/* nag_zggesx (f08xpc) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/
#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx02.h>
#include <nagx04.h>
#ifdef __cplusplus
extern "C"
{
#endif
static Nag_Boolean NAG_CALL selctg(const Complex a, const Complex b);
#ifdef __cplusplus
}
#endif
int main(void)
{
/* Scalars */
Complex alph, bet, z;
double abnorm, norma, normb, normd, norme, eps, tol;
Integer i, j, n, sdim, pda, pdb, pdc, pdd, pde, pdvsl, pdvsr;
Integer exit_status = 0;
/* Arrays */
Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *c = 0, *d = 0;
Complex *e = 0, *vsl = 0, *vsr = 0;
double rconde[2], rcondv[2];
char nag_enum_arg[40];
/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_LeftVecsType jobvsl;
Nag_RightVecsType jobvsr;
Nag_SortEigValsType sort = Nag_SortEigVals;
Nag_RCondType sense;
#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_zggesx (f08xpc) 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);
scanf(" %39s%*[^\n]", nag_enum_arg);
sense = (Nag_RCondType) 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)) ||
!(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 matrices A and B to matrices D and E using nag_zge_copy (f16tfc),
* Complex valued general matrix copy.
* The copies will be used as comparison against reconstructed matrices.
*/
nag_zge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_copy (f16tfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
nag_zge_copy(order, Nag_NoTrans, n, n, b, pdb, e, pde, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_copy (f16tfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_zge_norm (f16uac): Find norms of input matrices A and B. */
nag_zge_norm(order, Nag_FrobeniusNorm, n, n, a, pda, &norma, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
nag_zge_norm(order, Nag_FrobeniusNorm, n, n, b, pdb, &normb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_gen_complx_mat_print_comp (x04dbc): Print matrices A and B. */
fflush(stdout);
nag_gen_complx_mat_print_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_gen_complx_mat_print_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
fflush(stdout);
nag_gen_complx_mat_print_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_gen_complx_mat_print_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Find the generalized Schur form using nag_zggesx (f08xpc). */
nag_zggesx(order, jobvsl, jobvsr, sort, selctg, sense, n, a, pda, b, pdb,
&sdim, alpha, beta, vsl, pdvsl, vsr, pdvsr, rconde, rcondv,
&fail);
if (fail.code != NE_NOERROR && fail.code != NE_SCHUR_REORDER_SELECT) {
printf("Error from nag_zggesx (f08xpc).\n%s\n", fail.message);
exit_status = 1;
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_zge_copy (f16tfc).
* C = C*S (S in a, upper triangular) using nag_ztrmm (f16zfc).
* D = D - C*Z^H (Z in vsr) using nag_zgemm (f16zac).
*/
nag_zge_copy(order, Nag_NoTrans, n, n, vsl, pdvsl, c, pdc, &fail);
alph = nag_complex(1.0, 0.0);
/* nag_ztrmm (f16zfc) Triangular complex matrix-matrix multiply. */
nag_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_ztrmm (f16zfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
alph = nag_complex(-1.0, 0.0);
bet = nag_complex(1.0, 0.0);
nag_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_zgemm (f16zac).\n%s\n", fail.message);
exit_status = 1;
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_ztrmm (f16zfc).
* E = E - Q*Z^H (Z in vsr) using nag_zgemm (f16zac).
*/
alph = nag_complex(1.0, 0.0);
/* nag_ztrmm (f16zfc) Triangular complex matrix-matrix multiply. */
nag_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_ztrmm (f16zfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
alph = nag_complex(-1.0, 0.0);
bet = nag_complex(1.0, 0.0);
nag_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_zgemm (f16zac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_zge_norm (f16uac): Find norms of difference matrices D and E. */
nag_zge_norm(order, Nag_FrobeniusNorm, n, n, d, pdd, &normd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
nag_zge_norm(order, Nag_FrobeniusNorm, n, n, e, pde, &norme, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 1;
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 = 1;
goto END;
}
/* Print details on eigenvalues */
printf("Number of sorted eigenvalues = %4" NAG_IFMT "\n\n", sdim);
if (fail.code == NE_SCHUR_REORDER_SELECT) {
printf("*** Note that rounding errors mean that leading eigenvalues in the"
" generalized\n Schur form no longer satisfy selctg = Nag_TRUE"
"\n\n");
}
else {
printf("The selected eigenvalues are:\n");
for (i = 0; i < sdim; i++) {
if (beta[i].re != 0.0 || beta[i].im != 0.0) {
z = nag_complex_divide(alpha[i], beta[i]);
printf("%3" NAG_IFMT " (%13.4e, %13.4e)\n", i + 1, z.re, z.im);
}
else
printf("%3" NAG_IFMT " Eigenvalue is infinite\n", i + 1);
}
}
abnorm = sqrt(pow(norma, 2) + pow(normb, 2));
tol = eps * abnorm;
if (sense == Nag_RCondEigVals || sense == Nag_RCondBoth) {
/* Print out the reciprocal condition number and error bound */
printf("\n");
printf("For the selected eigenvalues,\nthe reciprocals of projection "
"norms onto the deflating subspaces are\n");
printf(" for left subspace, rcond = %10.1e\n for right subspace, rcond = "
"%10.1e\n\n", rconde[0], rconde[1]);
printf(" asymptotic error bound = %10.1e\n\n", tol / rconde[0]);
}
if (sense == Nag_RCondEigVecs || sense == Nag_RCondBoth) {
/* Print out the reciprocal condition numbers and error bound. */
printf("For the left and right deflating subspaces,\n");
printf("reciprocal condition numbers are:\n");
printf(" for left subspace, rcond = %10.1e\n for right subspace, rcond = "
"%10.1e\n\n", rcondv[0], rcondv[1]);
printf(" approximate error bound = %10.1e\n", tol / rcondv[1]);
}
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);
return exit_status;
}
static Nag_Boolean NAG_CALL selctg(const Complex a, const Complex b)
{
/* Boolean function selctg for use with nag_zggesx (f08xpc)
* Returns the value Nag_TRUE if the absolute value of the eigenvalue
* a/b < 6.0
*/
return (nag_complex_abs(a) <
6.0 * nag_complex_abs(b) ? Nag_TRUE : Nag_FALSE);
}