/* nag_lapackeig_zggev3 (f08wqc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.3, 2022.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
#ifdef __cplusplus
extern "C" {
#endif
static Integer NAG_CALL compare(const Nag_Pointer a, const Nag_Pointer b);
static Integer normalize_vectors(Integer n, Complex v[], size_t rank[],
const char *title);
static Integer sort_values(Integer n, Complex e[], size_t rank[],
double emod[]);
#ifdef __cplusplus
}
#endif
int main(void) {
/* Scalars */
Integer i, isinf, j, n, pda, pdb, pdvl, pdvr;
Integer exit_status = 0;
/* Arrays */
Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *vl = 0, *vr = 0;
double *emod = 0;
size_t *rank = 0;
char nag_enum_arg[40];
/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_LeftVecsType jobvl;
Nag_RightVecsType jobvr;
INIT_FAIL(fail);
printf("nag_lapackeig_zggev3 (f08wqc) Example Program Results\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);
if (n < 0) {
printf("Invalid n\n");
exit_status = 1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
order = Nag_RowMajor;
#endif
scanf(" %39s%*[^\n]", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
jobvl = (Nag_LeftVecsType)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobvr = (Nag_RightVecsType)nag_enum_name_to_value(nag_enum_arg);
pda = n;
pdb = n;
pdvl = (jobvl == Nag_LeftVecs ? n : 1);
pdvr = (jobvr == Nag_RightVecs ? n : 1);
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) || !(alpha = NAG_ALLOC(n, Complex)) ||
!(b = NAG_ALLOC(n * n, Complex)) || !(beta = NAG_ALLOC(n, Complex)) ||
!(emod = NAG_ALLOC(n, double)) || !(rank = NAG_ALLOC(n, size_t)) ||
!(vl = NAG_ALLOC(pdvl * pdvl, Complex)) ||
!(vr = NAG_ALLOC(pdvr * pdvr, Complex))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read in the matrices A and B */
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
scanf("%*[^\n]");
/* Solve the generalized eigenvalue problem Ax = lambda Bx using the
* level 3 blocked routine nag_lapackeig_zggev3 (f08wqc) which returns:
* - eigenvalues as alpha[]./beta[];
* - left and right eigenvectors in vl and vr respectively.
*/
/* Solve the generalized eigenvalue problem using nag_lapackeig_zggev3
* (f08wqc). */
nag_lapackeig_zggev3(order, jobvl, jobvr, n, a, pda, b, pdb, alpha, beta, vl,
pdvl, vr, pdvr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zggev3 (f08wqc).\n%s\n", fail.message);
exit_status = 2;
goto END;
}
isinf = 0;
for (j = 0; j < n; ++j) {
/* Check for infinite eigenvalues */
if (nag_complex_abs(beta[j]) < x02ajc()) {
isinf = j + 1;
} else {
alpha[j] = nag_complex_divide(alpha[j], beta[j]);
}
}
if (isinf) {
printf("Eigenvalue %2" NAG_IFMT " is numerically infinite.\n", isinf);
} else {
/* Sort values by decreasing modulus and store in e[] */
exit_status = sort_values(n, alpha, rank, emod);
/* Print the (finite) eigenvalues
* using nag_file_print_matrix_complex_gen (x04dac).
*/
fflush(stdout);
printf("\n");
nag_file_print_matrix_complex_gen(Nag_ColMajor, Nag_GeneralMatrix,
Nag_NonUnitDiag, 1, n, alpha, 1,
"Eigenvalues:", NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen (x04dac).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}
}
/* Re-normalize, sort and print the eigenvectors */
if (jobvl == Nag_LeftVecs) {
exit_status = normalize_vectors(n, vl, rank, "Left Eigenvectors:");
if (exit_status)
goto END;
}
if (jobvr == Nag_RightVecs) {
exit_status = normalize_vectors(n, vr, rank, "Right Eigenvectors:");
}
END:
NAG_FREE(a);
NAG_FREE(alpha);
NAG_FREE(b);
NAG_FREE(beta);
NAG_FREE(vl);
NAG_FREE(vr);
NAG_FREE(emod);
NAG_FREE(rank);
return exit_status;
}
static Integer normalize_vectors(Integer n, Complex v[], size_t rank[],
const char *title) {
Complex scal;
double r, rr, rnrm;
Integer errors = 0, i, j, k, stride;
Nag_OrderType order;
NagError fail;
INIT_FAIL(fail);
#ifdef NAG_COLUMN_MAJOR
#define V(I, J) v[(J - 1) * n + I - 1]
order = Nag_ColMajor;
stride = n;
#else
#define V(I, J) v[(I - 1) * n + J - 1]
order = Nag_RowMajor;
stride = 1;
#endif
/* Re-normalize the eigenvectors, largest absolute element real */
for (i = 1; i <= n; i++) {
k = 0;
r = -1.0;
rnrm = 0.0;
for (j = 1; j <= n; j++) {
rr = nag_complex_abs(V(j, i));
rnrm = rnrm + rr * rr;
if (rr > r) {
r = rr;
k = j;
}
}
rnrm = sqrt(rnrm);
r = r * rnrm;
scal.re = V(k, i).re / r;
scal.im = -V(k, i).im / r;
for (j = 1; j <= n; j++) {
V(j, i) = nag_complex_multiply(V(j, i), scal);
}
V(k, i).im = 0.0;
}
/* Sort eigenvectors */
for (i = 1; i <= n; i++) {
/* Sort eigenvector row i using nag_sort_reorder_vector (m01esc). */
nag_sort_reorder_vector((Pointer)&V(i, 1), (size_t)n, sizeof(Complex),
(ptrdiff_t)(stride * sizeof(Complex)), rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sort_reorder_vector (m01esc).\n%s\n",
fail.message);
errors = 5;
goto END;
}
}
printf("\n");
/* Print eigenvectors using nag_file_print_matrix_complex_gen (x04dac). */
fflush(stdout);
nag_file_print_matrix_complex_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
n, n, v, n, title, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen (x04dac).\n%s\n",
fail.message);
errors = 5;
}
END:
#undef V
return errors;
}
static Integer sort_values(Integer n, Complex e[], size_t rank[],
double emod[]) {
Integer i, exit_status = 0;
NagError fail;
INIT_FAIL(fail);
for (i = 0; i < n; ++i) {
/* nag_complex_abs (a02ddc): Moduli of complex number. */
emod[i] = nag_complex_abs(e[i]);
}
/* Rank sort eigenvalues by absolute values using
* nag_sort_rank_sort (m01dsc).
*/
nag_sort_rank_sort((Pointer)emod, (size_t)n, (ptrdiff_t)(sizeof(double)),
compare, Nag_Descending, rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sort_rank_sort (m01dsc).\n%s\n", fail.message);
exit_status = 10;
goto END;
}
/* Turn ranks into indices using nag_sort_permute_invert (m01zac). */
nag_sort_permute_invert(rank, (size_t)n, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sort_permute_invert (m01zac).\n%s\n", fail.message);
exit_status = 11;
goto END;
}
/* Sort eigenvalues using nag_sort_reorder_vector (m01esc). */
nag_sort_reorder_vector((Pointer)e, (size_t)n, sizeof(Complex),
(ptrdiff_t)sizeof(Complex), rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sort_reorder_vector (m01esc).\n%s\n", fail.message);
exit_status = 12;
goto END;
}
END:
return exit_status;
}
static Integer NAG_CALL compare(const Nag_Pointer a, const Nag_Pointer b) {
double x = *((const double *)a) - *((const double *)b);
return (x < 0.0 ? -1 : (x == 0.0 ? 0 : 1));
}