/* nag_linsys_real_posdef_solve (f04bdc) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.2, 2023.
*/
#include <nag.h>
#include <stdio.h>
int main(void) {
/* Scalars */
double errbnd, rcond;
Integer exit_status, i, j, n, nrhs, pda, pdb;
/* Arrays */
char nag_enum_arg[40];
double *a = 0, *b = 0;
/* Nag Types */
Nag_OrderType order;
Nag_UploType uplo;
NagError fail;
#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
exit_status = 0;
INIT_FAIL(fail);
printf("nag_linsys_real_posdef_solve (f04bdc) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &nrhs);
if (n >= 0 && nrhs >= 0) {
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * nrhs, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
pda = n;
pdb = n;
#else
pda = n;
pdb = nrhs;
#endif
} else {
printf("%s\n", "n and/or nrhs too small");
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
*/
uplo = (Nag_UploType)nag_enum_name_to_value(nag_enum_arg);
if (uplo == Nag_Upper) {
/* Read the upper triangular part of A from data file */
for (i = 1; i <= n; ++i) {
for (j = i; j <= n; ++j) {
scanf("%lf", &A(i, j));
}
}
scanf("%*[^\n] ");
} else {
/* Read the lower triangular part of A from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= i; ++j) {
scanf("%lf", &A(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_solve (f04bdc).
* Computes the solution and error-bound to a real symmetric
* positive-definite system of linear equations
*/
nag_linsys_real_posdef_solve(order, uplo, n, nrhs, a, pda, 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");
printf("%s\n%6s%10.1e\n", "Estimate of condition number", "", 1.0 / rcond);
printf("\n\n");
printf("%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_solve (f04bdc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(a);
NAG_FREE(b);
return exit_status;
}