static void make_filter(T *result_b, T *result_a, const complex4c *alpha, const complex4c *beta, int K, T sigma)
{
const double denom = sigma * M_SQRT2PI;
complex4c b[DERICHE_MAX_K], a[DERICHE_MAX_K + 1];
int k, j;
b[0] = alpha[0]; /* Initialize b/a = alpha[0] / (1 + beta[0] z^-1) */
a[0] = make_complex(1, 0);
a[1] = beta[0];
for (k = 1; k < K; ++k)
{ /* Add kth term, b/a += alpha[k] / (1 + beta[k] z^-1) */
b[k] = c_mul(beta[k], b[k-1]);
for (j = k - 1; j > 0; --j)
b[j] = c_add(b[j], c_mul(beta[k], b[j - 1]));
for (j = 0; j <= k; ++j)
b[j] = c_add(b[j], c_mul(alpha[k], a[j]));
a[k + 1] = c_mul(beta[k], a[k]);
for (j = k; j > 0; --j)
a[j] = c_add(a[j], c_mul(beta[k], a[j - 1]));
}
for (k = 0; k < K; ++k)
{
result_b[k] = (T)(b[k].real / denom);
result_a[k + 1] = (T)a[k + 1].real;
}
return;
}
/**
* \brief Expand pole product
* \param c resulting filter coefficients
* \param poles pole locations
* \param K number of poles
* \ingroup vyv_gaussian
*
* This routine expands the product to obtain the filter coefficients:
* \f[ \prod_{k=0}^{K-1}\frac{\mathrm{poles}[k]-1}{\mathrm{poles}[k]-z^{-1}}
= \frac{c[0]}{1+\sum_{k=1}^K c[k] z^{-k}}. \f]
*/
static void expand_pole_product(double *c, const complex4c *poles, int K)
{
complex4c denom[VYV_MAX_K + 1];
int k, j;
assert(K <= VYV_MAX_K);
denom[0] = poles[0];
denom[1] = make_complex(-1, 0);
for (k = 1; k < K; ++k)
{
denom[k + 1] = c_neg(denom[k]);
for (j = k; j > 0; --j)
denom[j] = c_sub(c_mul(denom[j], poles[k]), denom[j - 1]);
denom[0] = c_mul(denom[0], poles[k]);
}
for (k = 1; k <= K; ++k)
c[k] = c_div(denom[k], denom[0]).real;
for (c[0] = 1, k = 1; k <= K; ++k)
c[0] += c[k];
return;
}
struct c_complex Lentz_Dn(struct c_complex z,long n)
/*:10*/
#line 126 "./mie.w"
{
struct c_complex alpha_j1,alpha_j2,zinv,aj;
struct c_complex alpha,result,ratio,runratio;
/*12:*/
#line 156 "./mie.w"
zinv= c_sdiv(2.0,z);
alpha= c_smul(n+0.5,zinv);
aj= c_smul(-n-1.5,zinv);
alpha_j1= c_add(aj,c_inv(alpha));
alpha_j2= aj;
ratio= c_div(alpha_j1,alpha_j2);
runratio= c_mul(alpha,ratio);
/*:12*/
#line 131 "./mie.w"
do
/*13:*/
#line 179 "./mie.w"
{
aj.re= zinv.re-aj.re;
aj.im= zinv.im-aj.im;
alpha_j1= c_add(c_inv(alpha_j1),aj);
alpha_j2= c_add(c_inv(alpha_j2),aj);
ratio= c_div(alpha_j1,alpha_j2);
zinv.re*= -1;
zinv.im*= -1;
runratio= c_mul(ratio,runratio);
}
/*:13*/
#line 134 "./mie.w"
while(fabs(c_abs(ratio)-1.0)> 1e-12);
result= c_add(c_sdiv((double)-n,z),runratio);
return result;
}
/**
* \brief Derivative of variance with respect to q
* \param poles0 unscaled pole locations
* \param q rescaling parameter
* \param K number of poles
* \return derivative of variance with respect to q
* \ingroup vyv_gaussian
*
* This function is used by compute_q() in solving for q.
*/
static double dq_variance(const complex4c *poles0, int K, double q)
{
complex4c sum = { 0, 0 };
int k;
for (k = 0; k < K; ++k)
{
complex4c z = c_real_pow(poles0[k], 1 / q), w = z, denom = z;
w.real += 1;
denom.real -= 1;
/* Compute sum += z log(z) (z + 1) / (z - 1)^3 */
sum = c_add(sum, c_div(c_mul(c_mul(z, c_log(z)), w),
c_real_pow(denom, 3)));
}
return (2 / q) * sum.real;
}
/**
* \brief Compute the variance of the impulse response
* \param poles0 unscaled pole locations
* \param q rescaling parameter
* \param K number of poles
* \return variance achieved by poles = poles0^(1/q)
* \ingroup vyv_gaussian
*/
static double variance(const complex4c *poles0, int K, double q)
{
complex4c sum = { 0, 0 };
int k;
for (k = 0; k < K; ++k)
{
complex4c z = c_real_pow(poles0[k], 1 / q), denom = z;
denom.real -= 1;
/* Compute sum += z / (z - 1)^2. */
sum = c_add(sum, c_div(z, c_mul(denom, denom)));
}
return 2 * sum.real;
}
//傅里叶变化
void fft(int N,complex f[])
{
complex t,wn;//中间变量
int i,j,k,m,n,l,r,M;
int la,lb,lc;
/*----计算分解的级数M=log2(N)----*/
for(i=N,M=1;(i=i/2)!=1;M++);
/*----按照倒位序重新排列原信号----*/
for(i=1,j=N/2;i<=N-2;i++)
{
if(i<j)
{
t=f[j];
f[j]=f[i];
f[i]=t;
}
k=N/2;
while(k<=j)
{
j=j-k;
k=k/2;
}
j=j+k;
}
/*----FFT算法----*/
for(m=1;m<=M;m++)
{
la=pow(2,m); //la=2^m代表第m级每个分组所含节点数
lb=la/2; //lb代表第m级每个分组所含碟形单元数
//同时它也表示每个碟形单元上下节点之间的距离
/*----碟形运算----*/
for(l=1;l<=lb;l++)
{
r=(l-1)*pow(2,M-m);
for(n=l-1;n<N-1;n=n+la) //遍历每个分组，分组总数为N/la
{
lc=n+lb; //n,lc分别代表一个碟形单元的上、下节点编号
Wn_i(N,r,&wn,1);//wn=Wnr
c_mul(f[lc],wn,&t);//t = f[lc] * wn复数运算
c_sub(f[n],t,&(f[lc]));//f[lc] = f[n] - f[lc] * Wnr
c_plus(f[n],t,&(f[n]));//f[n] = f[n] + f[lc] * Wnr
}
}
}
}
void schurFactorization(long n, complex **A, complex **T, complex **U)
{
/* Schur factorization: A = U*T*U', T = upper triangular, U = unitary */
long i,j,iter,maxIter;
double tol, diff1,diff2;
complex T11, T12, T21, T22;
complex sigma1, sigma2, sigma;
complex z, z1, z2;
complex **P, **Q, **R;
/* Allocate auxiliary matrices */
P = (complex **)Mem(MEM_ALLOC,n, sizeof(complex *));
Q = (complex **)Mem(MEM_ALLOC,n, sizeof(complex *));
R = (complex **)Mem(MEM_ALLOC,n, sizeof(complex *));
for (i=0; i<n; i++){
P[i] = (complex *)Mem(MEM_ALLOC,n, sizeof(complex));
Q[i] = (complex *)Mem(MEM_ALLOC,n, sizeof(complex));
R[i] = (complex *)Mem(MEM_ALLOC,n, sizeof(complex));
}
/* ------------------------------------------------------------*/
/* Parameters for iteration */
maxIter = 500;
tol = 1E-30;
/* ------------------------------------------------------------*/
/* Init U = eye(n) (identity matrix) */
for (i=0; i<n; i++){
U[i][i].re = 1.0;
U[i][i].im = 0.0;
}
/* ------------------------------------------------------------*/
/* Reduce A to Hessenberg form */
hessFactorization(n,A,P,T);
/* ------------------------------------------------------------*/
/* Compute Schur factorization of Hessenberg matrix T */
for (j=n-1; j>0; j--){ /* Main loop */
for (iter=0; iter<maxIter; iter++){ /* Iteration loop */
sigma.re = T[j][j].re;
sigma.im = T[j][j].im;
/* -- Use Wilkinson shift -- */
/* submatrix considered in the shift */
T11 = T[j-1][j-1];
T12 = T[j-1][j];
T21 = T[j][j-1];
T22 = T[j][j];
/* Compute eigenvalues of submatrix */
z.re = 0.0;
z.im = 0.0;
z2.re = 0.0;
z2.im = 0.0;
/* z = T11*T11 + T22*T22 - 2*T11*T22 + 4*T12*T21 */
z1 = c_mul(T11,T11);
z = c_add(z ,z1);
z2 = c_add(z2,z1);
z1 = c_mul(T22,T22);
z = c_add(z ,z1);
z2 = c_add(z2,z1);
z1 = c_mul(T11,T22);
z1.re = -2.0 * z1.re;
z1.im = -2.0 * z1.im;
z = c_add(z,z1);
z1 = c_mul(T12,T21);
z1.re = 4.0 * z1.re;
z1.im = 4.0 * z1.im;
z = c_add(z,z1);
/* Square root*/
z = c_sqrt(z);
/* Eigenvalues */
sigma1 = c_add(z2,z);
sigma2 = c_sub(z2,z);
/* printf("sigma1 = %e %e\n", sigma1.re, sigma1.im); */
/* printf("sigma2 = %e %e\n", sigma2.re, sigma2.im); */
/* Select eigenvalue for shift*/
diff1 = c_norm( c_sub(T[j][j], sigma1) );
diff2 = c_norm( c_sub(T[j][j], sigma2) );
if (diff1 < diff2){
sigma.re = sigma1.re;
sigma.im = sigma1.im;
}else{
sigma.re = sigma2.re;
sigma.im = sigma2.im;
}
/* --- QR step with Wilkinson shift --- */
/* Shift: T(1:j,1:j) = T(1:j,1:j) - sigma * eye(j) */
for (i=0; i<j+1; i++){
CheckValue(FUNCTION_NAME, "T[i][i].re","", T[i][i].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "T[i][i].im","", T[i][i].im, -INFTY, INFTY);
T[i][i].re = T[i][i].re - sigma.re;
T[i][i].im = T[i][i].im - sigma.im;
}
/* Compute QR factorization of shifted Hessenberg matrix */
for (i=0; i<n; i++){
memset(Q[i], 0, n*sizeof(complex));
memset(R[i], 0, n*sizeof(complex));
}
QRfactorization(n,T,Q,R);
/* T = T_new = R * Q */
for (i=0; i<n; i++){
memset(T[i], 0, n*sizeof(complex));
}
matProduct(n, n, n, R, Q, T);
/* T(1:j,1:j) = T(1:j,1:j) + sigma * eye(j) */
for (i=0; i<j+1; i++){
T[i][i].re = T[i][i].re + sigma.re;
T[i][i].im = T[i][i].im + sigma.im;
}
/* R = U_new = U * Q */
for (i=0; i<n; i++){
memset(R[i], 0, n*sizeof(complex));
}
matProduct(n,n,n,U,Q,R);
/* U = R */
for (i=0; i<n; i++){
memcpy(U[i],R[i], n*sizeof(complex));
}
/* Check convergence */
if (c_norm( T[j][j-1] ) <= tol * (c_norm(T[j-1][j-1]) + c_norm(T[j][j]))){
T[j][j-1].re = 0.0;
T[j][j-1].im = 0.0;
break;
}
} /* end of iter loop */
} /* end of main loop */
/* -------------------------------------------------------------*/
/* U = P*U */
for (i=0; i<n; i++){
memset(U[i], 0, n*sizeof(complex));
}
matProduct(n,n,n,P,R,U);
/* -------------------------------------------------------------*/
/* Free auxiliary variables */
for (i=0; i<n; i++){
Mem(MEM_FREE,P[i]);
Mem(MEM_FREE,Q[i]);
Mem(MEM_FREE,R[i]);
}
Mem(MEM_FREE,P);
Mem(MEM_FREE,Q);
Mem(MEM_FREE,R);
/* Return */
return;
}
void QRfactorization(long n, complex **A, complex **Q, complex **R)
{
/* QR factorization based on Householder transformations */
long i,j,k,m;
double nrm;
complex z,z1,z2;
complex *vj;
/* Init. Q = eye(n) (identity matrix) */
for (i=0; i<n; i++){
Q[i][i].re = 1.0;
Q[i][i].im = 0.0;
}
/* Init. R = A */
for(j=0; j<n; j++){
for (i=0; i<n; i++){
R[i][j].re = A[i][j].re;
R[i][j].im = A[i][j].im;
CheckValue(FUNCTION_NAME, "A[i][j].re","", A[i][j].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "A[i][j].im","", A[i][j].im, -INFTY, INFTY);
}
}
/* Allocate auxiliary variables*/
vj = (complex *)Mem(MEM_ALLOC, n, sizeof(complex));
/* printf("begin calc, n = %d\n", n); */
/* ------------------------------------------------------------*/
for (j=0; j<n; j++){ /* Main loop */
/* R(j:end, j) */
for (i=j; i<n; i++){
vj[i-j].re = R[i][j].re;
vj[i-j].im = R[i][j].im;
}
nrm = vectorNorm(n-j, vj);
/* v(1) = v(1) + sign(R(j,j)) * norm(v) */
vj[0].re = vj[0].re + R[j][j].re / c_norm(R[j][j]) * nrm;
vj[0].im = vj[0].im + R[j][j].im / c_norm(R[j][j]) * nrm;
/* Update norm */
nrm = vectorNorm(n-j, vj);
/* v = v./norm(v) */
for (i=0; i<n-j; i++){
vj[i].re = vj[i].re / nrm;
vj[i].im = vj[i].im / nrm;
}
/* Update */
/* R(j:end, :) = R(j:end,:) - 2 * vj * vj' * R(j:end,:), : */
/* Q(:,j:end) = Q(:,j:end) - 2 * Q(:,j:end) * vj * vj^T */
for (k=0; k<n; k++){
/* (v * v' * A)_ik = v_i SUM_m Conj(v_m) A_mk */
z.re = 0.0;
z.im = 0.0;
for (m=j; m<n; m++){
z1 = c_con(vj[m-j]);
z1 = c_mul(z1, R[m][k]);
z = c_add(z,z1);
}
for (i=j; i<n; i++){
z2 = c_mul(vj[i-j],z);
/* Update R(i,k) */
R[i][k].re = R[i][k].re - 2.0 * z2.re;
R[i][k].im = R[i][k].im - 2.0 * z2.im;
CheckValue(FUNCTION_NAME, "R[i][k].re","", R[i][k].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "R[i][k].im","", R[i][k].im, -INFTY, INFTY);
}
/* (A * v * v^')_ki = v_i * SUM_m Conj(v_m) A_km */
z.re = 0.0;
z.im = 0.0;
for (m=j; m<n; m++){
z1 = vj[m-j];
z1 = c_mul(z1, Q[k][m]);
z = c_add(z,z1);
}
for (i=j; i<n; i++){
z1 = c_con(vj[i-j]);
z2 = c_mul(z1,z);
/* Update Q(k,i)*/
Q[k][i].re = Q[k][i].re - 2.0 * z2.re;
Q[k][i].im = Q[k][i].im - 2.0 * z2.im;
CheckValue(FUNCTION_NAME, "Q[k][i].re","", Q[k][i].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "Q[k][i].im","", Q[k][i].im, -INFTY, INFTY);
}
}
} /* End of main loop (j) */
/* -------------------------------------------------------------*/
/* Free auxiliary variables */
Mem(MEM_FREE, vj);
return;
}
int main()
{
struct compoundData cdtest;
int i;
XRayInit();
//if something goes wrong, the test will end with EXIT_FAILURE
//SetHardExit(1);
std::printf("Example of C++ program using xraylib\n");
std::printf("Ca K-alpha Fluorescence Line Energy: %f\n",
LineEnergy(20,KA_LINE));
std::printf("Fe partial photoionization cs of L3 at 6.0 keV: %f\n",CS_Photo_Partial(26,L3_SHELL,6.0));
std::printf("Zr L1 edge energy: %f\n",EdgeEnergy(40,L1_SHELL));
std::printf("Pb Lalpha XRF production cs at 20.0 keV (jump approx): %f\n",CS_FluorLine(82,LA_LINE,20.0));
std::printf("Pb Lalpha XRF production cs at 20.0 keV (Kissel): %f\n",CS_FluorLine_Kissel(82,LA_LINE,20.0));
std::printf("Bi M1N2 radiative rate: %f\n",RadRate(83,M1N2_LINE));
std::printf("U M3O3 Fluorescence Line Energy: %f\n",LineEnergy(92,M3O3_LINE));
//parser test for Ca(HCO3)2 (calcium bicarbonate)
if (CompoundParser("Ca(HCO3)2",&cdtest) == 0)
return 1;
std::printf("Ca(HCO3)2 contains %i atoms and %i elements\n",cdtest.nAtomsAll,cdtest.nElements);
for (i = 0 ; i < cdtest.nElements ; i++)
std::printf("Element %i: %lf %%\n",cdtest.Elements[i],cdtest.massFractions[i]*100.0);
FREE_COMPOUND_DATA(cdtest)
//parser test for SiO2 (quartz)
if (CompoundParser("SiO2",&cdtest) == 0)
return 1;
std::printf("SiO2 contains %i atoms and %i elements\n",cdtest.nAtomsAll,cdtest.nElements);
for (i = 0 ; i < cdtest.nElements ; i++)
std::printf("Element %i: %lf %%\n",cdtest.Elements[i],cdtest.massFractions[i]*100.0);
FREE_COMPOUND_DATA(cdtest)
std::printf("Ca(HCO3)2 Rayleigh cs at 10.0 keV: %f\n",CS_Rayl_CP("Ca(HCO3)2",10.0f) );
std::printf("CS2 Refractive Index at 10.0 keV : %f - %f i\n",Refractive_Index_Re("CS2",10.0f,1.261f),Refractive_Index_Im("CS2",10.0f,1.261f));
std::printf("C16H14O3 Refractive Index at 1 keV : %f - %f i\n",Refractive_Index_Re("C16H14O3",1.0f,1.2f),Refractive_Index_Im("C16H14O3",1.0f,1.2f));
std::printf("SiO2 Refractive Index at 5 keV : %f - %f i\n",Refractive_Index_Re("SiO2",5.0f,2.65f),Refractive_Index_Im("SiO2",5.0f,2.65f));
std::printf("Compton profile for Fe at pz = 1.1 : %f\n",ComptonProfile(26,1.1f));
std::printf("M5 Compton profile for Fe at pz = 1.1 : %f\n",ComptonProfile_Partial(26,M5_SHELL,1.1f));
std::printf("K atomic level width for Fe: %f\n", AtomicLevelWidth(26,K_SHELL));
std::printf("M1->M5 Coster-Kronig transition probability for Au : %f\n",CosKronTransProb(79,FM15_TRANS));
std::printf("L1->L3 Coster-Kronig transition probability for Fe : %f\n",CosKronTransProb(26,FL13_TRANS));
std::printf("Au Ma1 XRF production cs at 10.0 keV (Kissel): %f\n", CS_FluorLine_Kissel(79,MA1_LINE,10.0f));
std::printf("Au Mb XRF production cs at 10.0 keV (Kissel): %f\n", CS_FluorLine_Kissel(79,MB_LINE,10.0f));
std::printf("Au Mg XRF production cs at 10.0 keV (Kissel): %f\n", CS_FluorLine_Kissel(79,MG_LINE,10.0f));
std::printf("Bi L2-M5M5 Auger non-radiative rate: %f\n",AugerRate(86,L2_M5M5_AUGER));
std::printf("Pb Malpha XRF production cs at 20.0 keV with cascade effect: %f\n",CS_FluorLine_Kissel(82,MA1_LINE,20.0));
std::printf("Pb Malpha XRF production cs at 20.0 keV with radiative cascade effect: %f\n",CS_FluorLine_Kissel_Radiative_Cascade(82,MA1_LINE,20.0));
std::printf("Pb Malpha XRF production cs at 20.0 keV with non-radiative cascade effect: %f\n",CS_FluorLine_Kissel_Nonradiative_Cascade(82,MA1_LINE,20.0));
std::printf("Pb Malpha XRF production cs at 20.0 keV without cascade effect: %f\n",CS_FluorLine_Kissel_no_Cascade(82,MA1_LINE,20.0));
/* Si Crystal structure */
Crystal_Struct* cryst = Crystal_GetCrystal("Si", NULL);
if (cryst == NULL) return 1;
std::printf ("Si unit cell dimensions are %f %f %f\n", cryst->a, cryst->b, cryst->c);
std::printf ("Si unit cell angles are %f %f %f\n", cryst->alpha, cryst->beta, cryst->gamma);
std::printf ("Si unit cell volume is %f\n", cryst->volume);
std::printf ("Si atoms at:\n");
std::printf (" Z fraction X Y Z\n");
Crystal_Atom* atom;
for (i = 0; i < cryst->n_atom; i++) {
atom = &cryst->atom[i];
std::printf (" %3i %f %f %f %f\n", atom->Zatom, atom->fraction, atom->x, atom->y, atom->z);
}
/* Si diffraction parameters */
std::printf ("\nSi111 at 8 KeV. Incidence at the Bragg angle:\n");
float energy = 8;
float debye_temp_factor = 1.0;
float rel_angle = 1.0;
float bragg = Bragg_angle (cryst, energy, 1, 1, 1);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
float q = Q_scattering_amplitude (cryst, energy, 1, 1, 1, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
float f0, fp, fpp;
Atomic_Factors (14, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 14) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
Complex FH, F0;
FH = Crystal_F_H_StructureFactor (cryst, energy, 1, 1, 1, debye_temp_factor, rel_angle);
std::printf (" FH(1,1,1) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
/* Diamond diffraction parameters */
cryst = Crystal_GetCrystal("Diamond", NULL);
std::printf ("\nDiamond 111 at 8 KeV. Incidence at the Bragg angle:\n");
bragg = Bragg_angle (cryst, energy, 1, 1, 1);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
q = Q_scattering_amplitude (cryst, energy, 1, 1, 1, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
Atomic_Factors (6, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 6) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
FH = Crystal_F_H_StructureFactor (cryst, energy, 1, 1, 1, debye_temp_factor, rel_angle);
std::printf (" FH(1,1,1) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
Complex FHbar = Crystal_F_H_StructureFactor (cryst, energy, -1, -1, -1, debye_temp_factor, rel_angle);
float dw = 1e10 * 2 * (R_E / cryst->volume) * (KEV2ANGST * KEV2ANGST/ (energy * energy)) *
sqrt(c_abs(c_mul(FH, FHbar))) / PI / sin(2*bragg);
std::printf (" Darwin width: %f micro-radians\n", 1e6*dw);
/* Alpha Quartz diffraction parameters */
cryst = Crystal_GetCrystal("AlphaQuartz", NULL);
std::printf ("\nAlpha Quartz 020 at 8 KeV. Incidence at the Bragg angle:\n");
bragg = Bragg_angle (cryst, energy, 0, 2, 0);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
q = Q_scattering_amplitude (cryst, energy, 0, 2, 0, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
Atomic_Factors (8, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 8) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
FH = Crystal_F_H_StructureFactor (cryst, energy, 0, 2, 0, debye_temp_factor, rel_angle);
std::printf (" FH(0,2,0) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
/* Muscovite diffraction parameters */
cryst = Crystal_GetCrystal("Muscovite", NULL);
std::printf ("\nMuscovite 331 at 8 KeV. Incidence at the Bragg angle:\n");
bragg = Bragg_angle (cryst, energy, 3, 3, 1);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
q = Q_scattering_amplitude (cryst, energy, 3, 3, 1, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
Atomic_Factors (19, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 19) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
FH = Crystal_F_H_StructureFactor (cryst, energy, 3, 3, 1, debye_temp_factor, rel_angle);
std::printf (" FH(3,3,1) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
std::printf ("\n--------------------------- END OF XRLEXAMPLE6 -------------------------------\n");
return 0;
}
void simulation_solve(simulation_t *simulation)
{
int m,s;
int i,j,k, i_max, x;
m = simulation->n_vars;
int n = m+1;
s = simulation_context_get_n_samples(simulation->nodelist->netlist->sc);
for ( k = 0 ; k < m ; ++k )
{
//pivot is col k
//find a line with the maximum k
i_max = simulation_max(simulation, k,m);
if ( cell_is_zero(simulation, &simulation->cells[i_max][k]) )
{
fprintf(stderr,"singular matrix, zero found @ row %d col %d (mean = %.1f)\n", i_max, k,
(double)cell_mean(simulation,&simulation->cells[i_max][k]));
simulation_dump(simulation);
assert(0);
}
assert(i_max >= k);
if ( i_max != k )
{
cell_t *tmp;
tmp = simulation->cells[k];
simulation->cells[k] = simulation->cells[i_max];
simulation->cells[i_max] = tmp;
}
for ( i = k + 1 ; i < m ; i ++ )
{
if ( simulation->cells[i][k].state == CELL_ZERO )
{
//fprintf(stderr,"continue\n");
continue;
}
assert( i != k);
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( j = n - 1 ; j > k ; --j )
{
// Fij = Fij - Fkj * Fik/Fkk
assert( j != k );
cell_t *line_i = simulation->cells[i];
cell_t *line_k = simulation->cells[k];
line_i[j].state = CELL_SET;
for ( x = 0 ; x < s ; ++x )
{
//assert( line_k[k].state != CELL_ZERO && !cell_is_zero(simulation,&line_k[k]));
line_i[j].values[x] = c_let(
c_sub(line_i[j].values[x],
c_mul(line_k[j].values[x],
c_div( line_i[k].values[x], line_k[k].values[x] ))));
/*
line_i[j].values[x] =
line_i[j].values[x] - line_k[j].values[x]
* ( line_i[k].values[x] / line_k[k].values[x] );
*/
/*
assert( i != k );
line_i[j].values[x] =
line_i[j].values[x] * line_k[k].values[x]
- line_k[j].values[x] * line_i[k].values[x];
*/
}
}
simulation->cells[i][k].state = CELL_ZERO;
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[i][k].values[x]=0.L;
}
}
}
//simulation_dump(simulation);
//backward elimination
//simulation_dump(simulation);
if (1)
for ( k = m - 1 ; k >= 0 ; --k )
{
//set pivot to 1
// Lk = Lk / Fk,k
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( j = k+1 ; j < n ; ++j )
{
assert( j != k );
simulation->cells[k][j].state = CELL_SET;
for ( x = 0 ; x < s ; ++x )
{
//assert( simulation->cells[k][k].state != CELL_ZERO && !cell_is_zero(simulation, &simulation->cells[k][k]));
simulation->cells[k][j].values[x] =
c_let(
c_div(simulation->cells[k][j].values[x], simulation->cells[k][k].values[x] ));
/*
simulation->cells[k][j].values[x] =
simulation->cells[k][j].values[x] / simulation->cells[k][k].values[x];
*/
}
}
simulation->cells[k][k].state = CELL_POSITIVE_UNITY;
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[k][k].values[x] = 1.L + I * 0.L;
}
}
//zeroes pivot col
for ( k = m - 1 ; k >= 0 ; --k ) // vertical pivot Fk,k
{
assert( simulation->cells[k][k].state == CELL_POSITIVE_UNITY );
// Li = Li - Lk * Fik
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( i = 0 ; i < k ; ++i) // vertical
{
assert( i != k );
for ( j = k + 1 ; j < m ; ++ j )
assert( simulation->cells[i][j].state == CELL_ZERO );
// => Fir = Fir - Fik x Fkr
// => Fi,k = 0
int result_col = n - 1;
simulation->cells[i][result_col].state = CELL_SET;
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[i][result_col].values[x] = c_let(
c_sub(simulation->cells[i][result_col].values[x],
c_mul(simulation->cells[i][k].values[x], simulation->cells[k][result_col].values[x])));
/*
simulation->cells[i][j].values[x] =
simulation->cells[i][j].values[x]
- simulation->cells[i][k].values[x] * simulation->cells[k][j].values[x];
*/
}
simulation->cells[i][k].state = CELL_ZERO;
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[i][k].values[x] = 0.L;
}
}
}
//sanity check
assert( m == simulation->n_vars );
assert( n == simulation->n_vars+1 );
for ( i = 0 ; i < m ; ++ i )
for ( j = 0 ; j < m ; ++ j )
if ( i==j )
assert(simulation->cells[i][j].state == CELL_POSITIVE_UNITY );
else
assert(simulation->cells[i][j].state == CELL_ZERO );
}
void LUdecomposition(long n, complex **A, complex *b, complex *x)
{
long i,j,k,*p;
complex akk, bk, z, sum;
complex *Ak;
/* Allocate auxiliary variables */
p = (long *)Mem(MEM_ALLOC, n, sizeof(long));
/* Gaussian elimination with partial pivoting */
for (k=0; k<n-1; k++){ /* columns of A */
/* --- Pivoting --- */
akk.re = 0.0;
akk.im = 0.0;
j = k;
for (i=k; i<n; i++){
if ( c_norm(A[i][k]) > c_norm(akk)){
akk = A[i][k];
CheckValue(FUNCTION_NAME, "A[i][k].re","", A[i][k].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "A[i][k].im","", A[i][k].im, -INFTY, INFTY);
j = i;
}
}
if (j != k){ /* swap rows j and k*/
Ak = A[k];
A[k] = A[j]; /* swap pointers*/
A[j] = Ak;
bk = b[k];
b[k] = b[j];
b[j] = bk;
}
p[k] = j; /* Keep list of permutations */
/* Sanity check */
if (akk.re != A[k][k].re && akk.im != A[k][k].im){
Die(FUNCTION_NAME, "Something went wrong with pivoting?");
return;
}
if (akk.re == 0.0 && akk.im == 0.0){
Die(FUNCTION_NAME, "Matrix singular?");
return;
}
/* Store L part */
for (i=k+1;i<n; i++){
A[i][k] = c_div(A[i][k],A[k][k]);
CheckValue(FUNCTION_NAME, "A[i][k].re","", A[i][k].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "A[i][k].im","", A[i][k].im, -INFTY, INFTY);
}
/* Update */
for (i=k+1; i<n; i++){
/* update b */
z = c_mul(A[i][k], b[k]);
b[i] = c_sub(b[i], z);
CheckValue(FUNCTION_NAME, "b[i].re","", b[i].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "b[i].im","", b[i].im, -INFTY, INFTY);
for (j=k+1; j<n; j++){
/* Update U part of A */
z = c_mul( A[i][k], A[k][j]);
A[i][j] = c_sub(A[i][j],z);
CheckValue(FUNCTION_NAME, "A[i][j].re","", A[i][j].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "A[i][j].im","", A[i][j].im, -INFTY, INFTY);
}
}
}
/* Solve x */
x[n-1] = c_div(b[n-1],A[n-1][n-1]);
for (i=n-2; i>=0; i--){
sum.re = 0.0;
sum.im = 0.0;
for (j=i+1; j<n; j++){
z = c_mul(A[i][j], x[j]);
sum = c_add(sum, z);
}
z = c_sub(b[i], sum);
x[i] = c_div(z, A[i][i]);
}
Mem(MEM_FREE, p);
/* Return */
return;
}
int main()
{
struct compoundData *cdtest;
int i;
XRayInit();
SetErrorMessages(0);
//if something goes wrong, the test will end with EXIT_FAILURE
//SetHardExit(1);
std::printf("Example of C++ program using xraylib\n");
std::printf("Density of pure Al: %f g/cm3\n", ElementDensity(13));
std::printf("Ca K-alpha Fluorescence Line Energy: %f\n",
LineEnergy(20,KA_LINE));
std::printf("Fe partial photoionization cs of L3 at 6.0 keV: %f\n",CS_Photo_Partial(26,L3_SHELL,6.0));
std::printf("Zr L1 edge energy: %f\n",EdgeEnergy(40,L1_SHELL));
std::printf("Pb Lalpha XRF production cs at 20.0 keV (jump approx): %f\n",CS_FluorLine(82,LA_LINE,20.0));
std::printf("Pb Lalpha XRF production cs at 20.0 keV (Kissel): %f\n",CS_FluorLine_Kissel(82,LA_LINE,20.0));
std::printf("Bi M1N2 radiative rate: %f\n",RadRate(83,M1N2_LINE));
std::printf("U M3O3 Fluorescence Line Energy: %f\n",LineEnergy(92,M3O3_LINE));
//parser test for Ca(HCO3)2 (calcium bicarbonate)
if ((cdtest = CompoundParser("Ca(HCO3)2")) == NULL)
return 1;
std::printf("Ca(HCO3)2 contains %g atoms, %i elements and has a molar mass of %g g/mol\n", cdtest->nAtomsAll, cdtest->nElements, cdtest->molarMass);
for (i = 0 ; i < cdtest->nElements ; i++)
std::printf("Element %i: %f %% and %g atoms\n", cdtest->Elements[i], cdtest->massFractions[i]*100.0, cdtest->nAtoms[i]);
FreeCompoundData(cdtest);
//parser test for SiO2 (quartz)
if ((cdtest = CompoundParser("SiO2")) == NULL)
return 1;
std::printf("SiO2 contains %g atoms, %i elements and has a molar mass of %g g/mol\n", cdtest->nAtomsAll, cdtest->nElements, cdtest->molarMass);
for (i = 0 ; i < cdtest->nElements ; i++)
std::printf("Element %i: %f %% and %g atoms\n", cdtest->Elements[i], cdtest->massFractions[i]*100.0, cdtest->nAtoms[i]);
FreeCompoundData(cdtest);
std::printf("Ca(HCO3)2 Rayleigh cs at 10.0 keV: %f\n",CS_Rayl_CP("Ca(HCO3)2",10.0f) );
std::printf("CS2 Refractive Index at 10.0 keV : %f - %f i\n",Refractive_Index_Re("CS2",10.0f,1.261f),Refractive_Index_Im("CS2",10.0f,1.261f));
std::printf("C16H14O3 Refractive Index at 1 keV : %f - %f i\n",Refractive_Index_Re("C16H14O3",1.0f,1.2f),Refractive_Index_Im("C16H14O3",1.0f,1.2f));
std::printf("SiO2 Refractive Index at 5 keV : %f - %f i\n",Refractive_Index_Re("SiO2",5.0f,2.65f),Refractive_Index_Im("SiO2",5.0f,2.65f));
std::printf("Compton profile for Fe at pz = 1.1 : %f\n",ComptonProfile(26,1.1f));
std::printf("M5 Compton profile for Fe at pz = 1.1 : %f\n",ComptonProfile_Partial(26,M5_SHELL,1.1f));
std::printf("K atomic level width for Fe: %f\n", AtomicLevelWidth(26,K_SHELL));
std::printf("M1->M5 Coster-Kronig transition probability for Au : %f\n",CosKronTransProb(79,FM15_TRANS));
std::printf("L1->L3 Coster-Kronig transition probability for Fe : %f\n",CosKronTransProb(26,FL13_TRANS));
std::printf("Au Ma1 XRF production cs at 10.0 keV (Kissel): %f\n", CS_FluorLine_Kissel(79,MA1_LINE,10.0f));
std::printf("Au Mb XRF production cs at 10.0 keV (Kissel): %f\n", CS_FluorLine_Kissel(79,MB_LINE,10.0f));
std::printf("Au Mg XRF production cs at 10.0 keV (Kissel): %f\n", CS_FluorLine_Kissel(79,MG_LINE,10.0f));
std::printf("Bi L2-M5M5 Auger non-radiative rate: %f\n",AugerRate(86,L2_M5M5_AUGER));
std::printf("Bi L3 Auger yield: %f\n", AugerYield(86, L3_SHELL));
std::printf("Sr anomalous scattering factor Fi at 10.0 keV: %f\n", Fi(38, 10.0));
std::printf("Sr anomalous scattering factor Fii at 10.0 keV: %f\n", Fii(38, 10.0));
char *symbol = AtomicNumberToSymbol(26);
std::printf("Symbol of element 26 is: %s\n",symbol);
xrlFree(symbol);
std::printf("Number of element Fe is: %i\n",SymbolToAtomicNumber("Fe"));
std::printf("Pb Malpha XRF production cs at 20.0 keV with cascade effect: %f\n",CS_FluorLine_Kissel(82,MA1_LINE,20.0));
std::printf("Pb Malpha XRF production cs at 20.0 keV with radiative cascade effect: %f\n",CS_FluorLine_Kissel_Radiative_Cascade(82,MA1_LINE,20.0));
std::printf("Pb Malpha XRF production cs at 20.0 keV with non-radiative cascade effect: %f\n",CS_FluorLine_Kissel_Nonradiative_Cascade(82,MA1_LINE,20.0));
std::printf("Pb Malpha XRF production cs at 20.0 keV without cascade effect: %f\n",CS_FluorLine_Kissel_no_Cascade(82,MA1_LINE,20.0));
std::printf("Al mass energy-absorption cs at 20.0 keV: %f\n", CS_Energy(13, 20.0));
std::printf("Pb mass energy-absorption cs at 40.0 keV: %f\n", CS_Energy(82, 40.0));
std::printf("CdTe mass energy-absorption cs at 40.0 keV: %f\n", CS_Energy_CP("CdTe", 40.0));
/* Si Crystal structure */
Crystal_Struct* cryst = Crystal_GetCrystal("Si", NULL);
if (cryst == NULL) return 1;
std::printf ("Si unit cell dimensions are %f %f %f\n", cryst->a, cryst->b, cryst->c);
std::printf ("Si unit cell angles are %f %f %f\n", cryst->alpha, cryst->beta, cryst->gamma);
std::printf ("Si unit cell volume is %f\n", cryst->volume);
std::printf ("Si atoms at:\n");
std::printf (" Z fraction X Y Z\n");
Crystal_Atom* atom;
for (i = 0; i < cryst->n_atom; i++) {
atom = &cryst->atom[i];
std::printf (" %3i %f %f %f %f\n", atom->Zatom, atom->fraction, atom->x, atom->y, atom->z);
}
/* Si diffraction parameters */
std::printf ("\nSi111 at 8 KeV. Incidence at the Bragg angle:\n");
double energy = 8;
double debye_temp_factor = 1.0;
double rel_angle = 1.0;
double bragg = Bragg_angle (cryst, energy, 1, 1, 1);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
double q = Q_scattering_amplitude (cryst, energy, 1, 1, 1, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
double f0, fp, fpp;
Atomic_Factors (14, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 14) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
xrlComplex FH, F0;
FH = Crystal_F_H_StructureFactor (cryst, energy, 1, 1, 1, debye_temp_factor, rel_angle);
std::printf (" FH(1,1,1) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
/* Diamond diffraction parameters */
cryst = Crystal_GetCrystal("Diamond", NULL);
std::printf ("\nDiamond 111 at 8 KeV. Incidence at the Bragg angle:\n");
bragg = Bragg_angle (cryst, energy, 1, 1, 1);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
q = Q_scattering_amplitude (cryst, energy, 1, 1, 1, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
Atomic_Factors (6, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 6) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
FH = Crystal_F_H_StructureFactor (cryst, energy, 1, 1, 1, debye_temp_factor, rel_angle);
std::printf (" FH(1,1,1) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
xrlComplex FHbar = Crystal_F_H_StructureFactor (cryst, energy, -1, -1, -1, debye_temp_factor, rel_angle);
double dw = 1e10 * 2 * (R_E / cryst->volume) * (KEV2ANGST * KEV2ANGST/ (energy * energy)) *
std::sqrt(c_abs(c_mul(FH, FHbar))) / PI / std::sin(2*bragg);
std::printf (" Darwin width: %f micro-radians\n", 1e6*dw);
/* Alpha Quartz diffraction parameters */
cryst = Crystal_GetCrystal("AlphaQuartz", NULL);
std::printf ("\nAlpha Quartz 020 at 8 KeV. Incidence at the Bragg angle:\n");
bragg = Bragg_angle (cryst, energy, 0, 2, 0);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
q = Q_scattering_amplitude (cryst, energy, 0, 2, 0, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
Atomic_Factors (8, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 8) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
FH = Crystal_F_H_StructureFactor (cryst, energy, 0, 2, 0, debye_temp_factor, rel_angle);
std::printf (" FH(0,2,0) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
/* Muscovite diffraction parameters */
cryst = Crystal_GetCrystal("Muscovite", NULL);
std::printf ("\nMuscovite 331 at 8 KeV. Incidence at the Bragg angle:\n");
bragg = Bragg_angle (cryst, energy, 3, 3, 1);
std::printf (" Bragg angle: Rad: %f Deg: %f\n", bragg, bragg*180/PI);
q = Q_scattering_amplitude (cryst, energy, 3, 3, 1, rel_angle);
std::printf (" Q Scattering amplitude: %f\n", q);
Atomic_Factors (19, energy, q, debye_temp_factor, &f0, &fp, &fpp);
std::printf (" Atomic factors (Z = 19) f0, fp, fpp: %f, %f, i*%f\n", f0, fp, fpp);
FH = Crystal_F_H_StructureFactor (cryst, energy, 3, 3, 1, debye_temp_factor, rel_angle);
std::printf (" FH(3,3,1) structure factor: (%f, %f)\n", FH.re, FH.im);
F0 = Crystal_F_H_StructureFactor (cryst, energy, 0, 0, 0, debye_temp_factor, rel_angle);
std::printf (" F0=FH(0,0,0) structure factor: (%f, %f)\n", F0.re, F0.im);
char **crystals;
crystals = Crystal_GetCrystalsList(NULL, NULL);
std::printf ("List of available crystals:\n");
for (i = 0 ; crystals[i] != NULL ; i++) {
std::printf (" Crystal %i: %s\n", i, crystals[i]);
xrlFree(crystals[i]);
}
xrlFree(crystals);
std::printf ("\n");
/* compoundDataNIST tests */
struct compoundDataNIST *cdn;
cdn = GetCompoundDataNISTByName("Uranium Monocarbide");
std::printf ("Uranium Monocarbide\n");
std::printf (" Name: %s\n", cdn->name);
std::printf (" Density: %lf g/cm3\n", cdn->density);
for (i = 0 ; i < cdn->nElements ; i++) {
std::printf(" Element %i: %lf %%\n",cdn->Elements[i],cdn->massFractions[i]*100.0);
}
FreeCompoundDataNIST(cdn);
cdn = NULL;
cdn = GetCompoundDataNISTByIndex(NIST_COMPOUND_BRAIN_ICRP);
std::printf ("NIST_COMPOUND_BRAIN_ICRP\n");
std::printf (" Name: %s\n", cdn->name);
std::printf (" Density: %lf g/cm3\n", cdn->density);
for (i = 0 ; i < cdn->nElements ; i++) {
std::printf(" Element %i: %lf %%\n",cdn->Elements[i],cdn->massFractions[i]*100.0);
}
FreeCompoundDataNIST(cdn);
cdn = NULL;
char **nistCompounds = GetCompoundDataNISTList(NULL);
std::printf ("List of available NIST compounds:\n");
for (i = 0 ; nistCompounds[i] != NULL ; i++) {
std::printf (" Compound %i: %s\n", i, nistCompounds[i]);
xrlFree(nistCompounds[i]);
}
xrlFree(nistCompounds);
std::printf ("\n");
/* radioNuclideData tests */
struct radioNuclideData *rnd;
rnd = GetRadioNuclideDataByName("109Cd");
std::printf ("109Cd\n");
std::printf (" Name: %s\n", rnd->name);
std::printf (" Z: %i\n", rnd->Z);
std::printf (" A: %i\n", rnd->A);
std::printf (" N: %i\n", rnd->N);
std::printf (" Z_xray: %i\n", rnd->Z_xray);
std::printf (" X-rays:\n");
for (i = 0 ; i < rnd->nXrays ; i++)
std::printf (" %f keV -> %f\n", LineEnergy(rnd->Z_xray, rnd->XrayLines[i]), rnd->XrayIntensities[i]);
std::printf (" Gamma rays:\n");
for (i = 0 ; i < rnd->nGammas ; i++)
std::printf (" %f keV -> %f\n", rnd->GammaEnergies[i], rnd->GammaIntensities[i]);
FreeRadioNuclideData(rnd);
rnd = GetRadioNuclideDataByIndex(RADIO_NUCLIDE_125I);
std::printf ("RADIO_NUCLIDE_125I\n");
std::printf (" Name: %s\n", rnd->name);
std::printf (" Z: %i\n", rnd->Z);
std::printf (" A: %i\n", rnd->A);
std::printf (" N: %i\n", rnd->N);
std::printf (" Z_xray: %i\n", rnd->Z_xray);
std::printf (" X-rays:\n");
for (i = 0 ; i < rnd->nXrays ; i++)
std::printf (" %f keV -> %f\n", LineEnergy(rnd->Z_xray, rnd->XrayLines[i]), rnd->XrayIntensities[i]);
std::printf (" Gamma rays:\n");
for (i = 0 ; i < rnd->nGammas ; i++)
std::printf (" %f keV -> %f\n", rnd->GammaEnergies[i], rnd->GammaIntensities[i]);
FreeRadioNuclideData(rnd);
char **radioNuclides;
radioNuclides = GetRadioNuclideDataList(NULL);
std::printf ("List of available radionuclides:\n");
for (i = 0 ; radioNuclides[i] != NULL ; i++) {
std::printf (" Radionuclide %i: %s\n", i, radioNuclides[i]);
xrlFree(radioNuclides[i]);
}
xrlFree(radioNuclides);
std::printf ("\n--------------------------- END OF XRLEXAMPLE6 -------------------------------\n");
return 0;
}
void Mie(double x,struct c_complex m,double*mu,long nangles,struct c_complex*s1,
struct c_complex*s2,double*qext,double*qsca,double*qback,double*g)
/*:34*/
#line 519 "./mie.w"
{
/*36:*/
#line 546 "./mie.w"
struct c_complex*D;
struct c_complex z1,an,bn,bnm1,anm1,qbcalc;
double*pi0,*pi1,*tau;
struct c_complex xi,xi0,xi1;
double psi,psi0,psi1;
double alpha,beta,factor;
long n,k,nstop,sign;
*qext= -1;
*qsca= -1;
*qback= -1;
*g= -1;
/*:36*/
#line 522 "./mie.w"
/*37:*/
#line 559 "./mie.w"
if(m.im> 0.0){
mie_error("This program requires m.im>=0",1);
return;
}
if(x<=0.0){
mie_error("This program requires positive sphere sizes",2);
return;
}
if(nangles<0){
mie_error("This program requires non-negative angle sizes",3);
return;
}
if(nangles<0){
mie_error("This program requires non-negative angle sizes",4);
return;
}
if((nangles> 0)&&(s1==NULL)){
mie_error("Space must be allocated for s1 if nangles!=0",5);
return;
}
if((nangles> 0)&&(s2==NULL)){
mie_error("Space must be allocated for s2if nangles!=0",6);
return;
}
if(x> 20000){
mie_error("Program not validated for spheres with x>20000",7);
return;
}
/*:37*/
#line 524 "./mie.w"
/*38:*/
#line 589 "./mie.w"
if((m.re==0)&&(x<0.1)){
small_conducting_Mie(x,m,mu,nangles,s1,s2,qext,qsca,qback,g);
return;
}
if((m.re> 0.0)&&(c_abs(m)*x<0.1)){
small_Mie(x,m,mu,nangles,s1,s2,qext,qsca,qback,g);
return;
}
/*:38*/
#line 525 "./mie.w"
/*40:*/
#line 616 "./mie.w"
nstop= floor(x+4.05*pow(x,0.33333)+2.0);
/*:40*/
#line 527 "./mie.w"
/*39:*/
#line 600 "./mie.w"
if(nangles> 0){
set_carray(s1,nangles,c_set(0.0,0.0));
set_carray(s2,nangles,c_set(0.0,0.0));
pi0= new_darray(nangles);
pi1= new_darray(nangles);
tau= new_darray(nangles);
set_darray(pi0,nangles,0.0);
set_darray(tau,nangles,0.0);
set_darray(pi1,nangles,1.0);
}
/*:39*/
#line 529 "./mie.w"
if(m.re> 0)
/*41:*/
#line 634 "./mie.w"
{
struct c_complex z;
z= c_smul(x,m);
D= new_carray(nstop+1);
if(D==NULL){
mie_error("Cannot allocate log array",8);
return;
}
if(fabs(m.im*x)<((13.78*m.re-10.8)*m.re+3.9))
Dn_up(z,nstop,D);
else
Dn_down(z,nstop,D);
}
/*:41*/
#line 531 "./mie.w"
/*42:*/
#line 671 "./mie.w"
psi0= sin(x);
psi1= psi0/x-cos(x);
xi0= c_set(psi0,cos(x));
xi1= c_set(psi1,cos(x)/x+sin(x));
*qsca= 0.0;
*g= 0.0;
*qext= 0.0;
sign= 1;
qbcalc= c_set(0.0,0.0);
anm1= c_set(0.0,0.0);
bnm1= c_set(0.0,0.0);
/*:42*/
#line 533 "./mie.w"
for(n= 1;n<=nstop;n++){
/*43:*/
#line 696 "./mie.w"
if(m.re==0.0){
an= c_sdiv(n*psi1/x-psi0,c_sub(c_smul(n/x,xi1),xi0));
bn= c_sdiv(psi1,xi1);
}else if(m.im==0.0){
z1.re= D[n].re/m.re+n/x;
an= c_sdiv(z1.re*psi1-psi0,c_sub(c_smul(z1.re,xi1),xi0));
z1.re= D[n].re*m.re+n/x;
bn= c_sdiv(z1.re*psi1-psi0,c_sub(c_smul(z1.re,xi1),xi0));
}else{
z1= c_div(D[n],m);
z1.re+= n/x;
an= c_div(c_set(z1.re*psi1-psi0,z1.im*psi1),c_sub(c_mul(z1,xi1),xi0));
z1= c_mul(D[n],m);
z1.re+= n/x;
bn= c_div(c_set(z1.re*psi1-psi0,z1.im*psi1),c_sub(c_mul(z1,xi1),xi0));
}
/*:43*/
#line 536 "./mie.w"
/*44:*/
#line 734 "./mie.w"
for(k= 0;k<nangles;k++){
factor= (2.0*n+1.0)/(n+1.0)/n;
tau[k]= n*mu[k]*pi1[k]-(n+1)*pi0[k];
alpha= factor*pi1[k];
beta= factor*tau[k];
s1[k].re+= alpha*an.re+beta*bn.re;
s1[k].im+= alpha*an.im+beta*bn.im;
s2[k].re+= alpha*bn.re+beta*an.re;
s2[k].im+= alpha*bn.im+beta*an.im;
}
for(k= 0;k<nangles;k++){
factor= pi1[k];
pi1[k]= ((2.0*n+1.0)*mu[k]*pi1[k]-(n+1.0)*pi0[k])/n;
pi0[k]= factor;
}
/*:44*/
#line 537 "./mie.w"
/*45:*/
#line 780 "./mie.w"
factor= 2.0*n+1.0;
*g+= (n-1.0/n)*(anm1.re*an.re+anm1.im*an.im+bnm1.re*bn.re+bnm1.im*bn.im);
*g+= factor/n/(n+1.0)*(an.re*bn.re+an.im*bn.im);
*qsca+= factor*(c_norm(an)+c_norm(bn));
*qext+= factor*(an.re+bn.re);
sign*= -1;
qbcalc.re+= sign*factor*(an.re-bn.re);
qbcalc.im+= sign*factor*(an.im-bn.im);
/*:45*/
#line 538 "./mie.w"
/*46:*/
#line 804 "./mie.w"
factor= (2.0*n+1.0)/x;
xi= c_sub(c_smul(factor,xi1),xi0);
xi0= xi1;
xi1= xi;
psi= factor*psi1-psi0;
psi0= psi1;
psi1= xi1.re;
anm1= an;
bnm1= bn;
/*:46*/
#line 539 "./mie.w"
}
/*47:*/
#line 817 "./mie.w"
*qsca*= 2/(x*x);
*qext*= 2/(x*x);
*g*= 4/(*qsca)/(x*x);
*qback= c_norm(qbcalc)/(x*x);
/*:47*/
#line 542 "./mie.w"
/*48:*/
#line 823 "./mie.w"
if(m.re> 0)free_carray(D);
if(nangles> 0){
free_darray(pi0);
free_darray(pi1);
free_darray(tau);
}
/*:48*/
#line 543 "./mie.w"
}
void small_Mie(double x,struct c_complex m,double*mu,
long nangles,struct c_complex*s1,
struct c_complex*s2,double*qext,double*qsca,
double*qback,double*g)
/*:22*/
#line 285 "./mie.w"
{
struct c_complex ahat1,ahat2,bhat1;
struct c_complex z0,m2,m4;
double x2,x3,x4;
if((s1==NULL)||(s2==NULL))nangles= 0;
m2= c_sqr(m);
m4= c_sqr(m2);
x2= x*x;
x3= x2*x;
x4= x2*x2;
z0.re= -m2.im;
z0.im= m2.re-1;
/*24:*/
#line 319 "./mie.w"
{struct c_complex z1,z2,z3,z4,D;
z1= c_smul(2.0/3.0,z0);
z2.re= 1.0-0.1*x2+(4.0*m2.re+5.0)*x4/1400.0;
z2.im= 4.0*x4*m2.im/1400.0;
z3= c_mul(z1,z2);
z4= c_smul(x3*(1.0-0.1*x2),z1);
D.re= 2.0+m2.re+(1-0.7*m2.re)*x2-(8.0*m4.re-385.0*m2.re+350.0)/1400.0*x4+z4.re;
D.im= m2.im+(-0.7*m2.im)*x2-(8.0*m4.im-385.0*m2.im)/1400.0*x4+z4.im;
ahat1= c_div(z3,D);
}
/*:24*/
#line 302 "./mie.w"
/*25:*/
#line 339 "./mie.w"
{
struct c_complex z2,z6,z7;
z2= c_smul(x2/45.0,z0);
z6.re= 1.0+(2.0*m2.re-5.0)*x2/70.0;
z6.im= m2.im*x2/35.0;
z7.re= 1.0-(2.0*m2.re-5.0)*x2/30.0;
z7.im= -m2.im*x2/15.0;
bhat1= c_mul(z2,c_div(z6,z7));
}
/*:25*/
#line 303 "./mie.w"
/*26:*/
#line 354 "./mie.w"
{struct c_complex z3,z8;
z3= c_smul((1.0-x2/14.0)*x2/15.0,z0);
z8.re= 2.0*m2.re+3.0-(m2.re/7.0-0.5)*x2;
z8.im= 2.0*m2.im-m2.im/7.0*x2;
ahat2= c_div(z3,z8);
}
/*:26*/
#line 304 "./mie.w"
/*28:*/
#line 396 "./mie.w"
{struct c_complex ss1;
double T;
T= c_norm(ahat1)+c_norm(bhat1)+(5.0/3.0)*c_norm(ahat2);
*qsca= 6.0*x4*T;
*qext= 6.0*x*(ahat1.re+bhat1.re+(5.0/3.0)*ahat2.re);
*g= (ahat1.re*(ahat2.re+bhat1.re)+ahat1.im*(ahat2.im+bhat1.im))/T;
ss1.re= 1.5*x2*(ahat1.re-bhat1.re-(5.0/3.0)*ahat2.re);
ss1.im= 1.5*x2*(ahat1.im-bhat1.im-(5.0/3.0)*ahat2.im);
*qback= 4*c_norm(ss1);
}
/*:28*/
#line 305 "./mie.w"
/*29:*/
#line 418 "./mie.w"
{
double muj,angle;
long j;
x3*= 1.5;
ahat1.re*= x3;
ahat1.im*= x3;
bhat1.re*= x3;
bhat1.im*= x3;
ahat2.re*= x3*(5.0/3.0);
ahat2.im*= x3*(5.0/3.0);
for(j= 0;j<nangles;j++){
muj= mu[j];
angle= 2.0*muj*muj-1.0;
s1[j].re= ahat1.re+(bhat1.re+ahat2.re)*muj;
s1[j].im= ahat1.im+(bhat1.im+ahat2.im)*muj;
s2[j].re= bhat1.re+ahat1.re*muj+ahat2.re*angle;
s2[j].im= bhat1.im+ahat1.im*muj+ahat2.im*angle;
}
}
/*:29*/
#line 306 "./mie.w"
}
complex c_pow(complex x, complex y) /* 累乗 $x^y$ */
{
return c_exp(c_mul(y, c_log(x)));
}
