/* nag_lapackeig_zgges3 (f08xqc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/
#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 sort_values(Integer n, Complex e[], size_t rank[],
double emod[]);
#ifdef __cplusplus
}
#endif
int main(void) {
/* Scalars */
Complex alph, bet;
double norma, normb, normd, norme, eps;
Integer i, j, n, sdim, pda, pdb, pdc, pdd, pde, pdvsl, pdvsr;
Integer exit_status = 0, isinf = 0;
/* Arrays */
Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *c = 0;
Complex *d = 0, *e = 0, *vsl = 0, *vsr = 0;
double *emod = 0;
size_t *rank = 0;
Nag_LeftVecsType jobvsl;
Nag_RightVecsType jobvsr;
char nag_enum_arg[40];
/* Nag Types */
NagError fail;
Nag_OrderType order;
#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
INIT_FAIL(fail);
printf("nag_lapackeig_zgges3 (f08xqc) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);
if (n < 0) {
printf("Invalid n\n");
exit_status = 1;
return exit_status;
}
scanf(" %39s%*[^\n]", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
jobvsl = (Nag_LeftVecsType)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobvsr = (Nag_RightVecsType)nag_enum_name_to_value(nag_enum_arg);
pdvsl = (jobvsl == Nag_LeftVecs ? n : 1);
pdvsr = (jobvsr == Nag_RightVecs ? n : 1);
pda = n;
pdb = n;
pdc = n;
pdd = n;
pde = n;
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) || !(b = NAG_ALLOC(n * n, Complex)) ||
!(c = NAG_ALLOC(n * n, Complex)) || !(d = NAG_ALLOC(n * n, Complex)) ||
!(e = NAG_ALLOC(n * n, Complex)) || !(emod = NAG_ALLOC(n, double)) ||
!(rank = NAG_ALLOC(n, size_t)) || !(alpha = NAG_ALLOC(n, Complex)) ||
!(beta = NAG_ALLOC(n, Complex)) ||
!(vsl = NAG_ALLOC(pdvsl * pdvsl, Complex)) ||
!(vsr = NAG_ALLOC(pdvsr * pdvsr, 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]");
/* Copy A and B to D and E respectively: nag_blast_zge_copy (f16tfc),
* Complex valued general matrix copy.
*/
nag_blast_zge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_copy (f16tfc).\n%s\n", fail.message);
exit_status = 2;
goto END;
}
nag_blast_zge_copy(order, Nag_NoTrans, n, n, b, pdb, e, pde, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_copy (f16tfc).\n%s\n", fail.message);
exit_status = 3;
goto END;
}
/* nag_blast_zge_norm (f16uac): Find norms of input matrices A and B. */
nag_blast_zge_norm(order, Nag_OneNorm, n, n, a, pda, &norma, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 4;
goto END;
}
nag_blast_zge_norm(order, Nag_OneNorm, n, n, b, pdb, &normb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 5;
goto END;
}
/* nag_file_print_matrix_complex_gen_comp (x04dbc): Print matrices A and B. */
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, Nag_BracketForm,
"%6.2f", "Matrix A", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0,
&fail);
printf("\n");
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 6;
goto END;
}
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b, pdb, Nag_BracketForm,
"%6.2f", "Matrix B", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0,
&fail);
printf("\n");
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 7;
goto END;
}
/* Find the generalized Schur form using nag_lapackeig_zgges3 (f08xqc). */
nag_lapackeig_zgges3(order, jobvsl, jobvsr, Nag_NoSortEigVals, NULLFN, n, a,
pda, b, pdb, &sdim, alpha, beta, vsl, pdvsl, vsr, pdvsr,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgges3 (f08xqc).\n%s\n", fail.message);
exit_status = 8;
goto END;
}
/* Check generalized Schur Form by reconstruction of Schur vectors are
* available.
*/
if (jobvsl == Nag_NotLeftVecs || jobvsr == Nag_NotRightVecs) {
/* Cannot check factorization by reconstruction Schur vectors. */
goto END;
}
/* Reconstruct A as Q*S*Z^H and subtract from original (D) using the steps
* C = Q (Q in vsl) using nag_blast_zge_copy (f16tfc).
* C = C*S (S in a, upper triangular) using nag_blast_ztrmm (f16zfc).
* D = D - C*Z^H (Z in vsr) using nag_blast_zgemm (f16zac).
*/
nag_blast_zge_copy(order, Nag_NoTrans, n, n, vsl, pdvsl, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_copy (f16tfc).\n%s\n", fail.message);
exit_status = 9;
goto END;
}
alph = nag_complex_create(1.0, 0.0);
/* nag_blast_ztrmm (f16zfc) Triangular complex matrix-matrix multiply. */
nag_blast_ztrmm(order, Nag_RightSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag,
n, n, alph, a, pda, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_ztrmm (f16zfc).\n%s\n", fail.message);
exit_status = 10;
goto END;
}
alph = nag_complex_create(-1.0, 0.0);
bet = nag_complex_create(1.0, 0.0);
nag_blast_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alph, c, pdc, vsr,
pdvsr, bet, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zgemm (f16zac).\n%s\n", fail.message);
exit_status = 11;
goto END;
}
/* Reconstruct B as Q*T*Z^H and subtract from original (E) using the steps
* Q = Q*T (Q in vsl, T in b, upper triangular) using nag_blast_ztrmm
* (f16zfc). E = E - Q*Z^H (Z in vsr) using nag_blast_zgemm (f16zac).
*/
alph = nag_complex_create(1.0, 0.0);
nag_blast_ztrmm(order, Nag_RightSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag,
n, n, alph, b, pdb, vsl, pdvsl, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_ztrmm (f16zfc).\n%s\n", fail.message);
exit_status = 12;
goto END;
}
alph = nag_complex_create(-1.0, 0.0);
bet = nag_complex_create(1.0, 0.0);
nag_blast_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alph, vsl, pdvsl,
vsr, pdvsr, bet, e, pde, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zgemm (f16zac).\n%s\n", fail.message);
exit_status = 13;
goto END;
}
/* nag_blast_zge_norm (f16uac): Find norms of difference matrices D and E. */
nag_blast_zge_norm(order, Nag_OneNorm, n, n, d, pdd, &normd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 14;
goto END;
}
nag_blast_zge_norm(order, Nag_OneNorm, n, n, e, pde, &norme, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 15;
goto END;
}
/* Get the machine precision, using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
if (MAX(normd, norme) > pow(eps, 0.8) * MAX(norma, normb)) {
printf("The norm of the error in the reconstructed matrices is greater "
"than expected.\nThe Schur factorization has failed.\n");
exit_status = 16;
goto END;
}
/* Print details on eigenvalues */
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;
}
}
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(alpha);
NAG_FREE(beta);
NAG_FREE(vsl);
NAG_FREE(vsr);
NAG_FREE(emod);
NAG_FREE(rank);
return exit_status;
}
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));
}