/* nag_sparse_real_symm_basic_setup (f11gdc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/
#include <math.h>
#include <nag.h>
int main(void) {
/* Scalars */
Integer exit_status = 0;
double anorm, dscale, dtol, sigerr, sigmax, sigtol, stplhs, stprhs, tol;
Integer i, irevcm, iterm, itn, its, la, lfill, lwork, lwreq, maxitn, maxits,
monit, n, nnz, nnzc, npivm;
/* Arrays */
char nag_enum_arg[100];
double *a = 0, *b = 0, *wgt = 0, *work = 0, *x = 0;
Integer *icol = 0, *ipiv = 0, *irow = 0, *istr = 0;
/* NAG types */
Nag_SparseSym_Piv pstrat;
Nag_SparseSym_Method method;
Nag_SparseSym_PrecType precon;
Nag_NormType norm;
Nag_SparseSym_Weight weight;
Nag_SparseSym_Fact mic;
Nag_Sparse_Comm comm;
Nag_SparseSym_Bisection sigcmp;
NagError fail, fail1;
INIT_FAIL(fail);
INIT_FAIL(fail1);
printf("nag_sparse_real_symm_basic_setup (f11gdc) Example Program Results\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);
scanf("%" NAG_IFMT "%*[^\n]", &nnz);
/* Read or initialize the parameters for the iterative solver */
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
scanf("%99s%*[^\n]", nag_enum_arg);
method = (Nag_SparseSym_Method)nag_enum_name_to_value(nag_enum_arg);
scanf("%99s%*[^\n]", nag_enum_arg);
precon = (Nag_SparseSym_PrecType)nag_enum_name_to_value(nag_enum_arg);
scanf("%99s%*[^\n]", nag_enum_arg);
sigcmp = (Nag_SparseSym_Bisection)nag_enum_name_to_value(nag_enum_arg);
scanf("%99s%*[^\n]", nag_enum_arg);
norm = (Nag_NormType)nag_enum_name_to_value(nag_enum_arg);
scanf("%99s%*[^\n]", nag_enum_arg);
weight = (Nag_SparseSym_Weight)nag_enum_name_to_value(nag_enum_arg);
scanf("%" NAG_IFMT "%*[^\n]", &iterm);
scanf("%lf%" NAG_IFMT "%*[^\n]", &tol, &maxitn);
scanf("%" NAG_IFMT "%*[^\n] ", &monit);
/* Read the parameters for the preconditioner */
scanf("%" NAG_IFMT "%lf%*[^\n]", &lfill, &dtol);
scanf("%99s%*[^\n]", nag_enum_arg);
mic = (Nag_SparseSym_Fact)nag_enum_name_to_value(nag_enum_arg);
scanf("%lf%*[^\n]", &dscale);
scanf("%99s%*[^\n]", nag_enum_arg);
pstrat = (Nag_SparseSym_Piv)nag_enum_name_to_value(nag_enum_arg);
la = 2 * nnz;
lwork = 120;
if (!(a = NAG_ALLOC(la, double)) || !(b = NAG_ALLOC(n, double)) ||
!(wgt = NAG_ALLOC(n, double)) || !(work = NAG_ALLOC(lwork, double)) ||
!(x = NAG_ALLOC(n, double)) || !(icol = NAG_ALLOC(la, Integer)) ||
!(ipiv = NAG_ALLOC(n, Integer)) || !(irow = NAG_ALLOC(la, Integer)) ||
!(istr = NAG_ALLOC(n + 1, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read the nonzero elements of the matrix A */
for (i = 0; i < nnz; i++)
scanf("%lf%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &a[i], &irow[i], &icol[i]);
/* Read right-hand side vector b and initial approximate solution x */
for (i = 0; i < n; i++)
scanf("%lf", &b[i]);
scanf("%*[^\n]");
for (i = 0; i < n; i++)
scanf("%lf", &x[i]);
printf("\nSolve a system of linear equations using the ");
if (method == Nag_SparseSym_CG)
printf("conjugate gradient method (CG)\n");
else if (method == Nag_SparseSym_SYMMLQ)
printf("Lanczos method (SYMMLQ)\n");
else if (method == Nag_SparseSym_MINRES)
printf("minimum residual method (MINRES)\n");
/* Calculate incomplete Cholesky factorization as preconditioner using
* nag_sparse_real_symm_precon_ichol (f11jac).
* Incomplete Cholesky factorization (symmetric)
*/
nag_sparse_real_symm_precon_ichol(n, nnz, &a, &la, &irow, &icol, lfill, dtol,
mic, dscale, pstrat, ipiv, istr, &nnzc,
&npivm, &comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_real_symm_precon_ichol (f11jac)\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Initialize the solver using nag_sparse_real_symm_basic_setup (f11gdc).
* Real sparse symmetric linear systems, setup for f11gec
*/
anorm = 0.0;
sigmax = 0.0;
sigtol = 0.01;
maxits = n;
while (1) {
nag_sparse_real_symm_basic_setup(
method, precon, sigcmp, norm, weight, iterm, n, tol, maxitn, anorm,
sigmax, sigtol, maxits, monit, &lwreq, work, lwork, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_real_symm_basic_setup (f11gdc)\n%s\n",
fail.message);
exit_status = 2;
goto END;
}
if (lwork >= lwreq)
break;
else {
NAG_FREE(work);
lwork = lwreq;
work = NAG_ALLOC(lwreq, double);
}
}
/* Call repeatedly to solve the equations
* Note that the arrays b and x are overwritten
* On final exit, x will contain the solution and b the residual vector
*/
irevcm = 0;
/* First call of nag_sparse_real_symm_basic_solver (f11gec).
* Real sparse symmetric linear systems, preconditioned conjugate
* gradient or Lanczos
*/
nag_sparse_real_symm_basic_solver(&irevcm, x, b, wgt, work, lwork, &fail);
while (irevcm != 4) {
switch (irevcm) {
case 1:
/* nag_sparse_real_symm_matvec (f11xec)
* Real sparse symmetric matrix vector multiply
*/
nag_sparse_real_symm_matvec(n, nnz, a, irow, icol, Nag_SparseSym_NoCheck,
x, b, &fail1);
break;
case 2:
/* nag_sparse_real_symm_precon_ichol_solve (f11jbc).
* Solution of linear system involving incomplete Cholesky
* preconditioning matrix generated by f11jac
*/
nag_sparse_real_symm_precon_ichol_solve(n, a, la, irow, icol, ipiv, istr,
Nag_SparseSym_NoCheck, x, b,
&fail1);
break;
case 3:
/* nag_sparse_real_symm_basic_diag (f11gfc).
* Real sparse symmetric linear systems, diagnostic for f11gec
*/
nag_sparse_real_symm_basic_diag(&itn, &stplhs, &stprhs, &anorm, &sigmax,
&its, &sigerr, work, lwork, &fail1);
printf("\nMonitoring at iteration no.%4" NAG_IFMT "\n", itn);
printf("residual norm: %14.4e\n", stplhs);
printf(" Solution vector Residual vector\n");
for (i = 0; i < n; i++)
printf("%16.4e%16.4e\n", x[i], b[i]);
printf("\n");
}
if (fail1.code != NE_NOERROR)
irevcm = 6;
/* Next call of nag_sparse_real_symm_basic_solver (f11gec). */
nag_sparse_real_symm_basic_solver(&irevcm, x, b, wgt, work, lwork, &fail);
}
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_real_symm_basic_solver (f11gec).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}
/* Obtain information about the computation using
* nag_sparse_real_symm_basic_diag (f11gfc).
* Real sparse symmetric linear systems, diagnostic for solver.
*/
nag_sparse_real_symm_basic_diag(&itn, &stplhs, &stprhs, &anorm, &sigmax, &its,
&sigerr, work, lwork, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_real_symm_basic_diag (f11gfc)\n%s\n",
fail.message);
exit_status = 4;
goto END;
}
/* Print the output data */
printf("Final Results\n");
printf("Number of iterations for convergence: %5" NAG_IFMT " \n", itn);
printf("Residual norm: %14.4e\n", stplhs);
printf("Right-hand side of termination criterion: %14.4e\n", stprhs);
printf("1-norm of matrix A: %14.4e\n", anorm);
printf("Largest singular value of A_bar: %14.4e\n\n", sigmax);
/* Output x */
printf("%14s%14s\n", "Solution", "Residual");
for (i = 0; i < n; i++)
printf("%14.4e%14.4e\n", x[i], b[i]);
printf("\n");
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(wgt);
NAG_FREE(work);
NAG_FREE(x);
NAG_FREE(icol);
NAG_FREE(ipiv);
NAG_FREE(irow);
NAG_FREE(istr);
return exit_status;
}