*z))/cjv[0];
-                cyv[lb] = (cjv[lb]*cyv0+2.0*cp12/(M_PI*z))/cjv[0];
-            }
-            else {
-                cyv[lb+1] = (cjv[lb+1]*cyv1-2.0*cp21/(M_PI*z))/cjv[1];
-                cyv[lb] = (cjv[lb]*cyv1+2.0*cp22/(M_PI*z))/cjv[1];
-            }
-            cyl2 = cyv[lb+1];
-            cyl1 = cyv[lb];
-            for (k=lb-1;k>=0;k--) {
-                cylk = 2.0*(k+v0+1.0)*cyl1/z-cyl2;
-                cyv[k] = cylk;
-                cyl2 = cyl1;
-                cyl1 = cylk;
-            }
-            cyl1 = cyv[lb];
-            cyl2 = cyv[lb+1];
-            for (k=lb+1;k<n;k++) {
-                cylk = 2.0*(k+v0)*cyl2/z-cyl1;
-                cyv[k+1] = cylk;
-                cyl1 = cyl2;
-                cyl2 = cylk;
-            }
-            for (k=2;k<=n;k++) {
-                wa = abs(cyv[k]);
-                if (wa < abs(cyv[k-1])) lb = k;
-            }
-        }
-    }
-    cyvp[0] = v0*cyv[0]/z-cyv[1];
-    for (k=1;k<=n;k++) {
-        cyvp[k] = cyv[k-1]-(k+v0)*cyv[k]/z;
-    }
-    vm = n+v0;
-    return 0;
-}
-
-
+//  cbessjy.cpp -- complex Bessel functions.
+//  Algorithms and coefficient values from "Computation of Special
+//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+#include <complex>
+using namespace std;
+#include "bessel.h"
+double gamma(double);
+
+static complex<double> cii(0.0,1.0);
+static complex<double> cone(1.0,0.0);
+static complex<double> czero(0.0,0.0);
+
+int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
+              complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
+              complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p)
+{
+    complex<double> z1,z2,cr,cp,cs,cp0,cq0,cp1,cq1,ct1,ct2,cu;
+    double a0,w0,w1;
+    int k,kz;
+
+    static double a[] = {
+        -7.03125e-2,
+        0.112152099609375,
+        -0.5725014209747314,
+        6.074042001273483,
+        -1.100171402692467e2,
+        3.038090510922384e3,
+        -1.188384262567832e5,
+        6.252951493434797e6,
+        -4.259392165047669e8,
+        3.646840080706556e10,
+        -3.833534661393944e12,
+        4.854014686852901e14,
+        -7.286857349377656e16,
+        1.279721941975975e19
+    };
+    static double b[] = {
+        7.32421875e-2,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1,
+        5.513358961220206e2,
+        -1.825775547429318e4,
+        8.328593040162893e5,
+        -5.006958953198893e7,
+        3.836255180230433e9,
+        -3.649010818849833e11,
+        4.218971570284096e13,
+        -5.827244631566907e15,
+        9.476288099260110e17,
+        -1.792162323051699e20
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947,
+        1.215978918765359e2,
+        -3.302272294480852e3,
+        1.276412726461746e5,
+        -6.656367718817688e6,
+        4.502786003050393e8,
+        -3.833857520742790e10,
+        4.011838599133198e12,
+        -5.060568503314727e14,
+        7.572616461117958e16,
+        -1.326257285320556e19
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1,
+        -6.038440767050702e2,
+        1.971837591223663e4,
+        -8.902978767070678e5,
+        5.310411010968522e7,
+        -4.043620325107754e9,
+        3.827011346598605e11,
+        -4.406481417852278e13,
+        6.065091351222699e15,
+        -9.833883876590679e17,
+        1.855045211579828e20
+    };
+
+    a0 = abs(z);
+    z2 = z*z;
+    z1 = z;
+    if (a0 == 0.0) {
+        cj0 = cone;
+        cj1 = czero;
+        cy0 = complex<double>(-1e308,0);
+        cy1 = complex<double>(-1e308,0);
+        cj0p = czero;
+        cj1p = complex<double>(0.5,0.0);
+        cy0p = complex<double>(1e308,0);
+        cy1p = complex<double>(1e308,0);
+        return 0;
+    }
+    if (real(z) < 0.0) z1 = -z;
+    if (a0 <= 12.0) {
+        cj0 = cone;
+        cr = cone;
+        for (k=1; k<=40; k++) {
+            cr *= -0.25*z2/(double)(k*k);
+            cj0 += cr;
+            if (abs(cr) < abs(cj0)*eps) break;
+        }
+        cj1 = cone;
+        cr = cone;
+        for (k=1; k<=40; k++) {
+            cr *= -0.25*z2/(k*(k+1.0));
+            cj1 += cr;
+            if (abs(cr) < abs(cj1)*eps) break;
+        }
+        cj1 *= 0.5*z1;
+        w0 = 0.0;
+        cr = cone;
+        cs = czero;
+        for (k=1; k<=40; k++) {
+            w0 += 1.0/k;
+            cr *= -0.25*z2/(double)(k*k);
+            cp = cr*w0;
+            cs += cp;
+            if (abs(cp) < abs(cs)*eps) break;
+        }
+        cy0 = M_2_PI*((log(0.5*z1)+el)*cj0-cs);
+        w1 = 0.0;
+        cr = cone;
+        cs = cone;
+        for (k=1; k<=40; k++) {
+            w1 += 1.0/k;
+            cr *= -0.25*z2/(k*(k+1.0));
+            cp = cr*(2.0*w1+1.0/(k+1.0));
+            cs += cp;
+            if (abs(cp) < abs(cs)*eps) break;
+        }
+        cy1 = M_2_PI*((log(0.5*z1)+el)*cj1-1.0/z1-0.25*z1*cs);
+    }
+    else {
+        if (a0 >= 50.0) kz = 8;         // can be changed to 10
+        else if (a0 >= 35.0) kz = 10;   //   "      "     "  12
+        else kz = 12;                   //   "      "     "  14
+        ct1 = z1 - M_PI_4;
+        cp0 = cone;
+        for (k=0; k<kz; k++) {
+            cp0 += a[k]*pow(z1,-2.0*k-2.0);
+        }
+        cq0 = -0.125/z1;
+        for (k=0; k<kz; k++) {
+            cq0 += b[k]*pow(z1,-2.0*k-3.0);
+        }
+        cu = sqrt(M_2_PI/z1);
+        cj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
+        cy0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
+        ct2 = z1 - 0.75*M_PI;
+        cp1 = cone;
+        for (k=0; k<kz; k++) {
+            cp1 += a1[k]*pow(z1,-2.0*k-2.0);
+        }
+        cq1 = 0.375/z1;
+        for (k=0; k<kz; k++) {
+            cq1 += b1[k]*pow(z1,-2.0*k-3.0);
+        }
+        cj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
+        cy1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
+    }
+    if (real(z) < 0.0) {
+        if (imag(z) < 0.0) {
+            cy0 -= 2.0*cii*cj0;
+            cy1 = -(cy1-2.0*cii*cj1);
+        }
+        else if (imag(z) > 0.0) {
+            cy0 += 2.0*cii*cj0;
+            cy1 = -(cy1+2.0*cii*cj1);
+        }
+        cj1 = -cj1;
+    }
+    cj0p = -cj1;
+    cj1p = cj0-cj1/z;
+    cy0p = -cy1;
+    cy1p = cy0-cy1/z;
+    return 0;
+}
+
+int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
+{
+    complex<double> cbj0,cbj1,cby0,cby1,cj0,cjk,cj1,cf,cf1,cf2;
+    complex<double> cs,cg0,cg1,cyk,cyl1,cyl2,cylk,cp11,cp12,cp21,cp22;
+    complex<double> ch0,ch1,ch2;
+    double a0,yak,ya1,ya0,wa;
+    int m,k,lb,lb0;
+
+    if (n < 0) return 1;
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            cj[k] = czero;
+            cy[k] = complex<double> (-1e308,0);
+            cjp[k] = czero;
+            cyp[k] = complex<double>(1e308,0);
+        }
+        cj[0] = cone;
+        cjp[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    cbessjy01(z,cj[0],cj[1],cy[0],cy[1],cjp[0],cjp[1],cyp[0],cyp[1]);
+    cbj0 = cj[0];
+    cbj1 = cj[1];
+    cby0 = cy[0];
+    cby1 = cy[1];
+    if (n <= 1) return 0;
+    if (n < (int)0.25*a0) {
+        cj0 = cbj0;
+        cj1 = cbj1;
+        for (k=2; k<=n; k++) {
+            cjk = 2.0*(k-1.0)*cj1/z-cj0;
+            cj[k] = cjk;
+            cj0 = cj1;
+            cj1 = cjk;
+        }
+    }
+    else {
+        m = msta1(a0,200);
+        if (m < n) nm = m;
+        else m = msta2(a0,n,15);
+        cf2 = czero;
+        cf1 = complex<double> (1.0e-100,0.0);
+        for (k=m; k>=0; k--) {
+            cf = 2.0*(k+1.0)*cf1/z-cf2;
+            if (k <=nm) cj[k] = cf;
+            cf2 = cf1;
+            cf1 = cf;
+        }
+        if (abs(cbj0) > abs(cbj1)) cs = cbj0/cf;
+        else cs = cbj1/cf2;
+        for (k=0; k<=nm; k++) {
+            cj[k] *= cs;
+        }
+    }
+    for (k=2; k<=nm; k++) {
+        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
+    }
+    ya0 = abs(cby0);
+    lb = 0;
+    cg0 = cby0;
+    cg1 = cby1;
+    for (k=2; k<=nm; k++) {
+        cyk = 2.0*(k-1.0)*cg1/z-cg0;
+        yak = abs(cyk);
+        ya1 = abs(cg0);
+        if ((yak < ya0) && (yak < ya1)) lb = k;
+        cy[k] = cyk;
+        cg0 = cg1;
+        cg1 = cyk;
+    }
+    lb0 = 0;
+    if ((lb > 4) && (imag(z) != 0.0)) {
+        while (lb != lb0) {
+            ch2 = cone;
+            ch1 = czero;
+            lb0 = lb;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*k*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp12 = ch0;
+            cp22 = ch2;
+            ch2 = czero;
+            ch1 = cone;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*k*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp11 = ch0;
+            cp21 = ch2;
+            if (lb == nm)
+                cj[lb+1] = 2.0*lb*cj[lb]/z-cj[lb-1];
+            if (abs(cj[0]) > abs(cj[1])) {
+                cy[lb+1] = (cj[lb+1]*cby0-2.0*cp11/(M_PI*z))/cj[0];
+                cy[lb] = (cj[lb]*cby0+2.0*cp12/(M_PI*z))/cj[0];
+            }
+            else {
+                cy[lb+1] = (cj[lb+1]*cby1-2.0*cp21/(M_PI*z))/cj[1];
+                cy[lb] = (cj[lb]*cby1+2.0*cp22/(M_PI*z))/cj[1];
+            }
+            cyl2 = cy[lb+1];
+            cyl1 = cy[lb];
+            for (k=lb-1; k>=0; k--) {
+                cylk = 2.0*(k+1.0)*cyl1/z-cyl2;
+                cy[k] = cylk;
+                cyl2 = cyl1;
+                cyl1 = cylk;
+            }
+            cyl1 = cy[lb];
+            cyl2 = cy[lb+1];
+            for (k=lb+1; k<n; k++) {
+                cylk = 2.0*k*cyl2/z-cyl1;
+                cy[k+1] = cylk;
+                cyl1 = cyl2;
+                cyl2 = cylk;
+            }
+            for (k=2; k<=nm; k++) {
+                wa = abs(cy[k]);
+                if (wa < abs(cy[k-1])) lb = k;
+            }
+        }
+    }
+    for (k=2; k<=nm; k++) {
+        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
+    }
+    return 0;
+}
+
+int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
+{
+    complex<double> cf,cf0,cf1,cf2,cbs,csu,csv,cs0,ce;
+    complex<double> ct1,cp0,cq0,cp1,cq1,cu,cbj0,cby0,cbj1,cby1;
+    complex<double> cyy,cbjk,ct2;
+    double a0,y0;
+    int k,m;
+    static double a[] = {
+        -0.7031250000000000e-1,
+        0.1121520996093750,
+        -0.5725014209747314,
+        6.074042001273483
+    };
+    static double b[] = {
+        0.7324218750000000e-1,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1
+    };
+
+    y0 = abs(imag(z));
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            cj[k] = czero;
+            cy[k] = complex<double> (-1e308,0);
+            cjp[k] = czero;
+            cyp[k] = complex<double>(1e308,0);
+        }
+        cj[0] = cone;
+        cjp[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    if ((a0 <= 300.0) || (n > (int)(0.25*a0))) {
+        if (n == 0) nm = 1;
+        m = msta1(a0,200);
+        if (m < nm) nm = m;
+        else m = msta2(a0,nm,15);
+        cbs = czero;
+        csu = czero;
+        csv = czero;
+        cf2 = czero;
+        cf1 = complex<double> (1.0e-100,0.0);
+        for (k=m; k>=0; k--) {
+            cf = 2.0*(k+1.0)*cf1/z-cf2;
+            if (k <= nm) cj[k] = cf;
+            if (((k & 1) == 0) && (k != 0)) {
+                if (y0 <= 1.0) {
+                    cbs += 2.0*cf;
+                }
+                else {
+                    cbs += (-1)*((k & 2)-1)*2.0*cf;
+                }
+                csu += (double)((-1)*((k & 2)-1))*cf/(double)k;
+            }
+            else if (k > 1) {
+                csv += (double)((-1)*((k & 2)-1)*k)*cf/(double)(k*k-1.0);
+            }
+            cf2 = cf1;
+            cf1 = cf;
+        }
+        if (y0 <= 1.0) cs0 = cbs+cf;
+        else cs0 = (cbs+cf)/cos(z);
+        for (k=0; k<=nm; k++) {
+            cj[k] /= cs0;
+        }
+        ce = log(0.5*z)+el;
+        cy[0] = M_2_PI*(ce*cj[0]-4.0*csu/cs0);
+        cy[1] = M_2_PI*(-cj[0]/z+(ce-1.0)*cj[1]-4.0*csv/cs0);
+    }
+    else {
+        ct1 = z-M_PI_4;
+        cp0 = cone;
+        for (k=0; k<4; k++) {
+            cp0 += a[k]*pow(z,-2.0*k-2.0);
+        }
+        cq0 = -0.125/z;
+        for (k=0; k<4; k++) {
+            cq0 += b[k] *pow(z,-2.0*k-3.0);
+        }
+        cu = sqrt(M_2_PI/z);
+        cbj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
+        cby0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
+        cj[0] = cbj0;
+        cy[0] = cby0;
+        ct2 = z-0.75*M_PI;
+        cp1 = cone;
+        for (k=0; k<4; k++) {
+            cp1 += a1[k]*pow(z,-2.0*k-2.0);
+        }
+        cq1 = 0.375/z;
+        for (k=0; k<4; k++) {
+            cq1 += b1[k]*pow(z,-2.0*k-3.0);
+        }
+        cbj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
+        cby1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
+        cj[1] = cbj1;
+        cy[1] = cby1;
+        for (k=2; k<=n; k++) {
+            cbjk = 2.0*(k-1.0)*cbj1/z-cbj0;
+            cj[k] = cbjk;
+            cbj0 = cbj1;
+            cbj1 = cbjk;
+        }
+    }
+    cjp[0] = -cj[1];
+    for (k=1; k<=nm; k++) {
+        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
+    }
+    if (abs(cj[0]) > 1.0)
+        cy[1] = (cj[1]*cy[0]-2.0/(M_PI*z))/cj[0];
+    for (k=2; k<=nm; k++) {
+        if (abs(cj[k-1]) >= abs(cj[k-2]))
+            cyy = (cj[k]*cy[k-1]-2.0/(M_PI*z))/cj[k-1];
+        else
+            cyy = (cj[k]*cy[k-2]-4.0*(k-1.0)/(M_PI*z*z))/cj[k-2];
+        cy[k] = cyy;
+    }
+    cyp[0] = -cy[1];
+    for (k=1; k<=nm; k++) {
+        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
+    }
+
+    return 0;
+}
+
+int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
+              complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp)
+{
+    complex<double> z1,z2,zk,cjvl,cr,ca,cjv0,cjv1,cpz,crp;
+    complex<double> cqz,crq,ca0,cck,csk,cyv0,cyv1,cju0,cju1,cb;
+    complex<double> cs,cs0,cr0,cs1,cr1,cec,cf,cf0,cf1,cf2;
+    complex<double> cfac0,cfac1,cg0,cg1,cyk,cp11,cp12,cp21,cp22;
+    complex<double> ch0,ch1,ch2,cyl1,cyl2,cylk;
+
+    double a0,v0,pv0,pv1,vl,ga,gb,vg,vv,w0,w1,ya0,yak,ya1,wa;
+    int j,n,k,kz,l,lb,lb0,m;
+
+    a0 = abs(z);
+    z1 = z;
+    z2 = z*z;
+    n = (int)v;
+
+
+    v0 = v-n;
+
+    pv0 = M_PI*v0;
+    pv1 = M_PI*(1.0+v0);
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            cjv[k] = czero;
+            cyv[k] = complex<double> (-1e308,0);
+            cjvp[k] = czero;
+            cyvp[k] = complex<double> (1e308,0);
+
+        }
+        if (v0 == 0.0) {
+            cjv[0] = cone;
+            cjvp[1] = complex<double> (0.5,0.0);
+        }
+        else {
+            cjvp[0] = complex<double> (1e308,0);
+        }
+        vm = v;
+        return 0;
+    }
+    if (real(z1) < 0.0) z1 = -z;
+    if (a0 <= 12.0) {
+        for (l=0; l<2; l++) {
+            vl = v0+l;
+            cjvl = cone;
+            cr = cone;
+            for (k=1; k<=40; k++) {
+                cr *= -0.25*z2/(k*(k+vl));
+                cjvl += cr;
+                if (abs(cr) < abs(cjvl)*eps) break;
+            }
+            vg = 1.0 + vl;
+            ga = gamma(vg);
+            ca = pow(0.5*z1,vl)/ga;
+            if (l == 0) cjv0 = cjvl*ca;
+            else cjv1 = cjvl*ca;
+        }
+    }
+    else {
+        if (a0 >= 50.0) kz = 8;
+        else if (a0 >= 35.0) kz = 10;
+        else kz = 11;
+        for (j=0; j<2; j++) {
+            vv = 4.0*(j+v0)*(j+v0);
+            cpz = cone;
+            crp = cone;
+            for (k=1; k<=kz; k++) {
+                crp = -0.78125e-2*crp*(vv-pow(4.0*k-3.0,2.0))*
+                      (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*z2);
+                cpz += crp;
+            }
+            cqz = cone;
+            crq = cone;
+            for (k=1; k<=kz; k++) {
+                crq = -0.78125e-2*crq*(vv-pow(4.0*k-1.0,2.0))*
+                      (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*z2);
+                cqz += crq;
+            }
+            cqz *= 0.125*(vv-1.0)/z1;
+            zk = z1-(0.5*(j+v0)+0.25)*M_PI;
+            ca0 = sqrt(M_2_PI/z1);
+            cck = cos(zk);
+            csk = sin(zk);
+            if (j == 0) {
+                cjv0 = ca0*(cpz*cck-cqz*csk);
+                cyv0 = ca0*(cpz*csk+cqz+cck);
+            }
+            else {
+                cjv1 = ca0*(cpz*cck-cqz*csk);
+                cyv1 = ca0*(cpz*csk+cqz*cck);
+            }
+        }
+    }
+    if (a0 <= 12.0) {
+        if (v0 != 0.0) {
+            for (l=0; l<2; l++) {
+                vl = v0+l;
+                cjvl = cone;
+                cr = cone;
+                for (k=1; k<=40; k++) {
+                    cr *= -0.25*z2/(k*(k-vl));
+                    cjvl += cr;
+                    if (abs(cr) < abs(cjvl)*eps) break;
+                }
+                vg = 1.0-vl;
+                gb = gamma(vg);
+                cb = pow(2.0/z1,vl)/gb;
+                if (l == 0) cju0 = cjvl*cb;
+                else cju1 = cjvl*cb;
+            }
+            cyv0 = (cjv0*cos(pv0)-cju0)/sin(pv0);
+            cyv1 = (cjv1*cos(pv1)-cju1)/sin(pv1);
+        }
+        else {
+            cec = log(0.5*z1)+el;
+            cs0 = czero;
+            w0 = 0.0;
+            cr0 = cone;
+            for (k=1; k<=30; k++) {
+                w0 += 1.0/k;
+                cr0 *= -0.25*z2/(double)(k*k);
+                cs0 += cr0*w0;
+            }
+            cyv0 = M_2_PI*(cec*cjv0-cs0);
+            cs1 = cone;
+            w1 = 0.0;
+            cr1 = cone;
+            for (k=1; k<=30; k++) {
+                w1 += 1.0/k;
+                cr1 *= -0.25*z2/(k*(k+1.0));
+                cs1 += cr1*(2.0*w1+1.0/(k+1.0));
+            }
+            cyv1 = M_2_PI*(cec*cjv1-1.0/z1-0.25*z1*cs1);
+        }
+    }
+    if (real(z) < 0.0) {
+        cfac0 = exp(pv0*cii);
+        cfac1 = exp(pv1*cii);
+        if (imag(z) < 0.0) {
+            cyv0 = cfac0*cyv0-2.0*cii*cos(pv0)*cjv0;
+            cyv1 = cfac1*cyv1-2.0*cii*cos(pv1)*cjv1;
+            cjv0 /= cfac0;
+            cjv1 /= cfac1;
+        }
+        else if (imag(z) > 0.0) {
+            cyv0 = cyv0/cfac0+2.0*cii*cos(pv0)*cjv0;
+            cyv1 = cyv1/cfac1+2.0*cii*cos(pv1)*cjv1;
+            cjv0 *= cfac0;
+            cjv1 *= cfac1;
+        }
+    }
+    cjv[0] = cjv0;
+    cjv[1] = cjv1;
+    if ((n >= 2) && (n <= (int)(0.25*a0))) {
+        cf0 = cjv0;
+        cf1 = cjv1;
+        for (k=2; k<= n; k++) {
+            cf = 2.0*(k+v0-1.0)*cf1/z-cf0;
+            cjv[k] = cf;
+            cf0 = cf1;
+            cf1 = cf;
+        }
+    }
+    else if (n >= 2) {
+        m = msta1(a0,200);
+        if (m < n) n = m;
+        else  m = msta2(a0,n,15);
+        cf2 = czero;
+        cf1 = complex<double>(1.0e-100,0.0);
+        for (k=m; k>=0; k--) {
+            cf = 2.0*(v0+k+1.0)*cf1/z-cf2;
+            if (k <= n) cjv[k] = cf;
+            cf2 = cf1;
+            cf1 = cf;
+        }
+        if (abs(cjv0) > abs(cjv1)) cs = cjv0/cf;
+        else cs = cjv1/cf2;
+        for (k=0; k<=n; k++) {
+            cjv[k] *= cs;
+        }
+    }
+    cjvp[0] = v0*cjv[0]/z-cjv[1];
+    for (k=1; k<=n; k++) {
+        cjvp[k] = -(k+v0)*cjv[k]/z+cjv[k-1];
+    }
+    cyv[0] = cyv0;
+    cyv[1] = cyv1;
+    ya0 = abs(cyv0);
+    lb = 0;
+    cg0 = cyv0;
+    cg1 = cyv1;
+    for (k=2; k<=n; k++) {
+        cyk = 2.0*(v0+k-1.0)*cg1/z-cg0;
+        yak = abs(cyk);
+        ya1 = abs(cg0);
+        if ((yak < ya0) && (yak< ya1)) lb = k;
+        cyv[k] = cyk;
+        cg0 = cg1;
+        cg1 = cyk;
+    }
+    lb0 = 0;
+    if ((lb > 4) && (imag(z) != 0.0)) {
+        while(lb != lb0) {
+            ch2 = cone;
+            ch1 = czero;
+            lb0 = lb;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*(k+v0)*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp12 = ch0;
+            cp22 = ch2;
+            ch2 = czero;
+            ch1 = cone;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*(k+v0)*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp11 = ch0;
+            cp21 = ch2;
+            if (lb == n)
+                cjv[lb+1] = 2.0*(lb+v0)*cjv[lb]/z-cjv[lb-1];
+            if (abs(cjv[0]) > abs(cjv[1])) {
+                cyv[lb+1] = (cjv[lb+1]*cyv0-2.0*cp11/(M_PI*z))/cjv[0];
+                cyv[lb] = (cjv[lb]*cyv0+2.0*cp12/(M_PI*z))/cjv[0];
+            }
+            else {
+                cyv[lb+1] = (cjv[lb+1]*cyv1-2.0*cp21/(M_PI*z))/cjv[1];
+                cyv[lb] = (cjv[lb]*cyv1+2.0*cp22/(M_PI*z))/cjv[1];
+            }
+            cyl2 = cyv[lb+1];
+            cyl1 = cyv[lb];
+            for (k=lb-1; k>=0; k--) {
+                cylk = 2.0*(k+v0+1.0)*cyl1/z-cyl2;
+                cyv[k] = cylk;
+                cyl2 = cyl1;
+                cyl1 = cylk;
+            }
+            cyl1 = cyv[lb];
+            cyl2 = cyv[lb+1];
+            for (k=lb+1; k<n; k++) {
+                cylk = 2.0*(k+v0)*cyl2/z-cyl1;
+                cyv[k+1] = cylk;
+                cyl1 = cyl2;
+                cyl2 = cylk;
+            }
+            for (k=2; k<=n; k++) {
+                wa = abs(cyv[k]);
+                if (wa < abs(cyv[k-1])) lb = k;
+            }
+        }
+    }
+    cyvp[0] = v0*cyv[0]/z-cyv[1];
+    for (k=1; k<=n; k++) {
+        cyvp[k] = cyv[k-1]-(k+v0)*cyv[k]/z;
+    }
+    vm = n+v0;
+    return 0;
+}
+
+
-__device__ double g(double v0, double v1)
-{
-	return (v0 + v1)*log(abs(v0+v1)) + (v0-v1)*log(abs(v0-v1));
-}
-
-__device__ double hfin(double v0, double v1, double dv)
-{
-	double e = 0.001;
-	double t0 = g(v0+e, v1-dv)/dv;
-	double t1 = 2*g(v0+e, v1)/dv;
-	double t2 = g(v0+e, v1+dv)/dv;
-
-	return -1.0/PI * (t0 - t1 + t2);
-}
-
-__global__ void devKramersKronig(double* gpuN, double* gpuK, int numVals, double nuStart, double nuEnd, double nOffset)
-{
-	int i = blockIdx.x * blockDim.x + threadIdx.x;
-
-	if(i >= numVals) return;
-	double nuDelta = (nuEnd - nuStart)/(numVals - 1);
-
-	double nu = nuStart + i*nuDelta;
-	double n = 0.0;
-	double jNu;
-	double jK;
-	for(int j=1; j<numVals-1; j++)
-	{
-		jNu = nuStart + j*nuDelta;
-		jK = gpuK[j];
-		n += hfin(nu, jNu, nuDelta) * jK;
-	}
-	gpuN[i] = n + nOffset;
-
-
-}
-
-void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset)
-{
-	double* gpuK;
-	HANDLE_ERROR(cudaMalloc(&gpuK, sizeof(double)*nVals));
-	HANDLE_ERROR(cudaMemcpy(gpuK, cpuK, sizeof(double)*nVals, cudaMemcpyHostToDevice));
-	double* gpuN;
-	HANDLE_ERROR(cudaMalloc(&gpuN, sizeof(double)*nVals));
-
-	dim3 block(BLOCK_SIZE*BLOCK_SIZE);
-	dim3 grid(nVals/block.x + 1);
-	devKramersKronig<<<grid, block>>>(gpuN, gpuK, nVals, nuStart, nuEnd, nOffset);
-
-	HANDLE_ERROR(cudaMemcpy(cpuN, gpuN, sizeof(double)*nVals, cudaMemcpyDeviceToHost));
-
-	//free resources
-	HANDLE_ERROR(cudaFree(gpuK));
-	HANDLE_ERROR(cudaFree(gpuN));
-}
-
-__global__ void devComputeSpectrum(double* I, double2* B, double* alpha, int Nl,
-								   int nSamples, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO)
-{
-	int i = blockIdx.x * blockDim.x + threadIdx.x;
-	if(i >= nLambda)
-        return;
-
-	//compute the delta-theta value
-	double dTheta = (oThetaO - oThetaI)/nSamples;
-
-	//allocate space for the Legendre polynomials
-	double Ptheta[2];
-
-	double cosTheta, theta;
-	cuDoubleComplex Us;
-	cuDoubleComplex UsSample;
-	cuDoubleComplex U;
-	//cuComplex Ui;
-	//Ui.x = 2*PI;
-	//Ui.y = 0.0;
-	cuDoubleComplex numer;
-	numer.x = 0.0;
-	cuDoubleComplex exp_numer;
-	cuDoubleComplex iL;
-	cuDoubleComplex imag;
-	imag.x = 0.0; imag.y = 1.0;
-	double realFac;
-	cuDoubleComplex complexFac;
-	double PlTheta;
-	double Isum = 0.0;
-	//float maxVal = 0;
-	//float val;
-	for(int iTheta = 0; iTheta < nSamples; iTheta++)
-	{
-		//calculate theta
-		theta = iTheta * dTheta + oThetaI;
-		cosTheta = cos(theta);
-
-		//initialize the theta Legendre polynomial
-		Ptheta[0] = 1.0;
-		Ptheta[1] = cosTheta;
-
-		//initialize the scattered field
-		Us.x = Us.y = 0.0;
-		iL.x = 1.0;
-		iL.y = 0.0;
-		for(int l = 0; l<Nl; l++)
-		{
-			//compute the theta legendre polynomial
-			if(l == 0)
-				PlTheta = Ptheta[0];
-			else if(l == 1)
-				PlTheta = Ptheta[1];
-			else
-			{
-				PlTheta = ((2*l - 1)*cosTheta*Ptheta[1] - (l - 1)*Ptheta[0])/l;
-				Ptheta[0] = Ptheta[1];
-				Ptheta[1] = PlTheta;
-			}
-
-			//compute the real components of the scattered field
-			realFac = alpha[l] * PlTheta;
-
-			//compute the complex components of the scattered field
-			numer.x = 0.0;
-			numer.y = -(l*PI)/2.0;
-			exp_numer = cExp(numer);
-
-			complexFac = cMult(B[Nl * i + l], exp_numer);
-			complexFac = cMult(complexFac, iL);
-
-
-			//combine the real and complex components
-			UsSample = cMult(complexFac, realFac);
-			Us = cAdd(Us, UsSample);
-
-			//increment the imaginary exponent i^l
-			iL = cMult(iL, imag);
-
-
-		}
-
-		//sum the scattered and incident fields
-		if(theta >= cThetaI && theta <= cThetaO)
-			U = cAdd(Us, 2*PI);
-		else
-			U = Us;
-		Isum += (U.x*U.x + U.y*U.y) * sin(theta) * 2 * PI * dTheta;
-	}
-
-	I[i] = Isum;
-}
-
-void cudaComputeSpectrum(double* cpuI, double* cpuB, double* cpuAlpha,
-						 int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples)
-{
-	//copy everything to the GPU
-	double2* gpuB;
-	HANDLE_ERROR(cudaMalloc(&gpuB, sizeof(double2) * nLambda * Nl));
-	HANDLE_ERROR(cudaMemcpy(gpuB, cpuB, sizeof(double2) * nLambda * Nl, cudaMemcpyHostToDevice));
-
-
-	double* gpuAlpha;
-	HANDLE_ERROR(cudaMalloc(&gpuAlpha, sizeof(double) * Nl));
-	HANDLE_ERROR(cudaMemcpy(gpuAlpha, cpuAlpha, sizeof(double) * Nl, cudaMemcpyHostToDevice));
-
-	double* gpuI;
-	HANDLE_ERROR(cudaMalloc(&gpuI, sizeof(double) * nLambda));
-	HANDLE_ERROR(cudaMemset(gpuI, 0, sizeof(double) * nLambda));
-
-
-	//call the kernel to compute the spectrum
-	dim3 block(BLOCK_SIZE*BLOCK_SIZE);
-	dim3 grid(nLambda/block.x + 1);
-
-	//devComputeSpectrum
-	devComputeSpectrum<<<grid, block>>>(gpuI, (double2*)gpuB, gpuAlpha, Nl,
-										nSamples, nLambda, oThetaI, oThetaO, cThetaI, cThetaO);
-
-	HANDLE_ERROR(cudaMemcpy(cpuI, gpuI, sizeof(double) * nLambda, cudaMemcpyDeviceToHost));
-
-	//printf("Final array value: %f\n", cpuI[nLambda-1]);
-
-	HANDLE_ERROR(cudaFree(gpuB));
-	HANDLE_ERROR(cudaFree(gpuAlpha));
-	HANDLE_ERROR(cudaFree(gpuI));
-
-
-
-
+#include <iostream>
+using namespace std;
+
+__device__ double g(double v0, double v1)
+{
+    return (v0 + v1)*log(abs(v0+v1)) + (v0-v1)*log(abs(v0-v1));
+}
+
+__device__ double hfin(double v0, double v1, double dv)
+{
+    double e = 0.001;
+    double t0 = g(v0+e, v1-dv)/dv;
+    double t1 = 2*g(v0+e, v1)/dv;
+    double t2 = g(v0+e, v1+dv)/dv;
+
+    return -1.0/PI * (t0 - t1 + t2);
+}
+
+__global__ void devKramersKronig(double* gpuN, double* gpuK, int numVals, double nuStart, double nuEnd, double nOffset)
+{
+    int i = blockIdx.x * blockDim.x + threadIdx.x;
+
+    if(i >= numVals) return;
+    double nuDelta = (nuEnd - nuStart)/(numVals - 1);
+
+    double nu = nuStart + i*nuDelta;
+    double n = 0.0;
+    double jNu;
+    double jK;
+    for(int j=1; j<numVals-1; j++)
+    {
+        jNu = nuStart + j*nuDelta;
+        jK = gpuK[j];
+        n += hfin(nu, jNu, nuDelta) * jK;
+    }
+    gpuN[i] = n + nOffset;
+
+
+}
+
+void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset)
+{
+    cout<<"Computing Kramers Kronig."<<endl;
+    //This function computes n given k
+
+    double* gpuK;
+    HANDLE_ERROR(cudaMalloc(&gpuK, sizeof(double)*nVals));
+    HANDLE_ERROR(cudaMemcpy(gpuK, cpuK, sizeof(double)*nVals, cudaMemcpyHostToDevice));
+    double* gpuN;
+    HANDLE_ERROR(cudaMalloc(&gpuN, sizeof(double)*nVals));
+
+    dim3 block(BLOCK_SIZE*BLOCK_SIZE);
+    dim3 grid(nVals/block.x + 1);
+    devKramersKronig<<<grid, block>>>(gpuN, gpuK, nVals, nuStart, nuEnd, nOffset);
+
+    HANDLE_ERROR(cudaMemcpy(cpuN, gpuN, sizeof(double)*nVals, cudaMemcpyDeviceToHost));
+
+    //free resources
+    HANDLE_ERROR(cudaFree(gpuK));
+    HANDLE_ERROR(cudaFree(gpuN));
+}
+
+__global__ void devComputeSpectrum(double* I, double2* B, double* alpha, int Nl,
+                                   int nSamples, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO)
+{
+    int i = blockIdx.x * blockDim.x + threadIdx.x;
+    if(i >= nLambda)
+        return;
+
+    //compute the delta-theta value
+    double dTheta = (oThetaO - oThetaI)/nSamples;
+
+    //allocate space for the Legendre polynomials
+    double Ptheta[2];
+
+    double cosTheta, theta;
+    cuDoubleComplex Us;
+    cuDoubleComplex UsSample;
+    cuDoubleComplex U;
+    //cuComplex Ui;
+    //Ui.x = 2*PI;
+    //Ui.y = 0.0;
+    cuDoubleComplex numer;
+    numer.x = 0.0;
+    cuDoubleComplex exp_numer;
+    cuDoubleComplex iL;
+    cuDoubleComplex imag;
+    imag.x = 0.0;
+    imag.y = 1.0;
+    double realFac;
+    cuDoubleComplex complexFac;
+    double PlTheta;
+    double Isum = 0.0;
+    //float maxVal = 0;
+    //float val;
+    for(int iTheta = 0; iTheta < nSamples; iTheta++)
+    {
+        //calculate theta
+        theta = iTheta * dTheta + oThetaI;
+        cosTheta = cos(theta);
+
+        //initialize the theta Legendre polynomial
+        Ptheta[0] = 1.0;
+        Ptheta[1] = cosTheta;
+
+        //initialize the scattered field
+        Us.x = Us.y = 0.0;
+        iL.x = 1.0;
+        iL.y = 0.0;
+        for(int l = 0; l<Nl; l++)
+        {
+            //compute the theta legendre polynomial
+            if(l == 0)
+                PlTheta = Ptheta[0];
+            else if(l == 1)
+                PlTheta = Ptheta[1];
+            else
+            {
+                PlTheta = ((2*l - 1)*cosTheta*Ptheta[1] - (l - 1)*Ptheta[0])/l;
+                Ptheta[0] = Ptheta[1];
+                Ptheta[1] = PlTheta;
+            }
+
+            //compute the real components of the scattered field
+            realFac = alpha[l] * PlTheta;
+
+            //compute the complex components of the scattered field
+            numer.x = 0.0;
+            numer.y = -(l*PI)/2.0;
+            exp_numer = cExp(numer);
+
+            complexFac = cMult(B[Nl * i + l], exp_numer);
+            complexFac = cMult(complexFac, iL);
+
+
+            //combine the real and complex components
+            UsSample = cMult(complexFac, realFac);
+            Us = cAdd(Us, UsSample);
+
+            //increment the imaginary exponent i^l
+            iL = cMult(iL, imag);
+
+
+        }
+
+        //sum the scattered and incident fields
+        if(theta >= cThetaI && theta <= cThetaO)
+            U = cAdd(Us, 2*PI);
+        else
+            U = Us;
+        Isum += (U.x*U.x + U.y*U.y) * sin(theta) * 2 * PI * dTheta;
+    }
+
+    I[i] = Isum;
+}
+
+void cudaComputeSpectrum(double* cpuI, double* cpuB, double* cpuAlpha,
+                         int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples)
+{
+    //copy everything to the GPU
+    double2* gpuB;
+    HANDLE_ERROR(cudaMalloc(&gpuB, sizeof(double2) * nLambda * Nl));
+    HANDLE_ERROR(cudaMemcpy(gpuB, cpuB, sizeof(double2) * nLambda * Nl, cudaMemcpyHostToDevice));
+
+
+    double* gpuAlpha;
+    HANDLE_ERROR(cudaMalloc(&gpuAlpha, sizeof(double) * Nl));
+    HANDLE_ERROR(cudaMemcpy(gpuAlpha, cpuAlpha, sizeof(double) * Nl, cudaMemcpyHostToDevice));
+
+    double* gpuI;
+    HANDLE_ERROR(cudaMalloc(&gpuI, sizeof(double) * nLambda));
+    HANDLE_ERROR(cudaMemset(gpuI, 0, sizeof(double) * nLambda));
+
+
+    //call the kernel to compute the spectrum
+    dim3 block(BLOCK_SIZE*BLOCK_SIZE);
+    dim3 grid(nLambda/block.x + 1);
+
+    //devComputeSpectrum
+    devComputeSpectrum<<<grid, block>>>(gpuI, (double2*)gpuB, gpuAlpha, Nl,
+                                        nSamples, nLambda, oThetaI, oThetaO, cThetaI, cThetaO);
+
+    HANDLE_ERROR(cudaMemcpy(cpuI, gpuI, sizeof(double) * nLambda, cudaMemcpyDeviceToHost));
+
+    //printf("Final array value: %f\n", cpuI[nLambda-1]);
+
+    HANDLE_ERROR(cudaFree(gpuB));
+    HANDLE_ERROR(cudaFree(gpuAlpha));
+    HANDLE_ERROR(cudaFree(gpuI));
+
+
+
+
 }
-#include "cuComplex.h"
-#include "cudaHandleError.h"
-
-
-#define PI 3.14159
-#define BLOCK_SIZE 16
-
-__device__ cuDoubleComplex cMult(cuDoubleComplex a, cuDoubleComplex b)
-{
-	cuDoubleComplex result;
-	result.x = a.x * b.x - a.y * b.y;
-	result.y = a.x * b.y + a.y * b.x;
-
-	return result;
-}
-
-__device__ cuDoubleComplex cMult(cuDoubleComplex a, float b)
-{
-	cuDoubleComplex result;
-	result.x = a.x * b;
-	result.y = a.y * b;
-
-	return result;
-}
-
-__device__ cuDoubleComplex cAdd(cuDoubleComplex a, cuDoubleComplex b)
-{
-	cuDoubleComplex r;
-	r.x = a.x + b.x;
-	r.y = a.y + b.y;
-
-	return r;
-}
-
-__device__ cuDoubleComplex cAdd(cuDoubleComplex a, float b)
-{
-	cuDoubleComplex r;
-	r.x = a.x + b;
-	r.y = a.y;
-
-	return r;
-}
-
-__device__ cuDoubleComplex cExp(cuDoubleComplex a)
-{
-	cuDoubleComplex r;
-
-	r.x = exp(a.x) * cos(a.y);
-	r.y = exp(a.x) * sin(a.y);
-
-	return r;
-}
-
-__device__ double cMag(cuDoubleComplex a)
-{
-	double r = sqrt(a.x * a.x + a.y * a.y);
-	return r;
-}
-
-#include "cudaKK.h"
-
+#include "cuComplex.h"
+#include "cudaHandleError.h"
+
+
+#define PI 3.14159
+#define BLOCK_SIZE 16
+
+__device__ cuDoubleComplex cMult(cuDoubleComplex a, cuDoubleComplex b)
+{
+    cuDoubleComplex result;
+    result.x = a.x * b.x - a.y * b.y;
+    result.y = a.x * b.y + a.y * b.x;
+
+    return result;
+}
+
+__device__ cuDoubleComplex cMult(cuDoubleComplex a, float b)
+{
+    cuDoubleComplex result;
+    result.x = a.x * b;
+    result.y = a.y * b;
+
+    return result;
+}
+
+__device__ cuDoubleComplex cAdd(cuDoubleComplex a, cuDoubleComplex b)
+{
+    cuDoubleComplex r;
+    r.x = a.x + b.x;
+    r.y = a.y + b.y;
+
+    return r;
+}
+
+__device__ cuDoubleComplex cAdd(cuDoubleComplex a, float b)
+{
+    cuDoubleComplex r;
+    r.x = a.x + b;
+    r.y = a.y;
+
+    return r;
+}
+
+__device__ cuDoubleComplex cExp(cuDoubleComplex a)
+{
+    cuDoubleComplex r;
+
+    r.x = exp(a.x) * cos(a.y);
+    r.y = exp(a.x) * sin(a.y);
+
+    return r;
+}
+
+__device__ double cMag(cuDoubleComplex a)
+{
+    double r = sqrt(a.x * a.x + a.y * a.y);
+    return r;
+}
+
+#include "cudaKK.h"
+
+nu	n	k
+800	1.441201025	0.002370971
+802	1.442449524	0.002279499
+804	1.443622415	0.002218164
+806	1.444731575	0.00217471
+808	1.445769313	0.002154818
+810	1.446735153	0.002133884
+812	1.447631537	0.002093632
+814	1.448499976	0.002020828
+816	1.449371594	0.001935851
+818	1.450245111	0.001882509
+820	1.451098381	0.001845384
+822	1.451931801	0.001835367
+824	1.452743077	0.001859742
+826	1.453538627	0.001906472
+828	1.454316144	0.001993264
+830	1.455057831	0.002134999
+832	1.455752574	0.002332258
+834	1.456373935	0.00257594
+836	1.45689904	0.00287502
+838	1.457307689	0.003187541
+840	1.457541056	0.00349171
+842	1.457622779	0.003661082
+844	1.45763705	0.003626834
+846	1.457709742	0.003400597
+848	1.457929984	0.003056081
+850	1.458311946	0.002701293
+852	1.458792141	0.002396757
+854	1.459332546	0.002178644
+856	1.459889834	0.002030216
+858	1.460439885	0.001936861
+860	1.460982928	0.001877498
+862	1.461517236	0.00185772
+864	1.462038725	0.001889109
+866	1.462531922	0.001950935
+868	1.462978568	0.00204692
+870	1.463376438	0.002155221
+872	1.463691463	0.002260164
+874	1.463946436	0.002246045
+876	1.46431344	0.002102302
+878	1.464835949	0.001997437
+880	1.465438552	0.001992183
+882	1.46608463	0.002084809
+884	1.466770232	0.002282701
+886	1.467508982	0.002620306
+888	1.468317634	0.00319353
+890	1.469128024	0.004219724
+892	1.46954514	0.006023859
+894	1.468393318	0.00840405
+896	1.465223625	0.009006755
+898	1.463241024	0.006966132
+900	1.463248052	0.004995548
+902	1.463894773	0.003838499
+904	1.464602858	0.003205237
+906	1.465241891	0.00285555
+908	1.465786159	0.002664765
+910	1.466248706	0.002546277
+912	1.466651178	0.002453415
+914	1.467032669	0.002364593
+916	1.467407655	0.002292823
+918	1.46779669	0.00223036
+920	1.468201898	0.002212279
+922	1.468611417	0.002242387
+924	1.469017595	0.002350077
+926	1.469359926	0.002567263
+928	1.469513165	0.00284644
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-3900	1.47583333559154
-3902	1.47583798052018
-3904	1.47584349792097
-3906	1.47584878503057
-3908	1.47585104104660
-3910	1.47584786442429
-3912	1.47584503864650
-3914	1.47584772763597
-3916	1.47585513011730
-3918	1.47586161194681
-3920	1.47586680114244
-3922	1.47586801742881
-3924	1.47586285228063
-3926	1.47585768990955
-3928	1.47585725672200
-3930	1.47586502926929
-3932	1.47587638834149
-3934	1.47588758559686
-3936	1.47589600406114
-3938	1.47590331354213
-3940	1.47591060804636
-3942	1.47591789591720
-3944	1.47592457142526
-3946	1.47593081059303
-3948	1.47593398581283
-3950	1.47593295565452
-3952	1.47592878275285
-3954	1.47592684349640
-3956	1.47592986168501
-3958	1.47593628896516
-3960	1.47594351825970
-3962	1.47595186222678
-3964	1.47595911320580
-3966	1.47596854991323
-3968	1.47597712871599
-3970	1.47598746992252
-3972	1.47600004422535
-3974	1.47601337421929
-3976	1.47602692154134
-3978	1.47603405627977
-3980	1.47602817354059
-3982	1.47601874488156
-3984	1.47602563707167
-3986	1.47604367443527
-3988	1.47606327560645
-3990	1.47608304122308
-3992	1.47610269526207
-3994	1.47612262206064
-3996	1.47614078459134
-3998	1.47615752083133
-4000	1.47617133599432
 \ No newline at end of file
-#ifndef GLOBALS_H
-#define GLOBALS_H
-
-#include <vector>
-#include <string>
-#include <iostream>
-#include "PerformanceData.h"
-#include <complex>
-using namespace std;
-
-typedef float rtsFloat;
-
-struct SpecPair{
-	double nu;
-	double A;
-};
-
-struct Material{
-	vector<double> nu;
-	vector<complex<double> > eta;
-	string name;
-};
-
-enum SpecType {AbsorbanceSpecType, IntensitySpecType};
-enum OpticsType {TransmissionOpticsType, ReflectionOpticsType};
-
-extern PerformanceData PD;
-
-
-extern vector<vector<SpecPair> > RefSpectrum;
-extern int currentSpec;
-extern vector<SpecPair> SimSpectrum;
-
-//IO Functions
-vector<SpecPair> LoadSpectrum(string filename);
-vector<SpecPair> SetReferenceSpectrum(char* text);
-void SaveState();
-void LoadState();
-void SetDefaults();
-void SaveSimulation(string fileName);
-void SaveK(string fileName);
-void SaveN(string fileName);
-void LoadMaterial(string fileNameK, string fileNameN, string materialName);
-void LoadMaterial(string fileNameK, string materialName);
-
-//Display Functions
-void FitDisplay();
-
-//Update Functions
-void UpdateDisplay();
-void SimulateSpectrum();
-void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset);
-void cudaComputeSpectrum(double* cpuI, double* cpuB, double* alpha,
-						 int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples);
-
-//Window Parameters
-extern double nuMin;
-extern double nuMax;
-extern double aMin;
-extern double aMax;
-extern double dNu;
-extern bool dispRefSpec;
-extern bool dispSimSpec;
-extern bool dispSimK;
-extern bool dispMatK;
-extern bool dispSimN;
-extern bool dispMatN;
-extern SpecType dispSimType;
-extern bool dispNormalize;
-extern double dispNormFactor;
-
-
-extern double dispScaleK;
-extern double dispScaleN;
-
-//material parameters
-extern double radius;
-extern double baseIR;
-extern double cA;
-extern vector<SpecPair> EtaK;
-extern vector<SpecPair> EtaN;
-extern bool applyMaterial;
-extern vector<Material> MaterialList;
-extern int currentMaterial;
-void ChangeAbsorbance();
-void SetMaterial();
-
-//source parameters
-extern vector<SpecPair> SourceSpectrum;
-extern vector<SpecPair> SourceResampled;
-void ResampleSource();	//resample a source profile to match the sample points of the current material
-extern bool useSourceSpectrum;
-
-//optical parameters
-extern double cNAi;
-extern double cNAo;
-extern double oNAi;
-extern double oNAo;
-extern OpticsType opticsMode;
-extern bool pointDetector;
-extern int objectiveSamples;
-
-//fitting parameters
-extern double minMSE;
-extern int maxFitIter;
-void EstimateMaterial();
-extern double scaleI0;
-extern double refSlope;
-
-
-//distortion maps
-double ComputeDistortion();
-void DistortionMap(float* distortionMap, int nSteps);
-
-
-
-
-#endif
+#ifndef GLOBALS_H
+#define GLOBALS_H
+
+#include <vector>
+#include <string>
+#include <iostream>
+#include "PerformanceData.h"
+#include <complex>
+using namespace std;
+
+typedef float rtsFloat;
+
+struct SpecPair {
+    double nu;
+    double A;
+};
+
+struct Material {
+    vector<double> nu;
+    vector<complex<double> > eta;
+    bool validN;
+    bool validK;
+    string name;
+};
+
+enum SpecType {AbsorbanceSpecType, IntensitySpecType};
+enum OpticsType {TransmissionOpticsType, ReflectionOpticsType};
+
+extern PerformanceData PD;
+
+
+extern vector<vector<SpecPair> > RefSpectrum;
+extern int currentSpec;
+extern vector<SpecPair> SimSpectrum;
+
+//IO Functions
+vector<SpecPair> LoadSpectrum(string filename);
+vector<SpecPair> SetReferenceSpectrum(char* text);
+void SaveState();
+void LoadState();
+void SetDefaults();
+void SaveSimulation(string fileName);
+//void SaveK(string fileName);
+void SaveMaterial(string fileName);
+//void LoadMaterial(string fileNameK, string fileNameN, string materialName);
+void LoadMaterial(string fileName, string materialName);
+
+//Display Functions
+void FitDisplay();
+
+//Update Functions
+void UpdateDisplay();
+void SimulateSpectrum();
+void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset);
+void cudaComputeSpectrum(double* cpuI, double* cpuB, double* alpha,
+                         int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples);
+
+//Window Parameters
+extern double nuMin;	//wavenumbers
+extern double nuMax;
+extern double aMin;		//absorbance
+extern double aMax;
+extern double dNu;
+extern double nMag;		//largest magnitude for n
+extern double kMax;			//highest extinction coefficient
+extern bool dispRefSpec;
+extern bool dispSimSpec;
+extern bool dispSimK;
+extern bool dispMatK;
+extern bool dispSimN;
+extern bool dispMatN;
+extern SpecType dispSimType;
+extern bool dispNormalize;
+extern double dispNormFactor;
+
+
+extern double dispScaleK;
+extern double dispScaleN;
+
+//material parameters
+extern double radius;
+extern double baseIR;
+extern double cA;
+extern vector<SpecPair> EtaK;
+extern vector<SpecPair> EtaN;
+extern bool applyMaterial;
+extern vector<Material> MaterialList;
+extern int currentMaterial;
+void ChangeAbsorbance();
+void SetMaterial();
+
+//source parameters
+extern vector<SpecPair> SourceSpectrum;
+extern vector<SpecPair> SourceResampled;
+void ResampleSource();	//resample a source profile to match the sample points of the current material
+extern bool useSourceSpectrum;
+
+//optical parameters
+extern double cNAi;
+extern double cNAo;
+extern double oNAi;
+extern double oNAo;
+extern OpticsType opticsMode;
+extern bool pointDetector;
+extern int objectiveSamples;
+
+//fitting parameters
+extern double minMSE;
+extern int maxFitIter;
+void EstimateMaterial();
+extern double scaleI0;
+extern double refSlope;
+
+
+//distortion maps
+double ComputeDistortion();
+void DistortionMap(float* distortionMap, int nSteps);
+
+
+
+
+#endif
-#include "interactivemie.h"
-#include <stdlib.h>
+#include "interactivemie.h"
+#include <stdlib.h>
 qtDistortionDialog* distortionDialog;
-
-InteractiveMie::InteractiveMie(QWidget *parent, Qt::WFlags flags)
-	: QMainWindow(parent, flags)
-{
-	ui.setupUi(this);
-}
-
-InteractiveMie::~InteractiveMie()
-{
-	updating = false;
+
+InteractiveMie::InteractiveMie(QWidget *parent, Qt::WFlags flags)
+    : QMainWindow(parent, flags)
+{
+    ui.setupUi(this);
+}
+
+InteractiveMie::~InteractiveMie()
+{
+    updating = false;
 }
 void InteractiveMie::closeEvent(QCloseEvent *event)
 {
-	cout<<"Exiting"<<endl;
+    cout<<"Exiting"<<endl;
     exit(0);
-}
+}
-#ifndef INTERACTIVEMIE_H
-#define INTERACTIVEMIE_H
-
-#include <QtGui/QMainWindow>
-#include <QDragEnterEvent>
-#include <qfiledialog.h>
-#include <qinputdialog.h>
-#include "ui_interactivemie.h"
-#include "qtDistortionDialog.h"
-#include "globals.h"
-
-extern qtDistortionDialog* distortionDialog;
-
-class InteractiveMie : public QMainWindow
-{
-	Q_OBJECT
-
-public:
-	InteractiveMie(QWidget *parent = 0, Qt::WFlags flags = 0);
-	~InteractiveMie();
-	void closeEvent(QCloseEvent *event);
-	bool updating;
-
-	void refreshUI()
-	{
-		updating = true;
-
-		ui.spinNuMin->setValue(nuMin);
-		ui.spinNuMax->setValue(nuMax);
-		ui.spinAMin->setValue(aMin);
-		ui.spinAMax->setValue(aMax);
-		ui.spinRadius->setValue(radius);
-		ui.spinBaseIR->setValue(baseIR);
-		ui.spinScaleK->setValue(cA);
-		ui.spinObjNAi->setValue(oNAi);
-		ui.spinObjNAo->setValue(oNAo);
-		ui.spinCondNAi->setValue(cNAi);
-		ui.spinCondNAo->setValue(cNAo);
-		ui.spinError->setValue(minMSE);
-		ui.spinMaxIter->setValue(maxFitIter);
-		ui.spinI0Scale->setValue(scaleI0);
-
-		//display spectra values
-		ui.chkDisplaySimSpec->setChecked(dispSimSpec);
-		ui.chkDisplayRefSpec->setChecked(dispRefSpec);
-		ui.chkDisplaySimK->setChecked(dispSimK);
-		ui.chkDisplayMatK->setChecked(dispMatK);
-		ui.chkDisplaySimN->setChecked(dispSimN);
-		ui.chkDisplayMatN->setChecked(dispMatN);
-		ui.spinDispScaleK->setValue(dispScaleK);
-		ui.spinDispScaleN->setValue(dispScaleN);
-
-		//material selection combo box
-		ui.cmbMaterial->clear();
-		for(unsigned int i=0; i<MaterialList.size(); i++)
-			ui.cmbMaterial->addItem(MaterialList[i].name.c_str(), i);
-		ui.cmbMaterial->setCurrentIndex(currentMaterial);
-
-		updating = false;
-	}
-
-	void dragEnterEvent(QDragEnterEvent *event)
-	{
-		cout<<"This is a test."<<endl;
-		QStringList s = event->mimeData()->formats();
-		if (event->mimeData()->hasFormat("application/x-qt-windows-mime;value=\"FileName\"") ||
-			event->mimeData()->hasFormat("text/plain"))
-		{
-			event->acceptProposedAction();
-
-		}
-	}
-
-	void dropEvent(QDropEvent *event)
-	{
-		//cout<<"Challenge Accepted."<<endl;
-		RefSpectrum.clear();
-		RefSpectrum.push_back(SetReferenceSpectrum(event->mimeData()->text().toAscii().data()));
-		UpdateDisplay();
-	}
-
-private:
-	Ui::InteractiveMieClass ui;
-
-public slots:
-	//display parameters
-	void on_spinNuMin_valueChanged(int i){
-		nuMin = (float)i;
-		UpdateDisplay();
-	}
-	void on_spinNuMax_valueChanged(int i){
-		nuMax = (float)i;
-		UpdateDisplay();
-	}
-	void on_spinAMin_valueChanged(double d){
-		aMin = d;
-		UpdateDisplay();
-	}
-	void on_spinAMax_valueChanged(double d){
-		aMax = d;
-		UpdateDisplay();
-	}
-	void on_chkDisplaySimSpec_clicked(bool b){
-		dispSimSpec = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplayRefSpec_clicked(bool b){
-		dispRefSpec = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplaySimK_clicked(bool b){
-		dispSimK = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplayMatK_clicked(bool b){
-		dispMatK = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplaySimN_clicked(bool b){
-		dispSimN = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplayMatN_clicked(bool b){
-		dispMatN = b;
-		UpdateDisplay();
-	}
-	void on_spinDispScaleK_valueChanged(double d){
-		dispScaleK = d;
-		UpdateDisplay();
-	}
-	void on_spinDispScaleN_valueChanged(double d){
-		dispScaleN = d;
-		UpdateDisplay();
-	}
-	void on_radDisplayAbsorbance_clicked(bool b){
-		dispSimType = AbsorbanceSpecType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_radDisplayIntensity_toggled(bool b){
-		dispSimType = IntensitySpecType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_chkNormalize_clicked(bool b){
-		dispNormalize = b;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinNormFactor_valueChanged(double d){
-		dispNormFactor = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-
-	//material parameters
-	void on_spinRadius_valueChanged(double d){
-		radius = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinBaseIR_valueChanged(double d){
-		baseIR = d;
-		ChangeAbsorbance();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinScaleK_valueChanged(double d){
-		cA = d;
-		ChangeAbsorbance();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_chkApplyMaterial_clicked(bool b){
-		applyMaterial = b;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_cmbMaterial_currentIndexChanged(int i){
-		if(updating) return;
-
-		currentMaterial = i;
-		SetMaterial();
-		SimulateSpectrum();
-		UpdateDisplay();
-		refreshUI();
-	}
-
-	//optical parameters
-	void on_spinCondNAi_valueChanged(double d){
-		cNAi = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinCondNAo_valueChanged(double d){
-		cNAo = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinObjNAi_valueChanged(double d){
-		oNAi = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinObjNAo_valueChanged(double d){
-		oNAo = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_radTransmissionOptics_clicked(bool d){
-		ui.spinCondNAi->setEnabled(true);
-		ui.spinCondNAo->setEnabled(true);
-		opticsMode = TransmissionOpticsType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_radReflectionOptics_clicked(bool d){
-		ui.spinCondNAi->setEnabled(false);
-		ui.spinCondNAo->setEnabled(false);
-		ui.radDisplayAbsorbance->setEnabled(false);
-		ui.radDisplayIntensity->setChecked(true);
-		opticsMode = ReflectionOpticsType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_chkPointDetector_clicked(bool b){
-		if(b)
-		{
-			pointDetector = true;
-			ui.spinObjectiveSamples->setEnabled(false);
-		}
-		else
-		{
-			pointDetector = false;
-			ui.spinObjectiveSamples->setEnabled(true);
-		}
-
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-
-	void on_spinObjectiveSamples_valueChanged(int i){
-		objectiveSamples = i;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-
-	//Fitting
-	void on_spinMaxIter_valueChanged(int i){
-		maxFitIter = i;
-	}
-	void on_spinError_valueChanged(double d){
-		minMSE = d;
-	}
-	void on_spinI0Scale_valueChanged(double d){
-		scaleI0 = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinRefSlope_valueChanged(double d){
-		refSlope = d;
-		UpdateDisplay();
-	}
-
-	//display settings
-
-	//Buttons
-	void on_btnFit_clicked(){
-		FitDisplay();
-		refreshUI();
-	}
-	void on_btnSave_clicked(){
-		SaveState();
-	}
-	void on_btnReset_clicked(){
-		SetDefaults();
-		SimulateSpectrum();
-		UpdateDisplay();
-		refreshUI();
-	}
-	void on_btnResetK_clicked(){
-		ChangeAbsorbance();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_btnEstimateK_clicked(){
-		EstimateMaterial();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_btnDistortion_clicked(){
-		//ComputeDistortion();
-		//DistortionMap();
-		cout<<"Distortion"<<endl;
-		distortionDialog->show();
-	}
-	void on_btnTimings_clicked(){
-		PD.PrintResults(cout);
-	}
-
-	//menu items
-	void on_mnuLoadReference_triggered(){
-		QString fileName = QFileDialog::getOpenFileName(this, tr("Open Reference Spectrum"));
-
-		if(fileName != QString::null){
-			RefSpectrum.clear();
-			RefSpectrum.push_back(LoadSpectrum(fileName.toAscii().data()));
-		}
-		UpdateDisplay();
-	}
-
-	void on_mnuLoadMaterial_triggered(){
-
-		//first load the imaginary part
-		QString kFileName = QFileDialog::getOpenFileName(this, tr("Open Imaginary (k) Spectrum"));
-
-		//exit if no file was selected
-		if(kFileName == QString::null)
-			return;
-
-		QString nFileName = QFileDialog::getOpenFileName(this, tr("Open Imaginary (n) Spectrum"));
-
-		//request the material name
-		QString matName = QInputDialog::getText(this, tr("Material Name"), tr("Enter material name:"));
-
-		//if a real part was given, load both
-		if(nFileName != QString::null)
-			LoadMaterial(kFileName.toAscii().data(), nFileName.toAscii().data(), matName.toAscii().data());
-		else
-			LoadMaterial(kFileName.toAscii().data(), matName.toAscii().data());
-
-		//add the new material to the combo box
-		refreshUI();
-	}
-	void on_mnuLoadSource_triggered(){
-		cout<<"Load source."<<endl;
-	}
-	void on_chkSourceSpectrum_clicked(bool b){
-		
-		useSourceSpectrum = b;
-		SimulateSpectrum();
-		UpdateDisplay();
-		
-	}
-
-	void on_mnuSaveSim_triggered(){
-		//first load the imaginary part
-		QString fileName = QFileDialog::getSaveFileName(this, tr("Save Simulated Spectrum"));
-		SaveSimulation(fileName.toAscii().data());
-	}
-
-	void on_mnuSaveK_triggered(){
-		//first load the imaginary part
-		QString fileName = QFileDialog::getSaveFileName(this, tr("Save Imaginary Index of Refraction (k)"));
-		SaveK(fileName.toAscii().data());
-	}
-
-	void on_mnuSaveN_triggered(){
-		//first load the imaginary part
-		QString fileName = QFileDialog::getSaveFileName(this, tr("Save Real Index of Refraction (n)"));
-		SaveN(fileName.toAscii().data());
-	}
-
-
-
-};
-
-#endif // INTERACTIVEMIE_H
+#ifndef INTERACTIVEMIE_H
+#define INTERACTIVEMIE_H
+
+#include <QtGui/QMainWindow>
+#include <QDragEnterEvent>
+#include <qfiledialog.h>
+#include <qinputdialog.h>
+#include "ui_interactivemie.h"
+#include "qtDistortionDialog.h"
+#include "globals.h"
+
+extern qtDistortionDialog* distortionDialog;
+
+class InteractiveMie : public QMainWindow
+{
+Q_OBJECT
+
+public:
+InteractiveMie(QWidget *parent = 0, Qt::WFlags flags = 0);
+~InteractiveMie();
+void closeEvent(QCloseEvent *event);
+bool updating;
+
+void refreshUI()
+{
+	updating = true;
+
+	ui.spinNuMin->setValue(nuMin);
+	ui.spinNuMax->setValue(nuMax);
+	ui.spinAMin->setValue(aMin);
+	ui.spinAMax->setValue(aMax);
+	ui.spinRadius->setValue(radius);
+	ui.spinBaseIR->setValue(baseIR);
+	ui.spinScaleK->setValue(cA);
+	ui.spinObjNAi->setValue(oNAi);
+	ui.spinObjNAo->setValue(oNAo);
+	ui.spinCondNAi->setValue(cNAi);
+	ui.spinCondNAo->setValue(cNAo);
+	ui.spinError->setValue(minMSE);
+	ui.spinMaxIter->setValue(maxFitIter);
+	ui.spinI0Scale->setValue(scaleI0);
+
+	//display spectra values
+	ui.chkDisplaySimSpec->setChecked(dispSimSpec);
+	ui.chkDisplayRefSpec->setChecked(dispRefSpec);
+	ui.chkDisplaySimK->setChecked(dispSimK);
+	ui.chkDisplayMatK->setChecked(dispMatK);
+	ui.chkDisplaySimN->setChecked(dispSimN);
+	ui.chkDisplayMatN->setChecked(dispMatN);
+	ui.spinDispScaleK->setValue(kMax);
+	ui.spinDispScaleN->setValue(nMag);
+
+	//material selection combo box
+	ui.cmbMaterial->clear();
+	for(unsigned int i=0; i<MaterialList.size(); i++)
+		ui.cmbMaterial->addItem(MaterialList[i].name.c_str(), i);
+	ui.cmbMaterial->setCurrentIndex(currentMaterial);
+
+	updating = false;
+}
+
+void dragEnterEvent(QDragEnterEvent *event)
+{
+	cout<<"This is a test."<<endl;
+	QStringList s = event->mimeData()->formats();
+	if (event->mimeData()->hasFormat("application/x-qt-windows-mime;value=\"FileName\"") ||
+			event->mimeData()->hasFormat("text/plain"))
+	{
+		event->acceptProposedAction();
+
+	}
+}
+
+void dropEvent(QDropEvent *event)
+{
+	//cout<<"Challenge Accepted."<<endl;
+	RefSpectrum.clear();
+	RefSpectrum.push_back(SetReferenceSpectrum(event->mimeData()->text().toAscii().data()));
+	UpdateDisplay();
+}
+
+private:
+Ui::InteractiveMieClass ui;
+
+public slots:
+//display parameters
+void on_spinNuMin_valueChanged(int i) {
+	if(updating) return;
+	nuMin = (float)i;
+	UpdateDisplay();
+}
+void on_spinNuMax_valueChanged(int i) {
+	if(updating) return;
+	nuMax = (float)i;
+	UpdateDisplay();
+}
+void on_spinAMin_valueChanged(double d) {
+	if(updating) return;
+	aMin = d;
+	UpdateDisplay();
+}
+void on_spinAMax_valueChanged(double d) {
+	if(updating) return;
+	aMax = d;
+	UpdateDisplay();
+}
+void on_chkDisplaySimSpec_clicked(bool b) {
+	if(updating) return;
+	dispSimSpec = b;
+	UpdateDisplay();
+}
+void on_chkDisplayRefSpec_clicked(bool b) {
+	if(updating) return;
+	dispRefSpec = b;
+	UpdateDisplay();
+}
+void on_chkDisplaySimK_clicked(bool b) {
+	if(updating) return;
+	dispSimK = b;
+	UpdateDisplay();
+}
+void on_chkDisplayMatK_clicked(bool b) {
+	if(updating) return;
+	dispMatK = b;
+	UpdateDisplay();
+}
+void on_chkDisplaySimN_clicked(bool b) {
+	if(updating) return;
+	dispSimN = b;
+	UpdateDisplay();
+}
+void on_chkDisplayMatN_clicked(bool b) {
+	if(updating) return;
+	dispMatN = b;
+	UpdateDisplay();
+}
+void on_spinDispScaleK_valueChanged(double d) {
+	if(updating) return;
+	kMax = d;
+	UpdateDisplay();
+}
+void on_spinDispScaleN_valueChanged(double d) {
+	if(updating) return;
+	nMag = d;
+	UpdateDisplay();
+}
+void on_radDisplayAbsorbance_clicked(bool b) {
+	if(updating) return;
+	dispSimType = AbsorbanceSpecType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_radDisplayIntensity_toggled(bool b) {
+	if(updating) return;
+	dispSimType = IntensitySpecType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkNormalize_clicked(bool b) {
+	if(updating) return;
+	dispNormalize = b;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinNormFactor_valueChanged(double d) {
+	if(updating) return;
+	dispNormFactor = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+
+//material parameters
+void on_spinRadius_valueChanged(double d) {
+	if(updating) return;
+	radius = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkAdjustIR_clicked(bool b) {
+	if(updating) return;
+	//allow the user to change the mean n and k values
+	ui.spinBaseIR->setEnabled(b);
+	ui.spinScaleK->setEnabled(b);
+	
+}
+void on_spinBaseIR_valueChanged(double d) {
+	if(updating) return;
+	baseIR = d;
+	ChangeAbsorbance();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinScaleK_valueChanged(double d) {
+	if(updating) return;
+	cA = d;
+	ChangeAbsorbance();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkApplyMaterial_clicked(bool b) {
+	if(updating) return;
+	applyMaterial = b;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_cmbMaterial_currentIndexChanged(int i) {
+	if(updating) return;
+
+	currentMaterial = i;
+	SetMaterial();
+	SimulateSpectrum();
+	UpdateDisplay();
+	refreshUI();
+}
+
+//optical parameters
+void on_spinCondNAi_valueChanged(double d) {
+	cNAi = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinCondNAo_valueChanged(double d) {
+	cNAo = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinObjNAi_valueChanged(double d) {
+	oNAi = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinObjNAo_valueChanged(double d) {
+	oNAo = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_radTransmissionOptics_clicked(bool d) {
+	ui.spinCondNAi->setEnabled(true);
+	ui.spinCondNAo->setEnabled(true);
+	opticsMode = TransmissionOpticsType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_radReflectionOptics_clicked(bool d) {
+	ui.spinCondNAi->setEnabled(false);
+	ui.spinCondNAo->setEnabled(false);
+	ui.radDisplayAbsorbance->setEnabled(false);
+	ui.radDisplayIntensity->setChecked(true);
+	opticsMode = ReflectionOpticsType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkPointDetector_clicked(bool b) {
+	if(b)
+	{
+		pointDetector = true;
+		ui.spinObjectiveSamples->setEnabled(false);
+	}
+	else
+	{
+		pointDetector = false;
+		ui.spinObjectiveSamples->setEnabled(true);
+	}
+
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+
+void on_spinObjectiveSamples_valueChanged(int i) {
+	objectiveSamples = i;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+
+//Fitting
+void on_spinMaxIter_valueChanged(int i) {
+	maxFitIter = i;
+}
+void on_spinError_valueChanged(double d) {
+	minMSE = d;
+}
+void on_spinI0Scale_valueChanged(double d) {
+	scaleI0 = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinRefSlope_valueChanged(double d) {
+	refSlope = d;
+	UpdateDisplay();
+}
+
+//display settings
+
+//Buttons
+void on_btnFit_clicked() {
+	FitDisplay();
+	refreshUI();
+}
+void on_btnSave_clicked() {
+	SaveState();
+}
+void on_btnReset_clicked() {
+	SetDefaults();
+	SimulateSpectrum();
+	UpdateDisplay();
+	refreshUI();
+}
+void on_btnResetK_clicked() {
+	ChangeAbsorbance();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_btnEstimateK_clicked() {
+	EstimateMaterial();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_btnDistortion_clicked() {
+	//ComputeDistortion();
+	//DistortionMap();
+	cout<<"Distortion"<<endl;
+	distortionDialog->show();
+}
+void on_btnTimings_clicked() {
+	PD.PrintResults(cout);
+}
+
+//menu items
+void on_mnuLoadReference_triggered() {
+	QString fileName = QFileDialog::getOpenFileName(this, tr("Open Reference Spectrum"));
+
+	if(fileName != QString::null) {
+		RefSpectrum.clear();
+		RefSpectrum.push_back(LoadSpectrum(fileName.toAscii().data()));
+	}
+	UpdateDisplay();
+}
+
+void on_mnuLoadMaterial_triggered() {
+
+	//first load the imaginary part
+	QString fileName = QFileDialog::getOpenFileName(this, tr("Open Material Spectrum"));
+
+	//exit if no file was selected
+	/*if(kFileName == QString::null)
+		return;
+
+	QString nFileName = QFileDialog::getOpenFileName(this, tr("Open Imaginary (n) Spectrum"));*/
+
+	//request the material name
+	QString matName = QInputDialog::getText(this, tr("Material Name"), tr("Enter material name:"));
+
+	//if a real part was given, load both
+	/*if(nFileName != QString::null)
+		LoadMaterial(kFileName.toAscii().data(), nFileName.toAscii().data(), matName.toAscii().data());
+	else
+		LoadMaterial(kFileName.toAscii().data(), matName.toAscii().data());*/
+	LoadMaterial(fileName.toAscii().data(), matName.toAscii().data());
+
+	//add the new material to the combo box
+	refreshUI();
+}
+void on_mnuLoadSource_triggered() {
+	cout<<"Load source."<<endl;
+}
+void on_chkSourceSpectrum_clicked(bool b) {
+
+	useSourceSpectrum = b;
+	SimulateSpectrum();
+	UpdateDisplay();
+
+}
+
+void on_mnuSaveSim_triggered() {
+	//first load the imaginary part
+	QString fileName = QFileDialog::getSaveFileName(this, tr("Save Simulated Spectrum"));
+	SaveSimulation(fileName.toAscii().data());
+}
+
+/*void on_mnuSaveK_triggered() {
+	//first load the imaginary part
+	QString fileName = QFileDialog::getSaveFileName(this, tr("Save Imaginary Index of Refraction (k)"));
+	SaveK(fileName.toAscii().data());
+}*/
+
+void on_mnuSaveMaterial_triggered() {
+	//first load the imaginary part
+	QString fileName = QFileDialog::getSaveFileName(this, tr("Save Real Index of Refraction (n)"));
+	SaveMaterial(fileName.toAscii().data());
+}
+
+
+
+};
+
+#endif // INTERACTIVEMIE_H
@@ -23,13 +23,16 @@
       <x>20</x>
       <y>170</y>
       <width>151</width>
-      <height>161</height>
+      <height>191</height>
      </rect>
     </property>
     <property name="title">
      <string>Material</string>
     </property>
     <widget class="QDoubleSpinBox" name="spinScaleK">
+     <property name="enabled">
+      <bool>false</bool>
+     </property>
      <property name="geometry">
       <rect>
        <x>80</x>
@@ -39,13 +42,16 @@
       </rect>
      </property>
      <property name="singleStep">
-      <double>0.100000000000000</double>
+      <double>0.010000000000000</double>
      </property>
      <property name="value">
       <double>1.000000000000000</double>
      </property>
     </widget>
     <widget class="QDoubleSpinBox" name="spinBaseIR">
+     <property name="enabled">
+      <bool>false</bool>
+     </property>
      <property name="geometry">
       <rect>
        <x>80</x>
@@ -67,14 +73,17 @@
     <widget class="QLabel" name="label_8">
      <property name="geometry">
       <rect>
-       <x>30</x>
+       <x>20</x>
        <y>50</y>
        <width>46</width>
-       <height>13</height>
+       <height>21</height>
       </rect>
      </property>
      <property name="text">
-      <string>base IR</string>
+      <string>mean n</string>
+     </property>
+     <property name="alignment">
+      <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
      </property>
     </widget>
     <widget class="QDoubleSpinBox" name="spinRadius">
@@ -99,34 +108,40 @@
     <widget class="QLabel" name="label_4">
      <property name="geometry">
       <rect>
-       <x>30</x>
+       <x>20</x>
        <y>20</y>
        <width>46</width>
-       <height>13</height>
+       <height>21</height>
       </rect>
      </property>
      <property name="text">
       <string>radius</string>
      </property>
+     <property name="alignment">
+      <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
+     </property>
     </widget>
     <widget class="QLabel" name="label_9">
      <property name="geometry">
       <rect>
-       <x>30</x>
+       <x>20</x>
        <y>80</y>
        <width>46</width>
-       <height>13</height>
+       <height>21</height>
       </rect>
      </property>
      <property name="text">
-      <string>scale K</string>
+      <string>scale k</string>
+     </property>
+     <property name="alignment">
+      <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
      </property>
     </widget>
     <widget class="QCheckBox" name="chkApplyMaterial">
      <property name="geometry">
       <rect>
        <x>20</x>
-       <y>110</y>
+       <y>130</y>
        <width>121</width>
        <height>17</height>
       </rect>
@@ -142,12 +157,28 @@
      <property name="geometry">
       <rect>
        <x>20</x>
-       <y>140</y>
+       <y>160</y>
        <width>111</width>
        <height>22</height>
       </rect>
      </property>
     </widget>
+    <widget class="QCheckBox" name="chkAdjustIR">
+     <property name="geometry">
+      <rect>
+       <x>20</x>
+       <y>110</y>
+       <width>101</width>
+       <height>17</height>
+      </rect>
+     </property>
+     <property name="text">
+      <string>Adjust IR</string>
+     </property>
+     <property name="checked">
+      <bool>false</bool>
+     </property>
+    </widget>
    </widget>
    <widget class="QGroupBox" name="groupBox_2">
     <property name="geometry">
@@ -644,7 +675,7 @@
       </rect>
      </property>
      <property name="singleStep">
-      <double>0.100000000000000</double>
+      <double>0.010000000000000</double>
      </property>
     </widget>
     <widget class="QDoubleSpinBox" name="spinDispScaleN">
@@ -657,7 +688,7 @@
       </rect>
      </property>
      <property name="singleStep">
-      <double>0.100000000000000</double>
+      <double>0.010000000000000</double>
      </property>
     </widget>
     <widget class="QCheckBox" name="chkNormalize">
@@ -791,7 +822,7 @@
     <property name="geometry">
      <rect>
       <x>20</x>
-      <y>340</y>
+      <y>370</y>
       <width>201</width>
       <height>111</height>
      </rect>
@@ -860,7 +891,7 @@
       </rect>
      </property>
      <property name="text">
-      <string>Estimate K</string>
+      <string>Estimate k</string>
      </property>
     </widget>
     <widget class="QPushButton" name="btnResetK">
@@ -873,7 +904,7 @@
       </rect>
      </property>
      <property name="text">
-      <string>Reset K</string>
+      <string>Reset k</string>
      </property>
     </widget>
     <widget class="QLabel" name="label_5">
@@ -913,8 +944,7 @@
      <string>Save</string>
     </property>
     <addaction name="mnuSaveSim"/>
-    <addaction name="mnuSaveK"/>
-    <addaction name="mnuSaveN"/>
+    <addaction name="mnuSaveMaterial"/>
    </widget>
    <widget class="QMenu" name="menuVersion_0_6">
     <property name="title">
@@ -954,9 +984,9 @@
     <string>k</string>
    </property>
   </action>
-  <action name="mnuSaveN">
+  <action name="mnuSaveMaterial">
    <property name="text">
-    <string>n</string>
+    <string>Material</string>
    </property>
   </action>
   <action name="mnuLoadSource">
+nu	k
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 602	0.027446631
 604	0.02823961
+nu	k
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 \ No newline at end of file
@@ -8,15 +8,19 @@ using namespace std;
 #include <QGraphicsPixmapItem>
 #include <QLayout>
 #include "qtSpectrumDisplay.h"
+//#include "qwtSpectrumDisplay.h"
 #include "globals.h"
 #include "rtsGUIConsole.h"
 #include "PerformanceData.h"
 #include <complex>
+#include <sstream>
 //#include <direct.h>
+
 PerformanceData PD;
 qtSpectrumDisplay* gpSpectrumDisplay;
+//qwtSpectrumDisplay* SpectrumDisplay;
 QGraphicsScene* distortionScene = NULL;
 QGraphicsView* distortionWindow = NULL;
@@ -43,6 +47,9 @@ double dNu = 2;
 double aMin = 0;
 double aMax = 1;
+double nMag = 1.0;
+double kMax = 1.0;
+
 double scaleI0 = 1.0;
 double refSlope = 0.0;
@@ -67,7 +74,7 @@ double cA = 1.0;
 //vector<SpecPair> NMaterial;
 bool applyMaterial = true;
 vector<Material> MaterialList;
-int currentMaterial = 0;
+int currentMaterial = -1;
 //optical parameters
 double cNAi = 0.0;
@@ -91,93 +98,106 @@ void TempSimSpectrum()
 		temp.A = sin((double)i/200);
 		SimSpectrum.push_back(temp);
 	}
-}
+	}
-void UpdateDisplay(){
+	void UpdateDisplay() {
 	gpSpectrumDisplay->updateGL();
+	//SpectrumDisplay->replot();
 }
-void LoadMaterial(string fileNameK, string fileNameN, string materialName)
+void LoadMaterial(string fileName, string materialName)
 {
-	Material newMaterial;
-	newMaterial.name = materialName;
-
-	vector<SpecPair> KMaterial = LoadSpectrum(fileNameK.c_str());
-	vector<SpecPair> NMaterial = LoadSpectrum(fileNameN.c_str());
-
-	//make sure that the sizes are the same
-	if(KMaterial.size() != NMaterial.size()){
-		cout<<"Error, material properties don't match."<<endl;
-		exit(1);
+	//open the file
+	ifstream inFile(fileName.c_str());
+	if(!inFile)
+	{
+		cout<<"Error loading material: "<<fileName<<endl;
+		return;
 	}
-	complex<double> eta;
-	//int j;
-	for(unsigned int i=0; i<KMaterial.size(); i++){
-		newMaterial.nu.push_back(KMaterial[i].nu);
-		eta = complex<double>(NMaterial[i].A, KMaterial[i].A);
-		newMaterial.eta.push_back(eta);
+	Material newMaterial;
+	newMaterial.validN = false;
+	newMaterial.validK = false;
+	//read the header
+	string units;
+	getline(inFile, units, '\t');
+	char c = 0;
+	while(c != '\n')
+	{
+		inFile.get(c);
+		if(c == 'n') newMaterial.validN = true;
+		if(c == 'k') newMaterial.validK = true;
 	}
-	MaterialList.push_back(newMaterial);
-}
-
-void LoadMaterial(string fileNameK, string materialName){
-	//load the material absorbance
-	vector<SpecPair> KMaterial = LoadSpectrum(fileNameK.c_str());
-	vector<SpecPair> NMaterial;
-	//KMaterial = LoadSpectrum("eta_TolueneK.txt");
+	//read the entire refractive index (both real and imaginary)
+	float nu;
+	float n;
+	float k;
-	//compute the real IR using Kramers Kronig
-	//copy the absorbance values into a linear array
-	double* k = (double*)malloc(sizeof(double) * KMaterial.size());
-	double* n = (double*)malloc(sizeof(double) * KMaterial.size());
-	for(unsigned int i=0; i<KMaterial.size(); i++)
-		k[i] = KMaterial[i].A;
+	while(inFile>>nu)
+	{
+		n = 1.0;
+		k = 0.0;
+		if(newMaterial.validN)
+			inFile>>n;
+		if(newMaterial.validK)
+			inFile>>k;
+		//ignore the rest of the line
+		inFile.ignore();
+
+		newMaterial.nu.push_back(nu);
+		newMaterial.eta.push_back(complex<double>(n, k));
+	}
-	//use Kramers Kronig to determine the real part of the index of refraction
-	cudaKramersKronig(n, k, KMaterial.size(), KMaterial[0].nu, KMaterial.back().nu, baseIR);
-	SpecPair temp;
-	for(unsigned int i=0; i<KMaterial.size(); i++)
+	//iterate through the material to compute the necessary bounds for display
+	float minN = 9999;
+	float maxN = -9999;
+	float sumN = 0;
+	float maxK = 0;
+	for(int i = 0; i<newMaterial.nu.size(); i++)
 	{
-		temp.nu =  KMaterial[i].nu;
-		temp.A = n[i];
-		NMaterial.push_back(temp);
+		n = newMaterial.eta[i].real();
+		k = newMaterial.eta[i].imag();
+
+		if(n < minN) minN = n;
+		if(n > maxN) maxN = n;
+		if(k > maxK) maxK = k;
+		sumN += n;
 	}
+	float meanN = sumN / newMaterial.nu.size();
-	//create the material
-	Material newMaterial;
+	nMag = max(maxN - meanN, meanN - minN);
+	kMax = maxK;
+	baseIR = meanN;
+
+	//set the name of the material object
 	newMaterial.name = materialName;
-	complex<double> eta;
-	for(unsigned int i=0; i<KMaterial.size(); i++){
-		newMaterial.nu.push_back(KMaterial[i].nu);
-		eta = complex<double>(NMaterial[i].A, KMaterial[i].A);
-		newMaterial.eta.push_back(eta);
-	}
+	//add it to the material list
 	MaterialList.push_back(newMaterial);
+	currentMaterial = MaterialList.size() - 1;
 }
 void LoadSource(string fileNameSource)
 {
-	SourceSpectrum = LoadSpectrum(fileNameSource);  
+	SourceSpectrum = LoadSpectrum(fileNameSource);
 }
 void ResampleSource()
 {
 	//clear the current resampled spectrum
 	SourceResampled.clear();
-	
+
 	//get the number of source and material samples
 	int nMatSamples = EtaK.size();
 	int nSourceSamples = SourceSpectrum.size();
-	
+
 	float nu, I;
 	for(int i=0; i<nMatSamples; i++)
 	{
 		SpecPair newSample;
 		newSample.nu = EtaK[i].nu;
-		
+
 		//iterate through the SourceSpectrum to find the bounding wavelengths
 		if(newSample.nu < SourceSpectrum[0].nu)
 			newSample.A = 0.0;
@@ -188,20 +208,20 @@ void ResampleSource()
 			int k=1;
 			while(SourceSpectrum[k].nu < newSample.nu)
 				k++;
-			
+
 			//interpolate
 			float a = (newSample.nu - SourceSpectrum[k-1].nu)/(SourceSpectrum[k].nu - SourceSpectrum[k-1].nu);
 			newSample.A = a * SourceSpectrum[k].A + (1.0 - a) * SourceSpectrum[k-1].A;
 		}
-		
+
 		//insert the new spectral point into the resampled spectrum
 		SourceResampled.push_back(newSample);
 		//cout<<newSample.nu<<"   "<<newSample.A<<endl;
 	}
-  
+
 }
-void FitDisplay(){
+void FitDisplay() {
 	double minA = 99999.0;
 	double maxA = -99999.0;
 	double k, n;
@@ -265,7 +285,7 @@ void FitDisplay(){
 	UpdateDisplay();
 }
-void ChangeAbsorbance(){
+void ChangeAbsorbance() {
 	//compute the real part of the index of refraction
@@ -289,9 +309,9 @@ void ChangeAbsorbance(){
 	//load the imaginary IR from the absorbance data
 	double nu;
-	for(int i=0; i<nSamples; i++){
+	for(int i=0; i<nSamples; i++) {
 		nu = MaterialList[currentMaterial].nu[i];
-		if(nu >= nuMin && nu <= nuMax){
+		if(nu >= nuMin && nu <= nuMax) {
 			temp.nu = nu;
 			temp.A = k[i];
 			EtaK.push_back(temp);
@@ -309,6 +329,7 @@ void SetMaterial()
 {
 	EtaK.clear();
 	EtaN.clear();
+	if(currentMaterial == -1) return;
 	int nSamples = MaterialList[currentMaterial].eta.size();
 	double nu;
@@ -317,7 +338,7 @@ void SetMaterial()
 	//initialize the current nuMin and nuMax values
 	nuMin = MaterialList[currentMaterial].nu[0];
 	nuMax = nuMin;
-	for(int i=0; i<nSamples; i++){
+	for(int i=0; i<nSamples; i++) {
 		nu = MaterialList[currentMaterial].nu[i];
 		//if(nu >= nuMin && nu <= nuMax){
@@ -325,14 +346,14 @@ void SetMaterial()
 		if(nu < nuMin) nuMin = nu;
 		if(nu > nuMax) nuMax = nu;
-			temp.nu = nu;
-			temp.A = MaterialList[currentMaterial].eta[i].imag();
-			EtaK.push_back(temp);
-			temp.A = MaterialList[currentMaterial].eta[i].real();
-			EtaN.push_back(temp);
+		temp.nu = nu;
+		temp.A = MaterialList[currentMaterial].eta[i].imag();
+		EtaK.push_back(temp);
+		temp.A = MaterialList[currentMaterial].eta[i].real();
+		EtaN.push_back(temp);
 	}
 	cA = 1.0;
-	
+
 	//resample the source spectrum
 	if(SourceSpectrum.size() != 0)
 		ResampleSource();
@@ -348,22 +369,33 @@ int main(int argc, char *argv[])
 	//load the default project file (any previous optical settings)
 	LoadState();
+
 	//load the default materials
-	LoadMaterial("eta_TolueneK.txt", "eta_TolueneN.txt", "Toluene");
+	LoadMaterial("etaToluene.txt", "Toluene");
 	LoadMaterial("kPMMA.txt", "PMMA");
-	LoadMaterial("eta_polystyreneK.txt", "Polystyrene");
+	LoadMaterial("kPolyethylene.txt", "Polyethylene");
+	LoadMaterial("kPTFE.txt", "Teflon");
+
+
+	//LoadMaterial("eta_TolueneK.txt", "eta_TolueneN.txt", "Toluene");
+	//LoadMaterial("kPMMA.txt", "PMMA");
+	//LoadMaterial("eta_polystyreneK.txt", "Polystyrene");
 	//LoadMaterial("../../../../data/materials/rtsSU8_k.txt", "../../../../data/materials/rtsSU8_n.txt", "SU8");
 	SetMaterial();
-	
+
+
 	//load a mid-infrared source
 	LoadSource("source_midIR.txt");
+
 	ResampleSource();
 	//compute the analytical solution for the Mie scattered spectrum
 	SimulateSpectrum();
 	QApplication a(argc, argv);
-	
+
+	//SpectrumDisplay = new qwtSpectrumDisplay();
+
 	InteractiveMie w;
 	w.show() ;
 	w.move(0, 0);
@@ -385,6 +417,8 @@ int main(int argc, char *argv[])
 	gpSpectrumDisplay->move(uiFrame.width(), 0);
 	gpSpectrumDisplay->show();
+
+
 	//distortion dialog box
 	distortionDialog = new qtDistortionDialog();
 	distortionDialog->move(0, 0);
-#include "qtDistortionDialog.h"
-
-qtDistortionDialog::qtDistortionDialog(QWidget *parent, Qt::WFlags flags)
-	: QDialog(parent, flags)
-{
-	ui.setupUi(this);
-}
-
-qtDistortionDialog::~qtDistortionDialog()
-{
-	updating = false;
+#include "qtDistortionDialog.h"
+
+qtDistortionDialog::qtDistortionDialog(QWidget *parent, Qt::WFlags flags)
+    : QDialog(parent, flags)
+{
+    ui.setupUi(this);
+}
+
+qtDistortionDialog::~qtDistortionDialog()
+{
+    updating = false;
 }
@@ -17,18 +17,18 @@ extern QGraphicsPixmapItem* pixmapItem;
 class qtDistortionDialog : public QDialog
 {
-	Q_OBJECT
+    Q_OBJECT
 public:
-	qtDistortionDialog(QWidget *parent = 0, Qt::WFlags flags = 0);
-	~qtDistortionDialog();
-	bool updating;
+    qtDistortionDialog(QWidget *parent = 0, Qt::WFlags flags = 0);
+    ~qtDistortionDialog();
+    bool updating;
 private:
-	Ui::DistortionDialogClass ui;
+    Ui::DistortionDialogClass ui;
 public slots:
-    void on_btnComputeDistortionMap_clicked(){
+    void on_btnComputeDistortionMap_clicked() {
         int steps = 100;
@@ -49,7 +49,7 @@ public slots:
         //compute the extrema
         float minDistortion = 99999;
         float maxDistortion = distortionMap[0];
-        for(int i=1; i<steps*steps; i++){
+        for(int i=1; i<steps*steps; i++) {
             if(distortionMap[i] < minDistortion && distortionMap[i] > 0)
                 minDistortion = distortionMap[i];
             if(distortionMap[i] > maxDistortion)
@@ -62,11 +62,14 @@ public slots:
         float intensity;
         float v;
         for(i=0; i<steps; i++)
-            for(o=0; o<steps; o++){
+            for(o=0; o<steps; o++) {
                 v = distortionMap[o * steps + i];
                 intensity = (v - minDistortion) / (maxDistortion - minDistortion) * 255;
-                if(intensity < 0) {cout<<"low intensity"<<endl; intensity = 0;}
+                if(intensity < 0) {
+                    cout<<"low intensity"<<endl;
+                    intensity = 0;
+                }
                 //QColor color(intensity, (float)o / (float)steps * 255, (float)i / (float)steps * 255);
                 QColor color(intensity, intensity, intensity);
-#include <QtGui>
-#include <QtOpenGL/QtOpenGL>
-#include <GL/glu.h>
-
-#include <math.h>
-
-#include "qtSpectrumDisplay.h"
-
-qtSpectrumDisplay::qtSpectrumDisplay(QWidget *parent)
- : QGLWidget(parent)
-{
- object = 0;
- xRot = 0;
- yRot = 0;
- zRot = 0;
-
- qtGreen = QColor::fromCmykF(0.40, 0.0, 1.0, 0.0);
- qtPurple = QColor::fromCmykF(0.39, 0.39, 0.0, 0.0);
-}
-
-qtSpectrumDisplay::~qtSpectrumDisplay()
-{
- makeCurrent();
- glDeleteLists(object, 1);
-}
-
-QSize qtSpectrumDisplay::minimumSizeHint() const
-{
- return QSize(50, 50);
-}
-
-QSize qtSpectrumDisplay::sizeHint() const
-{
- return QSize(400, 400);
-}
-
-void qtSpectrumDisplay::initializeGL()
-{
- qglClearColor(qtPurple.dark());
- //object = makeObject();
- glShadeModel(GL_FLAT);
- glEnable(GL_DEPTH_TEST);
- glEnable(GL_CULL_FACE);
-}
-
-void qtSpectrumDisplay::printWavenumber(int xPos)
-{
- int viewParams[4];
- glGetIntegerv(GL_VIEWPORT, viewParams);
-
- float a = (float)xPos/(float)viewParams[2];
-
- int wn = a * (nuMax - nuMin) + nuMin;
- cout<<wn<<endl;
-
-
-
-}
-
-void qtSpectrumDisplay::paintGL()
+#include <QtGui>
+#include <QtOpenGL/QtOpenGL>
+#include <GL/glu.h>
+
+#include <math.h>
+
+#include "qtSpectrumDisplay.h"
+
+int axisMargins = 50;
+
+qtSpectrumDisplay::qtSpectrumDisplay(QWidget *parent)
+    : QGLWidget(parent)
+{
+    object = 0;
+    xRot = 0;
+    yRot = 0;
+    zRot = 0;
+
+    qtGreen = QColor::fromCmykF(0.40, 0.0, 1.0, 0.0);
+    qtPurple = QColor::fromCmykF(0.39, 0.39, 0.0, 0.0);
+}
+
+qtSpectrumDisplay::~qtSpectrumDisplay()
+{
+    makeCurrent();
+    glDeleteLists(object, 1);
+}
+
+QSize qtSpectrumDisplay::minimumSizeHint() const
 {
-    //prepare the projection (orthographic, bounded by spectral values)
-    glMatrixMode(GL_PROJECTION);
-    glLoadIdentity();
-    gluOrtho2D(nuMin, nuMax, aMin, aMax);
-    glMatrixMode(GL_MODELVIEW);
+    return QSize(50, 50);
+}
+
+QSize qtSpectrumDisplay::sizeHint() const
+{
+    return QSize(400, 400);
+}
+
+void qtSpectrumDisplay::initializeGL()
+{
+    //qglClearColor(qtPurple.dark());
+    glClearColor(0.0, 0.0, 0.0, 0.0);
+    //object = makeObject();
+    glShadeModel(GL_FLAT);
+    glEnable(GL_DEPTH_TEST);
+    glEnable(GL_CULL_FACE);
+}
+
+void qtSpectrumDisplay::printWavenumber(int xPos)
+{
+    int viewParams[4];
+    glGetIntegerv(GL_VIEWPORT, viewParams);
+
+    float a = (float)xPos/(float)viewParams[2];
+
+    int wn = a * (nuMax - nuMin) + nuMin;
+    cout<<wn<<endl;
+
+
+
+}
+
+void qtSpectrumDisplay::paintGL()
+{
+
+    //*************  Draw Absorbance/Intensity  **************************
+    //get the window size
+    int w = width();
+    int h = height();
+    glViewport(50, 30, w, h);
+
+    //prepare the projection for spectra (orthographic, bounded by spectral values)
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(nuMin, nuMax, aMin, aMax);
+    glMatrixMode(GL_MODELVIEW);
     glLoadIdentity();
     //clear the screen
-    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
-
-    //set the line width
-    glLineWidth(2);
-
-    //draw the simulated spectrum (in white)
-    if(dispSimSpec)
-    {
-     glColor3f(1.0, 1.0, 1.0);
-     glBegin(GL_LINE_STRIP);
-     for(unsigned int i=0; i<SimSpectrum.size(); i++)
-         glVertex2f(SimSpectrum[i].nu, SimSpectrum[i].A);
-     glEnd();
+    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
+
+    //set the line width
+    glLineWidth(1);
+
+    //draw the simulated spectrum (in white)
+    if(dispSimSpec)
+    {
+        glColor3f(1.0, 1.0, 1.0);
+        glBegin(GL_LINE_STRIP);
+        for(unsigned int i=0; i<SimSpectrum.size(); i++)
+            glVertex2f(SimSpectrum[i].nu, SimSpectrum[i].A);
+        glEnd();
+    }
+    //draw the reference spectrum in gray
+    if(dispRefSpec && RefSpectrum.size() > 0)
+    {
+        glColor3f(0.5, 0.5, 0.5);
+        glBegin(GL_LINE_STRIP);
+        float nu;
+        for(unsigned int i=0; i<RefSpectrum[currentSpec].size(); i++)
+        {
+            nu = RefSpectrum[currentSpec][i].nu;
+            glVertex2f(nu, RefSpectrum[currentSpec][i].A + nu * refSlope);
+        }
+        glEnd();
     }
-    //draw the reference spectrum in gray
-    if(dispRefSpec && RefSpectrum.size() > 0)
-    {
-     glColor3f(0.5, 0.5, 0.5);
-     glBegin(GL_LINE_STRIP);
-     float nu;
-     for(unsigned int i=0; i<RefSpectrum[currentSpec].size(); i++)
-     {
-         nu = RefSpectrum[currentSpec][i].nu;
-         glVertex2f(nu, RefSpectrum[currentSpec][i].A + nu * refSlope);
-     }
-     glEnd();
-    }
-
-    //draw the material properties
-
-    //change the viewport properties (materials are plotted on a different scale)
     //compute the maximum k and n
     int nSamples = MaterialList[currentMaterial].eta.size();
     float maxK = 0.0;
     float maxN = 0.0;
     float thisN, thisK;
-    for(int i=0; i<nSamples; i++)
+
+
+
+    //*************  Draw k  **************************
+    //change the viewport properties and draw n
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(nuMin, nuMax, 0.0, kMax);
+    //glMatrixMode(GL_MODELVIEW);
+    //glLoadIdentity();
+
+    float nu;
+    if(dispMatK)
+    {
+
+        glColor3f(1.0, 0.0, 0.0);
+        glBegin(GL_LINE_STRIP);
+        for(int i=0; i<nSamples; i++)
+        {
+            nu = MaterialList[currentMaterial].nu[i];
+            glVertex2f(nu, MaterialList[currentMaterial].eta[i].imag());
+        }
+        glEnd();
+    }
+    if(dispSimK)
     {
-        thisN = fabs(MaterialList[currentMaterial].eta[i].real() - 1.49);
-        if(thisN > maxN)
-            maxN = thisN;
-        thisK = fabs(MaterialList[currentMaterial].eta[i].imag());
-        if(thisK > maxK)
-            thisK = maxK;
+        glColor3f(1.0, 1.0, 0.0);
+        glBegin(GL_LINE_STRIP);
+        for(unsigned int i=0; i<EtaK.size(); i++)
+        {
+            nu = EtaK[i].nu;
+            glVertex2f(nu, EtaK[i].A);
+        }
+        glEnd();
     }
-    cout<<maxN<<"---------"<<maxK<<endl;
+    //*************  Draw n  **************************
+    //change the viewport properties and draw n
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    if(nMag < 0.1) nMag = 0.1;
+    gluOrtho2D(nuMin, nuMax, baseIR - nMag, baseIR + nMag);
+    if(dispMatN)
+    {
+        glColor3f(0.0, 1.0, 0.0);
+        glBegin(GL_LINE_STRIP);
+        for(int i=0; i<nSamples; i++)
+        {
+            nu = MaterialList[currentMaterial].nu[i];
+            glVertex2f(nu, MaterialList[currentMaterial].eta[i].real());
+        }
+        glEnd();
+    }
+    if(dispSimN)
+    {
+        glColor3f(0.0, 1.0, 1.0);
+        glBegin(GL_LINE_STRIP);
+        for(unsigned int i=0; i<EtaN.size(); i++)
+        {
+            nu = EtaN[i].nu;
+            glVertex2f(nu, EtaN[i].A);
+        }
+        glEnd();
+    }
-    glMatrixMode(GL_PROJECTION);
-    glLoadIdentity();
-    gluOrtho2D(nuMin, nuMax, aMin, aMax);
-
-
-    float nu;
-    //display absorbance
-    if(dispMatK)
-    {
-
-     glColor3f(1.0, 0.0, 0.0);
-     glBegin(GL_LINE_STRIP);
-     for(int i=0; i<nSamples; i++){
-         nu = MaterialList[currentMaterial].nu[i];
-         glVertex2f(nu, MaterialList[currentMaterial].eta[i].imag() * dispScaleK);
-     }
-     glEnd();
-    }
-    if(dispSimK)
-    {
-     glColor3f(1.0, 1.0, 0.0);
-     glBegin(GL_LINE_STRIP);
-     for(unsigned int i=0; i<EtaK.size(); i++){
-         glVertex2f(EtaK[i].nu, EtaK[i].A * dispScaleK);
-     }
-     glEnd();
-}
-
-//display refractive index (real)
-if(dispMatN)
-{
- glColor3f(0.0, 1.0, 0.0);
- glBegin(GL_LINE_STRIP);
- for(int i=0; i<nSamples; i++){
-     nu = MaterialList[currentMaterial].nu[i];
-     glVertex2f(nu, (MaterialList[currentMaterial].eta[i].real() - baseIR) * dispScaleN);
- }
- glEnd();
-}
-if(dispSimN)
-{
- glColor3f(0.0, 1.0, 1.0);
- glBegin(GL_LINE_STRIP);
- for(unsigned int i=0; i<EtaN.size(); i++)
-     glVertex2f(EtaN[i].nu, (EtaN[i].A - baseIR) * dispScaleN);
- glEnd();
-}
-
-
-glCallList(object);
-
-glFlush();
-
-//display the values at the mouse location
-renderText(50, 50, "test");
-}
-
-void qtSpectrumDisplay::resizeGL(int width, int height)
-{
- int side = qMin(width, height);
- glViewport(0, 0, width, height);
-
-}
-
-void qtSpectrumDisplay::mousePressEvent(QMouseEvent *event)
-{
- lastPos = event->pos();
-
- if(event->buttons() & Qt::LeftButton)
- {
-     int wn = 0;
-     printWavenumber(event->x());
- }
-}
-
-void qtSpectrumDisplay::mouseMoveEvent(QMouseEvent *event)
-{
- int dx = event->x() - lastPos.x();
- int dy = event->y() - lastPos.y();
-
- lastPos = event->pos();
-}
-
-void qtSpectrumDisplay::quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
-                 GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4)
-{
- qglColor(qtGreen);
-
- glVertex3d(x1, y1, -0.05);
- glVertex3d(x2, y2, -0.05);
- glVertex3d(x3, y3, -0.05);
- glVertex3d(x4, y4, -0.05);
-
- glVertex3d(x4, y4, +0.05);
- glVertex3d(x3, y3, +0.05);
- glVertex3d(x2, y2, +0.05);
- glVertex3d(x1, y1, +0.05);
-}
-
-void qtSpectrumDisplay::normalizeAngle(int *angle)
-{
- while (*angle < 0)
-     *angle += 360 * 16;
- while (*angle > 360 * 16)
-     *angle -= 360 * 16;
+
+    glCallList(object);
+
+    glFlush();
+
+    //***********************  Display axes values  ****************************
+
+
+    ostringstream buff;
+    glViewport(0, 0, w, h);
+    int nDivs = 11;
+    glColor3f(1.0, 1.0, 1.0);
+    for(int i = 0; i < nDivs; i++)
+    {
+        float divStep = (aMax - aMin)/(nDivs - 1);
+        float pixStep = (float)(h - 10)/(nDivs - 1);
+
+        buff<<aMin + i * divStep;
+        renderText(0, h - i * pixStep, buff.str().c_str());
+        buff.clear(); buff.str("");
+    }
+}
+
+void qtSpectrumDisplay::resizeGL(int width, int height)
+{
+    int side = qMin(width, height);
+
+
+}
+
+void qtSpectrumDisplay::mousePressEvent(QMouseEvent *event)
+{
+    lastPos = event->pos();
+
+    if(event->buttons() & Qt::LeftButton)
+    {
+        int wn = 0;
+        printWavenumber(event->x());
+    }
+}
+
+void qtSpectrumDisplay::mouseMoveEvent(QMouseEvent *event)
+{
+    int dx = event->x() - lastPos.x();
+    int dy = event->y() - lastPos.y();
+
+    lastPos = event->pos();
+}
+
+void qtSpectrumDisplay::quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
+                             GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4)
+{
+    qglColor(qtGreen);
+
+    glVertex3d(x1, y1, -0.05);
+    glVertex3d(x2, y2, -0.05);
+    glVertex3d(x3, y3, -0.05);
+    glVertex3d(x4, y4, -0.05);
+
+    glVertex3d(x4, y4, +0.05);
+    glVertex3d(x3, y3, +0.05);
+    glVertex3d(x2, y2, +0.05);
+    glVertex3d(x1, y1, +0.05);
+}
+
+void qtSpectrumDisplay::normalizeAngle(int *angle)
+{
+    while (*angle < 0)
+        *angle += 360 * 16;
+    while (*angle > 360 * 16)
+        *angle -= 360 * 16;
 }
- #ifndef GLWIDGET_H
- #define GLWIDGET_H
-
-#include <QtOpenGL/QGLWidget>
-#include "globals.h"
-
- class qtSpectrumDisplay : public QGLWidget
- {
-     Q_OBJECT
-
- public:
-     qtSpectrumDisplay(QWidget *parent = 0);
-     ~qtSpectrumDisplay();
-
-     QSize minimumSizeHint() const;
-     QSize sizeHint() const;
-
- public slots:
-     /*void setXRotation(int angle);
-     void setYRotation(int angle);
-     void setZRotation(int angle);*/
-
- signals:
-     void xRotationChanged(int angle);
-     void yRotationChanged(int angle);
-     void zRotationChanged(int angle);
-
- protected:
-     void initializeGL();
-     void paintGL();
-     void resizeGL(int width, int height);
-     void mousePressEvent(QMouseEvent *event);
-     void mouseMoveEvent(QMouseEvent *event);
-
- private:
-     //GLuint makeObject();
-     void quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
-               GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4);
-     //void extrude(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2);
-     void normalizeAngle(int *angle);
-	 void printWavenumber(int wn);
-
-     GLuint object;
-     int xRot;
-     int yRot;
-     int zRot;
-     QPoint lastPos;
-     QColor qtGreen;
-     QColor qtPurple;
- };
-
- #endif
 \ No newline at end of file
+#ifndef GLWIDGET_H
+#define GLWIDGET_H
+
+#include <QtOpenGL/QGLWidget>
+#include "globals.h"
+
+class qtSpectrumDisplay : public QGLWidget
+{
+    Q_OBJECT
+
+public:
+    qtSpectrumDisplay(QWidget *parent = 0);
+    ~qtSpectrumDisplay();
+
+    QSize minimumSizeHint() const;
+    QSize sizeHint() const;
+
+public slots:
+    /*void setXRotation(int angle);
+    void setYRotation(int angle);
+    void setZRotation(int angle);*/
+
+signals:
+    void xRotationChanged(int angle);
+    void yRotationChanged(int angle);
+    void zRotationChanged(int angle);
+
+protected:
+    void initializeGL();
+    void paintGL();
+    void resizeGL(int width, int height);
+    void mousePressEvent(QMouseEvent *event);
+    void mouseMoveEvent(QMouseEvent *event);
+
+private:
+    //GLuint makeObject();
+    void quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
+              GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4);
+    //void extrude(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2);
+    void normalizeAngle(int *angle);
+    void printWavenumber(int wn);
+
+    GLuint object;
+    int xRot;
+    int yRot;
+    int zRot;
+    QPoint lastPos;
+    QColor qtGreen;
+    QColor qtPurple;
+};
+
+#endif