/* nag_linsys_real_posdef_band_solve (f04bfc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/
#include <nag.h>
#include <stdio.h>
int main(void) {
/* Scalars */
double errbnd, rcond;
Integer exit_status, i, j, kd, n, nrhs, pdab, pdb;
/* Arrays */
char nag_enum_arg[20];
double *ab = 0, *b = 0;
/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_UploType uplo;
#ifdef NAG_COLUMN_MAJOR
#define AB_U(I, J) ab[(J - 1) * pdab + kd + I - J]
#define AB_L(I, J) ab[(J - 1) * pdab + I - J]
#define B(I, J) b[(J - 1) * pdb + I - 1]
order = Nag_ColMajor;
#else
#define AB_U(I, J) ab[(I - 1) * pdab + J - I]
#define AB_L(I, J) ab[(I - 1) * pdab + kd + J - I]
#define B(I, J) b[(I - 1) * pdb + J - 1]
order = Nag_RowMajor;
#endif
exit_status = 0;
INIT_FAIL(fail);
printf("nag_linsys_real_posdef_band_solve (f04bfc)"
" Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &kd, &nrhs);
if (n > 0 && kd > 0 && nrhs > 0) {
/* Allocate memory */
if (!(ab = NAG_ALLOC((kd + 1) * n, double)) ||
!(b = NAG_ALLOC(n * nrhs, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
pdab = kd + 1;
#ifdef NAG_COLUMN_MAJOR
pdb = n;
#else
pdb = nrhs;
#endif
} else {
printf("%s\n", "One or more of n, kd and nrhs is too small");
exit_status = 1;
return exit_status;
}
/* Read uplo storage name for the matrix A and convert to value. */
scanf("%19s%*[^\n] ", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
uplo = (Nag_UploType)nag_enum_name_to_value(nag_enum_arg);
if (uplo == Nag_Upper) {
for (i = 1; i <= n; ++i) {
for (j = i; j <= MIN(n, i + kd); ++j) {
scanf("%lf", &AB_U(i, j));
}
scanf("%*[^\n] ");
}
} else {
for (i = 1; i <= n; ++i) {
for (j = MAX(1, i - kd); j <= i; ++j) {
scanf("%lf", &AB_L(i, j));
}
scanf("%*[^\n] ");
}
}
/* Read B from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j) {
scanf("%lf", &B(i, j));
}
}
scanf("%*[^\n] ");
/* Solve the equations AX = B for X */
/* nag_linsys_real_posdef_band_solve (f04bfc).
* Computes the solution and error-bound to a real symmetric
* positive-definite banded system of linear equations
*/
nag_linsys_real_posdef_band_solve(order, uplo, n, kd, nrhs, ab, pdab, b, pdb,
&rcond, &errbnd, &fail);
if (fail.code == NE_NOERROR) {
/* Print solution, estimate of condition number and approximate */
/* error bound */
/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, b, pdb, "Solution", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
printf("\n%s\n%6s%10.1e\n\n", "Estimate of condition number", "",
1.0 / rcond);
printf("\n%s\n%6s%10.1e\n\n",
"Estimate of error bound for computed solutions", "", errbnd);
} else if (fail.code == NE_RCOND) {
/* Matrix A is numerically singular. Print estimate of */
/* reciprocal of condition number and solution */
printf("\n%s\n%6s%10.1e\n\n\n",
"Estimate of reciprocal of condition number", "", rcond);
/* nag_file_print_matrix_real_gen (x04cac), see above. */
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, b, pdb, "Solution", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
} else if (fail.code == NE_POS_DEF) {
/* The matrix A is not positive definite to working precision */
printf("%s%3" NAG_IFMT "%s\n\n", "The leading minor of order ", fail.errnum,
" is not positive definite");
} else {
printf("Error from nag_linsys_real_posdef_band_solve (f04bfc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(ab);
NAG_FREE(b);
return exit_status;
}