int
lls_complex_btransform(const gsl_vector *L, gsl_vector_complex *c,
lls_complex_workspace *w)
{
size_t p = c->size;
if (L->size != p)
{
GSL_ERROR("L and c vectors have different sizes", GSL_EBADLEN);
}
else
{
size_t i;
for (i = 0; i < p; ++i)
{
gsl_complex ci = gsl_vector_complex_get(c, i);
double Li = gsl_vector_get(L, i);
if (Li == 0.0)
{
GSL_ERROR("L matrix is singular", GSL_ESING);
}
gsl_vector_complex_set(c, i, gsl_complex_div_real(ci, Li));
}
return GSL_SUCCESS;
}
} /* lls_complex_btransform() */
gsl_complex
gsl_linalg_complex_LU_sgndet (gsl_matrix_complex * LU, int signum)
{
size_t i, n = LU->size1;
gsl_complex phase = gsl_complex_rect((double) signum, 0.0);
for (i = 0; i < n; i++)
{
gsl_complex z = gsl_matrix_complex_get (LU, i, i);
double r = gsl_complex_abs(z);
if (r == 0)
{
phase = gsl_complex_rect(0.0, 0.0);
break;
}
else
{
z = gsl_complex_div_real(z, r);
phase = gsl_complex_mul(phase, z);
}
}
return phase;
}
/* NOTE: Assumes z is in fundamental parallelogram */
void wP_and_prime(gsl_complex z, gsl_complex tau, const gsl_complex *g, gsl_complex *p, gsl_complex *pp)
{
int N = 6; /* Enough iterations for good P, not so good P' */
int i;
gsl_complex z0;
gsl_complex z02;
gsl_complex pout, ppout;
gsl_complex ppsolve;
z = near_origin(z,tau);
z0 = gsl_complex_div_real(z,(double)(1 << N));
z02 = gsl_complex_mul(z0,z0);
/* Laurent expansion: P \approx 1/z^2 + (g2/20)z^2 + (g3/28) z^4 */
pout = gsl_complex_add(gsl_complex_inverse(z02),
gsl_complex_add(gsl_complex_mul(z02,gsl_complex_mul_real(g[0],0.05)),
gsl_complex_mul(gsl_complex_mul(z02,z02),gsl_complex_mul_real(g[1],_CONST_1_28))));
/* Laurent expansion: P' \approx -2/z^3 + g2/10z + g3/7 z^3 */
ppout = gsl_complex_add(gsl_complex_mul_real(gsl_complex_inverse(gsl_complex_mul(z0,z02)),-2.0),
gsl_complex_add(gsl_complex_mul(z0,gsl_complex_mul_real(g[0],0.1)),
gsl_complex_mul(gsl_complex_mul(z0,z02),gsl_complex_mul_real(g[1],_CONST_1_7))));
for (i=0;i<N;i++) {
P_and_Pprime_doubler(&pout, &ppout, g);
}
/* At this point ppout is a decent but not great approximation of P'(z) */
/* Instead of using it directly, we use it as a guide for which square root of */
/* (4P^3 - g2 P - g3) should be selected. */
ppsolve = gsl_complex_sqrt(
gsl_complex_sub(
gsl_complex_mul_real(gsl_complex_mul(pout,gsl_complex_mul(pout,pout)),4.0),
gsl_complex_add(gsl_complex_mul(g[0],pout),g[1])
)
);
*p = pout;
if (gsl_complex_abs(gsl_complex_sub(ppsolve,ppout)) < gsl_complex_abs(gsl_complex_add(ppsolve,ppout)))
*pp = ppsolve;
else
*pp = gsl_complex_negative(ppsolve);
}
/* NOTE: Assumes z is in fundamental parallelogram */
gsl_complex wP(gsl_complex z, gsl_complex tau, const gsl_complex *g)
{
int N = 6;
int i;
gsl_complex z0;
gsl_complex z02;
gsl_complex p;
z = near_origin(z,tau);
z0 = gsl_complex_div_real(z,(double)(1 << N));
z02 = gsl_complex_mul(z0,z0);
/* Laurent expansion: P \approx 1/z^2 + (g2/20)z^2 + (g3/28) z^4 */
p = gsl_complex_add(gsl_complex_inverse(z02),
gsl_complex_add(gsl_complex_mul(z02,gsl_complex_mul_real(g[0],0.05)),
gsl_complex_mul(gsl_complex_mul(z02,z02),gsl_complex_mul_real(g[1],_CONST_1_28))));
for (i=0;i<N;i++) {
p = P_doubler(p,g);
}
return p;
}
/**
* Returns the symmetry axis for the given matrix
*
* According to ITA, 11.2 the axis of a symmetry operation can be determined by
* solving the Eigenvalue problem \f$Wu = u\f$ for rotations or \f$Wu = -u\f$
* for rotoinversions. This is implemented using the general real non-symmetric
* eigen-problem solver provided by the GSL.
*
* @param matrix :: Matrix of a SymmetryOperation
* @return Axis of symmetry element.
*/
V3R SymmetryElementWithAxisGenerator::determineAxis(
const Kernel::IntMatrix &matrix) const {
gsl_matrix *eigenMatrix = getGSLMatrix(matrix);
gsl_matrix *identityMatrix =
getGSLIdentityMatrix(matrix.numRows(), matrix.numCols());
gsl_eigen_genv_workspace *eigenWs = gsl_eigen_genv_alloc(matrix.numRows());
gsl_vector_complex *alpha = gsl_vector_complex_alloc(3);
gsl_vector *beta = gsl_vector_alloc(3);
gsl_matrix_complex *eigenVectors = gsl_matrix_complex_alloc(3, 3);
gsl_eigen_genv(eigenMatrix, identityMatrix, alpha, beta, eigenVectors,
eigenWs);
gsl_eigen_genv_sort(alpha, beta, eigenVectors, GSL_EIGEN_SORT_ABS_DESC);
double determinant = matrix.determinant();
Kernel::V3D eigenVector;
for (size_t i = 0; i < matrix.numCols(); ++i) {
double eigenValue = GSL_REAL(gsl_complex_div_real(
gsl_vector_complex_get(alpha, i), gsl_vector_get(beta, i)));
if (fabs(eigenValue - determinant) < 1e-9) {
for (size_t j = 0; j < matrix.numRows(); ++j) {
double element = GSL_REAL(gsl_matrix_complex_get(eigenVectors, j, i));
eigenVector[j] = element;
}
}
}
eigenVector *= determinant;
double sumOfElements = eigenVector.X() + eigenVector.Y() + eigenVector.Z();
if (sumOfElements < 0) {
eigenVector *= -1.0;
}
gsl_matrix_free(eigenMatrix);
gsl_matrix_free(identityMatrix);
gsl_eigen_genv_free(eigenWs);
gsl_vector_complex_free(alpha);
gsl_vector_free(beta);
gsl_matrix_complex_free(eigenVectors);
double min = 1.0;
for (size_t i = 0; i < 3; ++i) {
double absoluteValue = fabs(eigenVector[i]);
if (absoluteValue != 0.0 &&
(eigenVector[i] < min && (absoluteValue - fabs(min)) < 1e-9)) {
min = eigenVector[i];
}
}
V3R axis;
for (size_t i = 0; i < 3; ++i) {
axis[i] = static_cast<int>(boost::math::round(eigenVector[i] / min));
}
return axis;
}
complex& complex::operator/=(const double& a)
{
_complex = gsl_complex_div_real(_complex,a);
return *this;
}
complex complex::operator/(const double& a) const
{
gsl_complex rl = gsl_complex_div_real(_complex,a);
return complex(rl);
}
int
gsl_eigen_genv_sort (gsl_vector_complex * alpha, gsl_vector * beta,
gsl_matrix_complex * evec, gsl_eigen_sort_t sort_type)
{
if (evec->size1 != evec->size2)
{
GSL_ERROR ("eigenvector matrix must be square", GSL_ENOTSQR);
}
else if (alpha->size != evec->size1 || beta->size != evec->size1)
{
GSL_ERROR ("eigenvalues must match eigenvector matrix", GSL_EBADLEN);
}
else
{
const size_t N = alpha->size;
size_t i;
for (i = 0; i < N - 1; i++)
{
size_t j;
size_t k = i;
gsl_complex ak = gsl_vector_complex_get (alpha, i);
double bk = gsl_vector_get(beta, i);
gsl_complex ek;
if (bk < GSL_DBL_EPSILON)
{
GSL_SET_COMPLEX(&ek,
GSL_SIGN(GSL_REAL(ak)) ? GSL_POSINF : GSL_NEGINF,
GSL_SIGN(GSL_IMAG(ak)) ? GSL_POSINF : GSL_NEGINF);
}
else
ek = gsl_complex_div_real(ak, bk);
/* search for something to swap */
for (j = i + 1; j < N; j++)
{
int test;
const gsl_complex aj = gsl_vector_complex_get (alpha, j);
double bj = gsl_vector_get(beta, j);
gsl_complex ej;
if (bj < GSL_DBL_EPSILON)
{
GSL_SET_COMPLEX(&ej,
GSL_SIGN(GSL_REAL(aj)) ? GSL_POSINF : GSL_NEGINF,
GSL_SIGN(GSL_IMAG(aj)) ? GSL_POSINF : GSL_NEGINF);
}
else
ej = gsl_complex_div_real(aj, bj);
switch (sort_type)
{
case GSL_EIGEN_SORT_ABS_ASC:
test = (gsl_complex_abs (ej) < gsl_complex_abs (ek));
break;
case GSL_EIGEN_SORT_ABS_DESC:
test = (gsl_complex_abs (ej) > gsl_complex_abs (ek));
break;
case GSL_EIGEN_SORT_VAL_ASC:
case GSL_EIGEN_SORT_VAL_DESC:
default:
GSL_ERROR ("invalid sort type", GSL_EINVAL);
}
if (test)
{
k = j;
ek = ej;
}
}
if (k != i)
{
/* swap eigenvalues */
gsl_vector_complex_swap_elements (alpha, i, k);
gsl_vector_swap_elements (beta, i, k);
/* swap eigenvectors */
gsl_matrix_complex_swap_columns (evec, i, k);
}
}
return GSL_SUCCESS;
}
}
void smf_filter_mce( smfFilter *filt, int noinverse, int *status ) {
/* Filter parameters */
double B_1_1;
double B_1_2;
double B_2_1;
double B_2_2;
double CLOCK_PERIOD;
double ROW_DWELL;
double NUM_ROWS=41;
double DELTA_TIME;
double SRATE;
double datechange; /* UTC MJD for change in MCE filter parameters */
AstTimeFrame *tf=NULL; /* time frame for date conversion */
size_t i; /* Loop counter */
if( *status != SAI__OK ) return;
if( !filt ) {
*status = SAI__ERROR;
errRep( FUNC_NAME, "NULL smfFilter supplied.", status );
return;
}
if( filt->ndims != 1 ) {
*status = SAI__ERROR;
errRep( "", FUNC_NAME ": function only generates filters for time-series",
status );
return;
}
if( !filt->fdims[0] ) {
*status = SAI__ERROR;
errRep( "", FUNC_NAME ": 0-length smfFilter supplied.",
status );
return;
}
if( filt->dateobs == VAL__BADD ) {
*status = SAI__ERROR;
errRep( "", FUNC_NAME ": dateobs (date of data to which filter will be "
"applied) is not set - can't determine correct MCE filter "
"parameters.", status );
return;
}
/* If filt->real is NULL, create a complex identity filter first. Similarly,
if the filter is currently only real-valued, add an imaginary part. */
if( !filt->real ) {
smf_filter_ident( filt, 1, status );
if( *status != SAI__OK ) return;
} else if( !filt->imag ) {
filt->imag = astCalloc( filt->fdims[0], sizeof(*filt->imag) );
if( *status != SAI__OK ) return;
filt->isComplex = 1;
}
/* Set up filter parameters */
tf = astTimeFrame( " " );
astSet( tf, "TimeScale=UTC" );
astSet( tf, "TimeOrigin=%s", "2011-06-03T00:00:00" );
datechange = astGetD( tf, "TimeOrigin" );
tf = astAnnul( tf );
if( filt->dateobs > datechange ) {
/* Data taken after 20110603 */
B_1_1 = -1.9712524; /* -2.*32297./2.^15. */
B_1_2 = 0.97253418; /* 2.*15934./2.^15. */
B_2_1 = -1.9337769; /* -2.*31683./2.^15. */
B_2_2 = 0.93505859; /* 2.*15320./2.^15. */
ROW_DWELL = 94.; /* time to dwell at each row (in clocks) */
msgOutiff(MSG__DEBUG, "", FUNC_NAME
": filter for data UTC MJD %lf after %lf", status,
filt->dateobs, datechange );
} else {
/* Older data */
B_1_1 = -1.9587402; /* -2.*32092./2.^15. */
B_1_2 = 0.96130371; /* 2.*15750./2.^15. */
B_2_1 = -1.9066162; /* -2.*31238./2.^15. */
B_2_2 = 0.90911865; /* 2.*14895./2.^15. */
ROW_DWELL = 128.; /* time to dwell at each row (in clocks) */
msgOutiff(MSG__DEBUG, "", FUNC_NAME
": filter for data UTC MJD %lf before %lf", status,
filt->dateobs, datechange );
}
CLOCK_PERIOD = 20E-9; /* 50 MHz clock */
NUM_ROWS = 41.; /* number of rows addressed */
DELTA_TIME = (CLOCK_PERIOD*ROW_DWELL*NUM_ROWS); /* sample length */
SRATE = (1./DELTA_TIME); /* sample rate */
/* Loop over all frequencies in the filter */
for( i=0; i<filt->fdims[0]; i++ ) {
double cos_m_o;
double sin_m_o;
double cos_m_2o;
double sin_m_2o;
double f;
gsl_complex den;
gsl_complex h1_omega;
gsl_complex h2_omega;
gsl_complex h_omega;
gsl_complex num;
gsl_complex temp;
double omega;
f = filt->df[0]*i; /* Frequency at this step */
omega = (f / SRATE)*2*AST__DPI; /* Angular frequency */
cos_m_o = cos(-omega);
sin_m_o = sin(-omega);
cos_m_2o = cos(-2*omega);
sin_m_2o = sin(-2*omega);
/*
h1_omega=(1 + 2*complex(cos_m_o,sin_m_o) + complex(cos_m_2o,sin_m_2o)) /
(1 + b_1_1*complex(cos_m_o,sin_m_o) + b_1_2 * complex(cos_m_2o,sin_m_2o))
*/
/* numerator */
GSL_SET_COMPLEX(&num, 1, 0);
GSL_SET_COMPLEX(&temp, cos_m_o, sin_m_o);
num = gsl_complex_add( num, gsl_complex_mul_real(temp, 2) );
GSL_SET_COMPLEX(&temp, cos_m_2o, sin_m_2o);
num = gsl_complex_add( num, temp );
/* denominator */
GSL_SET_COMPLEX(&den, 1, 0);
GSL_SET_COMPLEX(&temp, cos_m_o, sin_m_o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_1_1) );
GSL_SET_COMPLEX(&temp, cos_m_2o, sin_m_2o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_1_2) );
/* quotient */
h1_omega = gsl_complex_div( num, den );
/*
h2_omega=(1 + 2*complex(cos_m_o,sin_m_o) + complex(cos_m_2o,sin_m_2o)) /
(1 + b_2_1*complex(cos_m_o,sin_m_o) + b_2_2*complex(cos_m_2o,sin_m_2o))
note: we can re-use numerator from above
*/
/* denominator */
GSL_SET_COMPLEX(&den, 1, 0);
GSL_SET_COMPLEX(&temp, cos_m_o, sin_m_o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_2_1) );
GSL_SET_COMPLEX(&temp, cos_m_2o, sin_m_2o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_2_2) );
/* quotient */
h2_omega = gsl_complex_div( num, den );
/* And finally...
h_omega=h1_omega*h2_omega/2048.
*/
h_omega = gsl_complex_mul( h1_omega, gsl_complex_div_real(h2_omega,2048.) );
/* Normally we are applying the inverse of the filter to remove
its effect from the time-series. */
if( !noinverse ) {
h_omega = gsl_complex_inverse( h_omega );
}
/* Then apply this factor to the filter. */
GSL_SET_COMPLEX( &temp, filt->real[i], filt->imag[i] );
temp = gsl_complex_mul( temp, h_omega );
filt->real[i] = GSL_REAL( temp );
filt->imag[i] = GSL_IMAG( temp );
}
}
void distribuzione_luce(grano* g){
int i;
double eta, h, fi, C, S;
tilacoide* tilacoide_figlio;
gsl_matrix* L_1 = gsl_matrix_alloc(2, 2);
gsl_matrix* L_2 = gsl_matrix_alloc(2, 2);
gsl_matrix* L_3 = gsl_matrix_alloc(2, 2);
gsl_matrix* L = gsl_matrix_alloc(2, 2);
// calcolo della matrice L
// itero sui tilacoidi
// primo stroma
// carico dati nella matrice L_1
tilacoide_figlio = g->tilacoidi_figli;//[0];
eta = in.n_st * in.k_onda;
h = tilacoide_figlio->st_succ->dim;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_1, 0, 0, C);
gsl_matrix_set(L_1, 0, 1, -S/eta);
gsl_matrix_set(L_1, 1, 0, eta*S);
gsl_matrix_set(L_1, 1, 1, C);
// itero dal secondo strato in poi
for(i = 0; i < g->N; i++) {
tilacoide_figlio = g->tilacoidi_figli +i;// [i];
// MEMEBRANA
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
// LUMEN
eta = in.n_lu * in.k_onda;
h = tilacoide_figlio->lu->dim;
fi = in.n_lu * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
// MEMEBRANA
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
// stroma
eta = in.n_st * in.k_onda;
h = tilacoide_figlio->st_succ->dim;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
}
// L <- L_3 - L CALCOLATA
gsl_matrix_memcpy (L, L_3);
// calcolo di A_n ampiezza del campo rifratto nell'ultimo mezzo
double eta_1, eta_n;
eta_1 = eta_n = in.n_st*in.k_onda;
double c11 = gsl_matrix_get(L, 0, 0);
double c12 = gsl_matrix_get(L, 0, 1);
double c21 = gsl_matrix_get(L, 1, 0);
double c22 = gsl_matrix_get(L, 1, 1);
//gsl_complex A_n = gsl_complex_rect(0, 0);
gsl_complex A_n = gsl_complex_div(gsl_complex_rect(2* eta_1 * in.A_1, 0),
gsl_complex_rect(eta_1 * c11+ eta_n * c22, eta_1 * eta_n * c12 - c21));
// output - cacolo intensita nelle membrane (a ritroso)
gsl_complex v_2[2];
gsl_complex v_1[2];
// primo passo, calcolo v_n, corrisponde allo stroma
v_2[0] = A_n;
v_2[1] = gsl_complex_mul_real(A_n, eta_n);
// calcolo v_{n-1}, corrisponde alla membrana
v_1[0] = v_2[0];
v_1[1] = v_2[1];
gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
g->tilacoidi_figli[(g->N-1)].me2->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// calcolo ultimo lumen
eta = in.n_lu * in.k_onda;
//h = g->tilacoidi_figli[(g->N-1)]->lu->dim;
h = g->tilacoidi_figli[(g->N-1)].lu->dim;
fi = in.n_lu * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L, 0, 0, C);
gsl_matrix_set(L, 0, 1, -S/eta);
gsl_matrix_set(L, 1, 0, eta*S);
gsl_matrix_set(L, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// penultima membrana
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
//gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
//gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
//g->tilacoidi_figli[(g->N-1)]->me1->I_luce = intensita(A, B);
g->tilacoidi_figli[(g->N-1)].me1->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// su tutti i tilacoidi
for(i = g->N-2; i >= 0; i--) {
tilacoide_figlio = g->tilacoidi_figli+i;//[i];
// stroma
eta = in.n_st * in.k_onda;
h = tilacoide_figlio->st_succ->dim;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L, 0, 0, C);
gsl_matrix_set(L, 0, 1, -S/eta);
gsl_matrix_set(L, 1, 0, eta*S);
gsl_matrix_set(L, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
v_2[0] = v_1[0];
v_2[1] = v_1[1];
//gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
//gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
tilacoide_figlio->me2->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// calcolo ultimo lumen
eta = in.n_lu * in.k_onda;
h = tilacoide_figlio->lu->dim;
fi = in.n_lu * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L, 0, 0, C);
gsl_matrix_set(L, 0, 1, -S/eta);
gsl_matrix_set(L, 1, 0, eta*S);
gsl_matrix_set(L, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// penultima membrana
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
//gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
//gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
tilacoide_figlio->me1->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
}
// libera memoria matrici
gsl_matrix_free(L_1);
gsl_matrix_free(L_2);
gsl_matrix_free(L_3);
gsl_matrix_free(L);
}
void Spectrometer::countDispersion_BS(Medium &Osrodek, QString DataName, QProgressBar *Progress, int factor) {
//lsfgerhla
double a=Osrodek.itsBasis.getLatticeConstant();
double thickness=Osrodek.itsStructure.getThickness();
int RecVec=itsRecVectors;
int k_prec=itsK_Precision;
double wi=itsFrequencies[0];
double w_prec=itsFrequencies[1];
double wf=itsFrequencies[2];
int half=3*(2*RecVec+1)*(2*RecVec+1);
int dimension=6*(2*RecVec+1)*(2*RecVec+1);
int EigValStrNumber=6*(2*RecVec+1)*(2*RecVec+1);
int EigValNumber=9*(2*RecVec+1)*(2*RecVec+1);
std::ofstream plik;
DataName="results/"+ DataName + ".dat";
QByteArray bytes = DataName.toAscii();
const char * CDataName = bytes.data();
plik.open(CDataName);
//inicjalizacje wektorów i macierzy
gsl_matrix *gammaA=gsl_matrix_calloc(dimension, dimension);
gsl_matrix *gammaB=gsl_matrix_calloc(dimension, dimension);
gsl_matrix *gammaC=gsl_matrix_calloc(dimension, dimension);
gsl_matrix *gammaD=gsl_matrix_calloc(dimension, dimension);
gsl_eigen_genv_workspace *wspce=gsl_eigen_genv_alloc(dimension);
gsl_eigen_genv_workspace *wspce2=gsl_eigen_genv_alloc(dimension);
gsl_vector_complex *StrAlpha =gsl_vector_complex_alloc(dimension);
gsl_vector *StrBeta = gsl_vector_alloc(dimension);
gsl_matrix_complex *StrEigenVec=gsl_matrix_complex_calloc(dimension, dimension);
gsl_vector_complex *BAlpha =gsl_vector_complex_alloc(dimension);
gsl_vector *BBeta = gsl_vector_alloc(dimension);
gsl_matrix_complex *BasisEigenVec=gsl_matrix_complex_calloc(dimension, dimension);
gsl_matrix_complex *ChosenVectors = gsl_matrix_complex_calloc(half, EigValNumber);
gsl_vector_complex *ChosenValues = gsl_vector_complex_calloc(EigValNumber);
gsl_matrix_complex *Boundaries=gsl_matrix_complex_calloc(EigValNumber, EigValNumber);
double kx, ky, krokx, kroky, boundary_x, boundary_y;
double k_zred, k_zred0;
double krok = M_PI/(k_prec*a);
for (int droga=0; droga<3; droga++) {
//int droga = 1;
if (droga==0) //droga M->Gamma
{
kx=-M_PI/a;
krokx=krok;
boundary_x=0;
ky=-M_PI/a;
kroky=krok;
boundary_y=0;
k_zred0=-1*sqrt(pow(kx/(2*M_PI/a), 2)+pow(ky/(2*M_PI/a), 2));
}
else if (droga==1)
{
kx=0; //droga Gamma->X
krokx=krok;
boundary_x=M_PI/a;
ky=0;
kroky=0;
boundary_y=0;
k_zred0=sqrt(2)/2;
//k_zred0=0;
}
else if (droga==2)
{
kx=M_PI/a; //Droga X->M
krokx=0;
boundary_x=M_PI/a;
ky=0;
kroky=krok;
boundary_y=M_PI/a;
k_zred0=sqrt(2)/2;
}
//petla dla wektorów falowych
for (; kx <= boundary_x && ky <= boundary_y; kx=kx+krokx, ky=ky+kroky)
{
if (droga==0) {
k_zred = abs(k_zred0 + sqrt( pow(kx/(2*M_PI/a), 2)+pow(ky/(2*M_PI/a), 2)));
} else {
k_zred = k_zred0 + kx/(2*M_PI/a) + ky/(2*M_PI/a);
}
int postep=int(100*k_zred/1.7);
Progress->setValue(postep);
Progress->update();
QApplication::processEvents();
//pętla dla częstości w
for (double w=wi; w<wf; w=w+w_prec)
{
gsl_matrix_complex_set_all(Boundaries, gsl_complex_rect (0,0)); //ustawienie wartosci wyznacznika na 0
gsl_matrix_set_all(gammaA, 0);
gsl_matrix_set_all(gammaB, 0);
gsl_matrix_set_all(gammaC, 0);
gsl_matrix_set_all(gammaD, 0);
gsl_vector_complex_set_all(StrAlpha, gsl_complex_rect (0,0));
gsl_vector_set_all(BBeta, 0);
gsl_vector_complex_set_all(BAlpha, gsl_complex_rect (0,0));
gsl_vector_set_all(StrBeta, 0);
gsl_matrix_complex_set_all(BasisEigenVec, gsl_complex_rect (0,0));
gsl_matrix_complex_set_all(StrEigenVec, gsl_complex_rect (0,0));
gsl_matrix_complex_set_all(ChosenVectors, gsl_complex_rect (0,0));
gsl_vector_complex_set_all(ChosenValues, gsl_complex_rect (0,0));
//gammaA,B dla struktury
//gammaA,B dla struktury
/*
S - numeruje transformaty tensora sprężystoci i gestosci
i - numeruje wiersze macierzy
j - numeruje kolumny macierzy
half - druga polowa macierzy
*/
for(int Nx=-RecVec, i=0, S=0; Nx<=RecVec; Nx++) {
for(int Ny=-RecVec; Ny<=RecVec; Ny++, i=i+3) {
for(int Nx_prim=-RecVec, j=0; Nx_prim<=RecVec; Nx_prim++) {
for(int Ny_prim=-RecVec; Ny_prim<=RecVec; Ny_prim++, j=j+3, S++) {
double Elasticity[6][6];
itsRecStructureSubstance[S].getElasticity(Elasticity);
double Density=itsRecStructureSubstance[S].getDensity();
double gx=2*M_PI*Nx/a;
double gy=2*M_PI*Ny/a;
double gx_prim=2*M_PI*Nx_prim/a;
double gy_prim=2*M_PI*Ny_prim/a;
gsl_matrix_set(gammaA, i, j, Elasticity[3][3]);
gsl_matrix_set(gammaA, i+1, j+1, Elasticity[3][3]);
gsl_matrix_set(gammaA, i+2, j+2, Elasticity[0][0]);
gsl_matrix_set(gammaB, i+2, j, -Elasticity[0][1]*(kx+gx_prim)-Elasticity[3][3]*(kx+gx));
gsl_matrix_set(gammaB, i+2, j+1, -Elasticity[0][1]*(ky+gy_prim)-Elasticity[3][3]*(ky+gy));
gsl_matrix_set(gammaB, i, j+2, -Elasticity[0][1]*(kx+gx)-Elasticity[3][3]*(kx+gx_prim));
gsl_matrix_set(gammaB, i+1, j+2, -Elasticity[0][1]*(ky+gy)-Elasticity[3][3]*(ky+gy_prim));
gsl_matrix_set(gammaB, i, j+half, -Elasticity[0][0]*(kx+gx)*(kx+gx_prim)-Elasticity[3][3]*(ky+gy)*(ky+gy_prim)+Density*w*w);
gsl_matrix_set(gammaB, i+1, j+half, -Elasticity[0][1]*(kx+gx_prim)*(ky+gy)-Elasticity[3][3]*(ky+gy_prim)*(kx+gx));
gsl_matrix_set(gammaB, i, j+half+1, -Elasticity[0][1]*(ky+gy_prim)*(kx+gx)-Elasticity[3][3]*(kx+gx_prim)*(ky+gy));
gsl_matrix_set(gammaB, i+1, j+half+1, -Elasticity[0][0]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
gsl_matrix_set(gammaB, i+2, j+half+2, -Elasticity[3][3]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
if (i==j) {
gsl_matrix_set(gammaA, i+half, j+half, 1);
gsl_matrix_set(gammaA, i+half+1, j+half+1, 1);
gsl_matrix_set(gammaA, i+half+2, j+half+2, 1);
gsl_matrix_set(gammaB, i+half, j, 1);
gsl_matrix_set(gammaB, i+half+1, j+1, 1);
gsl_matrix_set(gammaB, i+half+2, j+2, 1);
}
}
}
}
}
//rozwiazanie zagadnienienia własnego
gsl_eigen_genv(gammaB, gammaA, StrAlpha, StrBeta, StrEigenVec, wspce);
//gammaC,D dla Podłoża
for(int Nx=-RecVec, i=0, S=0; Nx<=RecVec; Nx++) {
for(int Ny=-RecVec; Ny<=RecVec; Ny++, i=i+3) {
for(int Nx_prim=-RecVec, j=0; Nx_prim<=RecVec; Nx_prim++) {
for(int Ny_prim=-RecVec; Ny_prim<=RecVec; Ny_prim++, j=j+3, S++) {
double Elasticity[6][6];
itsRecBasisSubstance[S].getElasticity(Elasticity);
double Density=itsRecBasisSubstance[S].getDensity();
double gx=2*M_PI*Nx/a;
double gy=2*M_PI*Ny/a;
double gx_prim=2*M_PI*Nx_prim/a;
double gy_prim=2*M_PI*Ny_prim/a;
gsl_matrix_set(gammaC, i, j, Elasticity[3][3]);
gsl_matrix_set(gammaC, i+1, j+1, Elasticity[3][3]);
gsl_matrix_set(gammaC, i+2, j+2, Elasticity[0][0]);
gsl_matrix_set(gammaD, i+2, j, -Elasticity[0][1]*(kx+gx_prim)-Elasticity[3][3]*(kx+gx));
gsl_matrix_set(gammaD, i+2, j+1, -Elasticity[0][1]*(ky+gy_prim)-Elasticity[3][3]*(ky+gy));
gsl_matrix_set(gammaD, i, j+2, -Elasticity[0][1]*(kx+gx)-Elasticity[3][3]*(kx+gx_prim));
gsl_matrix_set(gammaD, i+1, j+2, -Elasticity[0][1]*(ky+gy)-Elasticity[3][3]*(ky+gy_prim));
gsl_matrix_set(gammaD, i, j+half, -Elasticity[0][0]*(kx+gx)*(kx+gx_prim)-Elasticity[3][3]*(ky+gy)*(ky+gy_prim)+Density*w*w);
gsl_matrix_set(gammaD, i+1, j+half, -Elasticity[0][1]*(kx+gx_prim)*(ky+gy)-Elasticity[3][3]*(ky+gy_prim)*(kx+gx));
gsl_matrix_set(gammaD, i, j+half+1, -Elasticity[0][1]*(ky+gy_prim)*(kx+gx)-Elasticity[3][3]*(kx+gx_prim)*(ky+gy));
gsl_matrix_set(gammaD, i+1, j+half+1, -Elasticity[0][0]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
gsl_matrix_set(gammaD, i+2, j+half+2, -Elasticity[3][3]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
if (i==j) {
gsl_matrix_set(gammaC, i+half, j+half, 1);
gsl_matrix_set(gammaC, i+half+1, j+half+1, 1);
gsl_matrix_set(gammaC, i+half+2, j+half+2, 1);
gsl_matrix_set(gammaD, i+half, j, 1);
gsl_matrix_set(gammaD, i+half+1, j+1, 1);
gsl_matrix_set(gammaD, i+half+2, j+2, 1);
}
}
}
}
}
//rozwiazanie zagadnienienia własnego
gsl_eigen_genv(gammaD, gammaC, BAlpha, BBeta, BasisEigenVec, wspce2);
double imagL, realL; //części Re i Im wartości własnych
int n=0;
for (int i = 0; i<dimension; i++)
{
//przepisanie wartości i wektorów własnych struktury do macierzy Chosen*
gsl_complex StrValue;
StrValue= gsl_complex_div_real(gsl_vector_complex_get(StrAlpha, i), gsl_vector_get(StrBeta,i));
gsl_vector_complex_set(ChosenValues, i, StrValue);
for (int j = half, m=0; j < dimension; j++, m++)
{
gsl_matrix_complex_set(ChosenVectors, m, i, gsl_matrix_complex_get(StrEigenVec, j, i));
}
//wybieranie odpowiednich wartości i wektorów własnych dla podłoża i przepisanie do macierzy Chosen*
gsl_complex BValue;
BValue= gsl_complex_div_real(gsl_vector_complex_get(BAlpha, i), gsl_vector_get(BBeta,i));
imagL=GSL_IMAG(BValue);
realL=GSL_REAL(BValue);
if (imagL > 0.00001 && n+EigValStrNumber<EigValNumber) //warunek na wartości własne && żeby nie było ich więcej niż połowa
{
gsl_vector_complex_set(ChosenValues, n+EigValStrNumber, BValue); //wybranie wartości własnej
for (int j = half, m=0; j < dimension; j++, m++)
{
gsl_matrix_complex_set(ChosenVectors, m, n+EigValStrNumber, gsl_complex_mul_real(gsl_matrix_complex_get(BasisEigenVec, j, i), -1)); //wybranie drugiej połowy wektora własnego
}
n++;
}
}
if (n+EigValStrNumber<EigValNumber)
{
for (int i = 0; i<dimension; i++)
{
gsl_complex BValue;
BValue= gsl_complex_div_real(gsl_vector_complex_get(BAlpha, i), gsl_vector_get(BBeta,i));
imagL=GSL_IMAG(BValue);
realL=GSL_REAL(BValue);
if (imagL < 0.00001 && imagL > -0.00001 && realL < -0.00001 && n+EigValStrNumber<EigValNumber) //warunek na wartości własne && żeby nie było ich więcej niż połowa
{
gsl_vector_complex_set(ChosenValues, n+EigValStrNumber, BValue); //wybranie wartości własnej
for (int j = half, m=0; j < dimension; j++, m++)
{
gsl_matrix_complex_set(ChosenVectors, m, n+EigValStrNumber, gsl_complex_mul_real(gsl_matrix_complex_get(BasisEigenVec, j, i), -1)); //wybranie drugiej połowy wektora własnego
}
n++;
}
}
}
//wyznacznik warunków brzegowych - konstrukcja
/*
S, S' - numerujš transformaty tensora sprężystoci
i - numeruje wektory własne A w pętli dla G
j - numeruje warunki brzegowe dla kolejnych wektorow odwrotnych G
k - numeruje wektory własne A w pętli dla G'
L - numeruje wartoci własne
*/
for (int Nx=-RecVec, S=0, S_prim=0, i=0, j=0; Nx <= RecVec; Nx++) {
for (int Ny=-RecVec; Ny <= RecVec; Ny++, j=j+9, i=i+3) {
for (int L=0; L < EigValNumber; L++) {
S_prim = S;
for (int Nx_prim=-RecVec, k=0; Nx_prim <= RecVec; Nx_prim++) {
for (int Ny_prim=-RecVec; Ny_prim <= RecVec; Ny_prim++, S_prim++, k=k+3) {
double StrElasticity[6][6];
itsRecStructureSubstance[S_prim].getElasticity(StrElasticity);
double BasisElasticity[6][6];
itsRecBasisSubstance[S_prim].getElasticity(BasisElasticity);
double gx_prim=2*M_PI*Nx_prim/a;
double gy_prim=2*M_PI*Ny_prim/a;
if (L < EigValStrNumber)
{
//eksponens
gsl_complex exponent = gsl_complex_polar(exp(GSL_IMAG(gsl_vector_complex_get(ChosenValues, L))*thickness), -1*GSL_REAL(gsl_vector_complex_get(ChosenValues, L))*thickness);
//warunki zerowania się naprężenia na powierzchni
gsl_complex w1 = gsl_complex_mul_real(exponent, StrElasticity[3][3]);
gsl_complex w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (kx+gx_prim));
gsl_complex w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k, L));
gsl_complex BCjL = gsl_complex_add(gsl_complex_mul(gsl_complex_add(w2, w3), w1), gsl_matrix_complex_get(Boundaries, j, L));
gsl_matrix_complex_set(Boundaries, j, L, BCjL);
w1 = gsl_complex_mul_real(exponent, StrElasticity[3][3]);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+1, L));
BCjL = gsl_complex_add(gsl_complex_mul(gsl_complex_add(w2, w3), w1), gsl_matrix_complex_get(Boundaries, j+1, L));
gsl_matrix_complex_set(Boundaries, j+1, L, BCjL);
w1 = gsl_complex_mul_real(exponent, StrElasticity[0][0]);
gsl_complex w11 = gsl_complex_mul_real(exponent, StrElasticity[0][1]);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k, L), (kx+gx_prim));
gsl_complex w22 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+1, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+2, L));
gsl_complex w4 = gsl_complex_add(gsl_complex_mul(gsl_complex_add(w2, w22), w11), gsl_complex_mul(w3, w1));
BCjL = gsl_complex_add(w4, gsl_matrix_complex_get(Boundaries, j+2, L));
gsl_matrix_complex_set(Boundaries, j+2, L, BCjL);
//warunki równości naprężeń na granicy ośrodków - część dla struktury
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (kx+gx_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k, L));
BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), StrElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+3, L));
gsl_matrix_complex_set(Boundaries, j+3, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+1, L));
BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), StrElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+4, L));
gsl_matrix_complex_set(Boundaries, j+4, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k, L), (kx+gx_prim));
w22 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+1, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+2, L));
w4 = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w22), StrElasticity[0][1]), gsl_complex_mul_real(w3, StrElasticity[0][0]));
BCjL = gsl_complex_add(w4, gsl_matrix_complex_get(Boundaries, j+5, L));
gsl_matrix_complex_set(Boundaries, j+5, L, BCjL);
} else {
//warunki równości naprężeń na granicy ośrodków - część dla podłoża
gsl_complex w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (kx+gx_prim));
gsl_complex w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k, L));
gsl_complex BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), BasisElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+3, L));
gsl_matrix_complex_set(Boundaries, j+3, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+1, L));
BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), BasisElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+4, L));
gsl_matrix_complex_set(Boundaries, j+4, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k, L), (kx+gx_prim));
gsl_complex w22 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+1, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+2, L));
gsl_complex w4 = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w22), BasisElasticity[0][1]), gsl_complex_mul_real(w3, BasisElasticity[0][0]));
BCjL = gsl_complex_add(w4, gsl_matrix_complex_get(Boundaries, j+5, L));
gsl_matrix_complex_set(Boundaries, j+5, L, BCjL);
}
}
}
// warunek równości wychyleń na granicy ośrodków
gsl_matrix_complex_set(Boundaries, j+6, L, gsl_matrix_complex_get(ChosenVectors, i, L));
gsl_matrix_complex_set(Boundaries, j+7, L, gsl_matrix_complex_get(ChosenVectors, i+1, L));
gsl_matrix_complex_set(Boundaries, j+8, L, gsl_matrix_complex_get(ChosenVectors, i+2, L));
}
S=S_prim;
}
}
//skalowanie macierzy Boundaries
gsl_complex scale=gsl_complex_rect(pow(10, factor), 0);
gsl_matrix_complex_scale(Boundaries, scale);
//obliczenie wyznacznika z Boundaries
gsl_permutation *Bpermutation = gsl_permutation_alloc(EigValNumber);
int Bsignum;
gsl_linalg_complex_LU_decomp(Boundaries, Bpermutation, &Bsignum);
double DetVal = gsl_linalg_complex_LU_lndet(Boundaries);
//usuwanie NaN
if(DetVal != DetVal) DetVal = 0;
//zapisanie wartości do pliku
plik << k_zred << "\t" << w << "\t" << DetVal << "\n";
}
plik << "\n";
}
}
plik.close();
gsl_matrix_free(gammaA);
gsl_matrix_free(gammaB);
gsl_vector_free(BBeta);
gsl_vector_free(StrBeta);
gsl_matrix_free(gammaC);
gsl_matrix_free(gammaD);
gsl_vector_complex_free(StrAlpha);
gsl_vector_complex_free(BAlpha);
gsl_eigen_genv_free(wspce);
gsl_eigen_genv_free(wspce2);
gsl_matrix_complex_free(Boundaries);
gsl_matrix_complex_free(ChosenVectors);
gsl_vector_complex_free(ChosenValues);
}
int
main(int argc, char *argv[])
{
gen_workspace *gen_workspace_p;
lapack_workspace *lapack_workspace_p;
size_t N;
int c;
int lower;
int upper;
int incremental;
size_t nmat;
gsl_matrix *A, *B;
gsl_rng *r;
int s;
int compute_schur;
size_t i;
gsl_ieee_env_setup();
gsl_rng_env_setup();
N = 30;
lower = -10;
upper = 10;
incremental = 0;
nmat = 0;
compute_schur = 0;
while ((c = getopt(argc, argv, "ic:n:l:u:z")) != (-1))
{
switch (c)
{
case 'i':
incremental = 1;
break;
case 'n':
N = strtol(optarg, NULL, 0);
break;
case 'l':
lower = strtol(optarg, NULL, 0);
break;
case 'u':
upper = strtol(optarg, NULL, 0);
break;
case 'c':
nmat = strtoul(optarg, NULL, 0);
break;
case 'z':
compute_schur = 1;
break;
case '?':
default:
printf("usage: %s [-i] [-z] [-n size] [-l lower-bound] [-u upper-bound] [-c num]\n", argv[0]);
exit(1);
break;
} /* switch (c) */
}
A = gsl_matrix_alloc(N, N);
B = gsl_matrix_alloc(N, N);
gen_workspace_p = gen_alloc(N, compute_schur);
lapack_workspace_p = lapack_alloc(N);
r = gsl_rng_alloc(gsl_rng_default);
if (incremental)
{
make_start_matrix(A, lower);
/* we need B to be non-singular */
make_random_integer_matrix(B, r, lower, upper);
}
fprintf(stderr, "testing N = %d", N);
if (incremental)
fprintf(stderr, " incrementally");
else
fprintf(stderr, " randomly");
fprintf(stderr, " on element range [%d, %d]", lower, upper);
if (compute_schur)
fprintf(stderr, ", with Schur vectors");
fprintf(stderr, "\n");
while (1)
{
if (nmat && (count >= nmat))
break;
++count;
if (!incremental)
{
make_random_matrix(A, r, lower, upper);
make_random_matrix(B, r, lower, upper);
}
else
{
s = inc_matrix(A, lower, upper);
if (s)
break; /* all done */
make_random_integer_matrix(B, r, lower, upper);
}
/*if (count != 89120)
continue;*/
/* make copies of matrices */
gsl_matrix_memcpy(gen_workspace_p->A, A);
gsl_matrix_memcpy(gen_workspace_p->B, B);
gsl_matrix_transpose_memcpy(lapack_workspace_p->A, A);
gsl_matrix_transpose_memcpy(lapack_workspace_p->B, B);
/* compute eigenvalues with LAPACK */
s = lapack_proc(lapack_workspace_p);
if (s != GSL_SUCCESS)
{
printf("LAPACK failed, case %lu\n", count);
exit(1);
}
#if 0
print_matrix(A, "A");
print_matrix(B, "B");
gsl_matrix_transpose(lapack_workspace_p->A);
gsl_matrix_transpose(lapack_workspace_p->B);
print_matrix(lapack_workspace_p->A, "S_lapack");
print_matrix(lapack_workspace_p->B, "T_lapack");
#endif
/* compute eigenvalues with GSL */
s = gen_proc(gen_workspace_p);
if (s != GSL_SUCCESS)
{
printf("=========== CASE %lu ============\n", count);
printf("Failed to converge: found %u eigenvalues\n",
gen_workspace_p->n_evals);
print_matrix(A, "A");
print_matrix(B, "B");
print_matrix(gen_workspace_p->A, "Af");
print_matrix(gen_workspace_p->B, "Bf");
print_matrix(lapack_workspace_p->A, "Ae");
print_matrix(lapack_workspace_p->B, "Be");
exit(1);
}
#if 0
print_matrix(gen_workspace_p->A, "S_gsl");
print_matrix(gen_workspace_p->B, "T_gsl");
#endif
/* compute alpha / beta vectors */
for (i = 0; i < N; ++i)
{
double beta;
gsl_complex alpha, z;
beta = gsl_vector_get(gen_workspace_p->beta, i);
if (beta == 0.0)
GSL_SET_COMPLEX(&z, GSL_POSINF, GSL_POSINF);
else
{
alpha = gsl_vector_complex_get(gen_workspace_p->alpha, i);
z = gsl_complex_div_real(alpha, beta);
}
gsl_vector_complex_set(gen_workspace_p->evals, i, z);
beta = gsl_vector_get(lapack_workspace_p->beta, i);
GSL_SET_COMPLEX(&alpha,
lapack_workspace_p->alphar[i],
lapack_workspace_p->alphai[i]);
if (beta == 0.0)
GSL_SET_COMPLEX(&z, GSL_POSINF, GSL_POSINF);
else
z = gsl_complex_div_real(alpha, beta);
gsl_vector_complex_set(lapack_workspace_p->evals, i, z);
gsl_vector_complex_set(lapack_workspace_p->alpha, i, alpha);
}
#if 0
gsl_sort_vector(gen_workspace_p->beta);
gsl_sort_vector(lapack_workspace_p->beta);
sort_complex_vector(gen_workspace_p->alpha);
sort_complex_vector(lapack_workspace_p->alpha);
s = test_alpha(gen_workspace_p->alpha,
lapack_workspace_p->alpha,
A,
B,
"gen",
"lapack");
s = test_beta(gen_workspace_p->beta,
lapack_workspace_p->beta,
A,
B,
"gen",
"lapack");
#endif
#if 1
sort_complex_vector(gen_workspace_p->evals);
sort_complex_vector(lapack_workspace_p->evals);
s = test_evals(gen_workspace_p->evals,
lapack_workspace_p->evals,
A,
B,
"gen",
"lapack");
#endif
if (compute_schur)
{
test_schur(A,
gen_workspace_p->A,
gen_workspace_p->Q,
gen_workspace_p->Z);
test_schur(B,
gen_workspace_p->B,
gen_workspace_p->Q,
gen_workspace_p->Z);
}
}
gsl_matrix_free(A);
gsl_matrix_free(B);
gen_free(gen_workspace_p);
lapack_free(lapack_workspace_p);
if (r)
gsl_rng_free(r);
return 0;
} /* main() */
