int wrap_gsl_matrix_complex_scale(gsl_matrix_complex *a, pure_expr *x)
{
double d;
gsl_complex z;
if (pure_is_double(x, &d)) {
z.dat[0] = d; z.dat[1] = 0.0;
return gsl_matrix_complex_scale(a, z);
} else if (pure_is_complex(x, z.dat))
return gsl_matrix_complex_scale(a, z);
else
return 0;
}
static int _equalf(CMATRIX *a, double f)
{
bool result;
if (COMPLEX(a))
{
if (f == 0.0)
return gsl_matrix_complex_isnull(CMAT(a));
gsl_matrix_complex *m = gsl_matrix_complex_alloc(WIDTH(a), HEIGHT(a));
gsl_matrix_complex_set_identity(m);
gsl_matrix_complex_scale(m, gsl_complex_rect(f, 0));
result = gsl_matrix_complex_equal(CMAT(a), m);
gsl_matrix_complex_free(m);
}
else
{
if (f == 0.0)
return gsl_matrix_isnull(MAT(a));
gsl_matrix *m = gsl_matrix_alloc(WIDTH(a), HEIGHT(a));
gsl_matrix_set_identity(m);
gsl_matrix_scale(m, f);
result = gsl_matrix_equal(MAT(a), m);
gsl_matrix_free(m);
}
return result;
}
/*
* Calculate the matrix exponent of A and store in eA.
* Algorithm: Truncated Talyor series.
*
* WARNING: Large errors possible and it's slow.
*/
int
gsl_ext_expm_complex(gsl_matrix_complex *A, gsl_matrix_complex *eA)
{
int i;
gsl_complex alpha, beta, z;
gsl_matrix_complex *I, *T;
I = gsl_matrix_complex_alloc(A->size1, A->size2);
T = gsl_matrix_complex_alloc(A->size1, A->size2);
GSL_SET_COMPLEX(&alpha, 1.0, 0.0);
GSL_SET_COMPLEX(&beta, 0.0, 0.0);
gsl_matrix_complex_set_identity(I);
gsl_matrix_complex_set_identity(eA);
for (i = 50; i > 0; i--)
{
GSL_SET_COMPLEX(&z, 1.0 / i, 0.0);
gsl_matrix_complex_scale(eA, z);
gsl_blas_zgemm(CblasNoTrans, CblasNoTrans, alpha, eA, A, beta, T);
gsl_matrix_complex_add(T, I);
gsl_matrix_complex_memcpy(eA, T);
}
return 0;
}
/*
* FUNCTION
* Name: entropy_of_state
* Description: Calculate the Von Neumann entropy of state 'rho'
*
*/
double entropy_of_state ( const gsl_vector* rho )
{
double entr = 0 ;
/* Finding the eigenvalues */
gsl_eigen_herm_workspace* rho_ei = gsl_eigen_herm_alloc(2);
gsl_matrix_complex* dens = gsl_matrix_complex_calloc (2,2);
gsl_matrix_complex_set (dens, 0, 0, gsl_complex_rect(1+VECTOR(rho, 3),0));
gsl_matrix_complex_set (dens,0,1,gsl_complex_rect(VECTOR(rho,1),-VECTOR(rho,2)));
gsl_matrix_complex_set (dens,1,0,gsl_complex_rect(VECTOR(rho,1),VECTOR(rho,2)));
gsl_matrix_complex_set (dens,1,1,gsl_complex_rect(1-VECTOR(rho,3),0));
gsl_matrix_complex_scale (dens, gsl_complex_rect(0.5,0));
gsl_vector* eigenvalues = gsl_vector_calloc(2) ;
gsl_eigen_herm (dens, eigenvalues, rho_ei) ;
/* Calculating entropy */
double norm = gsl_hypot3( VECTOR(rho,1), VECTOR(rho,2), VECTOR(rho,3) ) ;
if ( gsl_fcmp(norm, 1, 1e-9) > 0 )
entr = 0 ;
else
entr = - (VECTOR(eigenvalues,0)*gsl_sf_log(VECTOR(eigenvalues,0)) +
VECTOR(eigenvalues,1)*gsl_sf_log(VECTOR(eigenvalues,1))) ;
return (entr);
} /* ----- end of function entropy_of_state ----- */
void
qdpack_matrix_scale(qdpack_matrix_t *op, qdpack_complex z)
{
if (op == NULL)
return;
gsl_matrix_complex_scale(op->data, z);
}
static void matrix_complex_add_identity(gsl_matrix_complex *m, gsl_complex c)
{
gsl_matrix_complex *id = gsl_matrix_complex_alloc(m->size1, m->size2);
gsl_matrix_complex_set_identity(id);
gsl_matrix_complex_scale(id, c);
gsl_matrix_complex_add(m, id);
gsl_matrix_complex_free(id);
}
static int
do_ccmul(lua_State *L, mMatComplex *a, double b_re, double b_im)
{
mMatComplex *r = qlua_newMatComplex(L, a->l_size, a->r_size);
gsl_complex z;
gsl_matrix_complex_memcpy(r->m, a->m);
GSL_SET_COMPLEX(&z, b_re, b_im);
gsl_matrix_complex_scale(r->m, z);
return 1;
}
static CMATRIX *_divo(CMATRIX *a, void *b, bool invert)
{
bool complex = COMPLEX(a);
CMATRIX *m;
gsl_complex c;
if (!GB.Is(b, CLASS_Complex))
return NULL;
c = ((CCOMPLEX *)b)->number;
if (invert)
{
void *inv = matrix_invert(MAT(a), complex);
if (!inv)
{
GB.Error(GB_ERR_ZERO);
return NULL;
}
m = MATRIX_create_from(inv, complex);
}
else
{
if (GSL_REAL(c) == 0 && GSL_IMAG(c) == 0)
{
GB.Error(GB_ERR_ZERO);
return NULL;
}
c = gsl_complex_inverse(c);
m = MATRIX_make(a);
}
MATRIX_ensure_complex(m);
gsl_matrix_complex_scale(CMAT(m), c);
return m;
}
static int _equalo(CMATRIX *a, void *b)
{
bool result;
CCOMPLEX *c;
if (!GB.Is(b, CLASS_Complex))
return -1;
c = (CCOMPLEX *)b;
if (GSL_IMAG(c->number) == 0.0)
return _equalf(a, GSL_REAL(c->number));
if (!COMPLEX(a))
return FALSE;
gsl_matrix_complex *m = gsl_matrix_complex_alloc(WIDTH(a), HEIGHT(a));
gsl_matrix_complex_set_identity(m);
gsl_matrix_complex_scale(m, c->number);
result = gsl_matrix_complex_equal(CMAT(a), m);
gsl_matrix_complex_free(m);
return result;
}
static CMATRIX *_divf(CMATRIX *a, double f, bool invert)
{
bool complex = COMPLEX(a);
CMATRIX *m;
if (invert)
{
void *inv = matrix_invert(MAT(a), complex);
if (!inv)
{
GB.Error(GB_ERR_ZERO);
return NULL;
}
m = MATRIX_create_from(inv, complex);
}
else
{
if (f == 0.0)
{
GB.Error(GB_ERR_ZERO);
return NULL;
}
f = 1 / f;
m = MATRIX_make(a);
}
if (complex)
gsl_matrix_complex_scale(CMAT(m), gsl_complex_rect(f, 0));
else
gsl_matrix_scale(MAT(m), f);
return m;
}
bool Matrix_Scale(gsl_matrix_complex *A, double _Complex s){
gsl_matrix_complex_scale(A, c2g(s));
return true;
}
bool Matrix_Scale(gsl_matrix_complex *A, gsl_complex s){
gsl_matrix_complex_scale(A, s);
return true;
}
int main(int argc, char * argv[])
{
int num,i,*states,num_e,j,k;
double *entry, *dos_vec, *eval_vec;
double coef;
char tmpc;
gsl_vector *eval;
gsl_matrix_view m;
gsl_eigen_symm_workspace *w;
gsl_matrix_complex * matrix2;
gsl_complex z;
gsl_permutation * p;
char name[25];
FILE *out;
if ((out = fopen(argv[1],"r")) != NULL)
{
num = 0;
printf("reading from file: %s....\n",argv[1]);
while(fscanf(out,"%lf",&coef) != EOF) num++;
if (modf(sqrt(num),&coef) != 0)
{
printf("not a square matrix!\n\n");
return 1;
}
//printf("%d\n",num);
fseek(out,0,SEEK_SET);
num = sqrt(num);
entry = (double *)malloc(sizeof(double) * num * num);
i = 0;
while (i < (num * num))
{
*(entry + i) = 0;
i++;
}
i = 0;
printf("loading matrix into memory...\n");
while(fscanf(out,"%lf",&coef) != EOF)
{
*(entry + i) = coef;
printf("entry %d = %g\n",i + 1,coef);
i++;
}
flags += NUMPRINT;
flags += READFROMFILE;
}
if (argc < 6 && (flags & READFROMFILE) == 0)
{
printf("usage: no. of layers, slope of cone/no. of atoms per layer, on-site energy, hopping parameter, model, (option)\n");
printf("\n Models are:\n1: Nanotube, square lattice\n2: Nanotube, hex lattice (armchair)\n");
printf("3: Nanohorn, square lattice\n4: Nanohorn hex lattice\n5: Nanotube, hex lattice (zig-zag)\n");
printf("\nOptions are: p - print symbolically\n n - print numerically\n\n");
return 1;
}
else if ((flags & READFROMFILE) != 0)
{
}
else
{
num = atoi(argv[1]);
Epsilon = atol(argv[3]);
Gamma = atol(argv[4]);
switch(atoi(argv[5]))
{
case 1: flags = flags + CNT_SQUARE;
Alpha = atoi(argv[2]);
num *= Alpha;
entry = (double *)malloc(sizeof(double) * num * num);
break;
case 2: flags = flags + CNT_HEX_ARM;
Alpha = atoi(argv[2]);
i = Alpha;
if ((i % 2) != 0)
{
printf("no. of atoms per layer must be even, changing to %d\n",i + 1);
Alpha += 1;
}
num *= (Alpha);
entry = (double *)malloc(sizeof(double) * num * num);
break;
case 3: flags = flags + HORN_SQUARE;
i = 1;
num_e = 0;
while (i <= num)
{
num_e += i;
i++;
}
num = num_e;
entry = (double *)malloc(sizeof(double) * num * num);
break;
case 4: flags = flags + HORN_HEX;
num = 0;
entry = NULL;
break;
case 5: flags = flags + CNT_HEX_ZIG;
Alpha = atoi(argv[2]);
i = Alpha;
while ((i % 4) != 0)
{
i++;
}
Alpha = i;
num *= Alpha;
entry = (double *)malloc(sizeof(double) * num * num);
break;
default: printf("No valid model choice!\n");
return 1;
break;
}
i = 0;
while (i < (num * num))
{
*(entry + i) = 0;
i++;
}
printf("Alpha = %g\n",Alpha);
}
printf("%d atoms\n",num);
if (argc > 6)
{
if (strcmp("p\0",argv[6]) == 0)
{
//printf("print");
flags = flags + PRINT;
}
if (strcmp("n\0", argv[6]) == 0)
{
flags = flags + NUMPRINT;
}
}
eval = gsl_vector_alloc(num);
//printf("flags %d\n",flags);
//k = (flags & PRINT);
//printf("print ? %d\n",k);
//printf("%lf",Alpha);
//printf("%d",num);
if (entry == NULL)
{
printf("could not allocate memory\n");
return 1;
}
i = 0;
if ((flags & READFROMFILE) == 0)
{
printf("Populating Matrix...\n");
PopulateMatrix(entry,num);
out = fopen("matrix","w");
i = 0;
while (i < (num * num))
{
fprintf(out,"%3.5lf ",*(entry + i));
if (((i + 1) % num) == 0) fprintf(out,"\n");
i++;
}
fclose(out);
}
else
{
}
printf("Printing Matrix\n");
PrintMatrix(entry,num);
//CalcEigenvalues(entry,num,eval);
//Eigenvalue Calculation
m = gsl_matrix_view_array (entry,num,num);
//printf("87\n");
w = gsl_eigen_symm_alloc (num);
//printf("89\n");
printf("Solving Eigenvalue equation....\n");
if(gsl_eigen_symm (&m.matrix, eval, w))
{
printf("an error occurred solving the eigenvalue equation\n");
return 1;
}
//printf("\nworkspace location = %#x",w);
gsl_eigen_symm_free(w);
printf("\n\n");
//if (flags & NUMPRINT != 0 || flags & PRINT != 0)
printf("Eigenvalues found. ");
eval_vec = malloc(sizeof(double) * num);
i = 0;
while (i < num)
{
*(eval_vec + i) = gsl_vector_get(eval,i);
i++;
}
gsl_vector_free(eval);
tmpc = 0;
printf("Ordering Eigenvalues...\n");
qsort(eval_vec,num,sizeof(double),comparedouble);
division = ((*(eval_vec + num - 1) - *eval_vec) / num) * 10 * INTERVAL;
num_e = ((*(eval_vec + num - 1) - *eval_vec))/ division;
num_e++; //just in case
while ((flags & FINISHED) == 0)
{
if (tmpc != -1) printf("(s)ave in file, (q)uit and discard, (p)rint (!), (d)ensity of states: ");
scanf("%c",&tmpc);
if (tmpc == 'p' || tmpc == 'P')
{
i = 0;
while (i < num)
{
printf("Eigenvalue %d\t: %g\n",(i + 1),*(eval_vec + i));
i++;
}
printf("\n");
tmpc = -1;
}
else if (tmpc == 'q' || tmpc == 'Q')
{
printf("\nexiting...\n\n");
flags += FINISHED;
}
else if (tmpc == 'd' || tmpc == 'D')
{
tmpc = 0;
dos_vec = malloc(sizeof(double) * num_e);
states = malloc(sizeof(int) * num_e);
printf("\nCalculating density of states...\n");
Calculate(eval_vec,num,dos_vec,states);
i = 0;
printf("\n");
out = fopen("dostube","w");
while (i < num_e && *(states + i) >= 0)
{
printf("Energy: % .5lf\tNo. of states: %d\n",*(dos_vec + i),*(states + i));
fprintf(out,"% .5lf\t%d\n",*(dos_vec + i),*(states + i));
i++;
}
num_e = i;
fclose(out);
flags += FINISHED;
flags += DOS;
}
else if (tmpc == -1) //WHY?!!
{
tmpc = 0;
}
else if (tmpc == 's' || tmpc == 'S') //broken for some reason
{
printf("\nchoose filename: ");
scanf("%s",name);
//printf("%s",name);
out = fopen(name,"r");
if (out != NULL)
{
printf("File already exists!\n");
fclose(out);
}
else
{
fclose(out);
out = fopen(name,"w");
printf("Writing to file: %s",name);
i = 0;
while (i < num)
{
fprintf(out,"Eigenvalue %d\t: %g\n",(i + 1),*(eval_vec + i));
i++;
}
fclose(out);
tmpc = -1;
}
}
else
{
printf("unrecognised option!\n");
}
}
if ((flags & DOS) != 0)
{
while (j < num_e)
{
matrix2 = gsl_matrix_complex_alloc(sizeof(gsl_complex) * num,sizeof(gsl_complex) * num);
i = 0;
gsl_matrix_complex_set_identity(matrix2);
z.dat[0] = *(dos_vec + j);
z.dat[1] = 0.0001;
gsl_matrix_complex_scale(matrix2,z);
while (i < num)
{
k = 0;
while(k < num)
{
z = gsl_matrix_complex_get(matrix2,i,k);
z.dat[0] -= *(entry + i + (k * num));
gsl_matrix_complex_set(matrix2,i,k,z);
k++;
}
i++;
}
out = fopen("matrix","w");
gsl_matrix_complex_fprintf(out,matrix2,"% 2.2lf");
fclose(out);
free(entry);
}
}
//printf("\neval location = %#x",eval);
return 0;
}
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);
}
