/* nag_real_sym_lin_solve (f04bhc) Example Program. * * Copyright 2004 Numerical Algorithms Group. * * Mark 8, 2004. */ #include #include #include #include #include int main(void) { /* Scalars */ double errbnd, rcond; Integer exit_status, i, j, n, nrhs, pda, pdb; /* Arrays */ char uplo[2]; double *a=0, *b=0; Integer *ipiv=0; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_UploType uplo_enum; #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); Vprintf("nag_real_sym_lin_solve (f04bhc) Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%ld%*[^\n] ", &n, &nrhs); if (n>0 && nrhs>0) { /* Allocate memory */ if ( !(a = NAG_ALLOC(n*n, double)) || !(b = NAG_ALLOC(n*nrhs, double)) || !(ipiv = NAG_ALLOC(n, Integer)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } #ifdef NAG_COLUMN_MAJOR pda = n; pdb = n; #else pda = n; pdb = nrhs; #endif } else { Vprintf("%s\n", "n and/or nrhs too small"); exit_status = 1; return exit_status; } Vscanf(" ' %1s '%*[^\n] ", uplo); if (*(unsigned char *)uplo == 'L') uplo_enum = Nag_Lower; else if (*(unsigned char *)uplo == 'U') uplo_enum = Nag_Upper; else { Vprintf("Unrecognised character for Nag_UploType type\n"); exit_status = -1; goto END; } if (uplo_enum == Nag_Upper) { /* Read the upper triangular part of A from data file */ for (i=1; i<=n; ++i) { for (j=i; j<=n; ++j) { Vscanf("%lf", &A(i,j)); } } Vscanf("%*[^\n] "); } else { /* Read the lower triangular part of A from data file */ for (i=1; i<=n; ++i) { for (j=1; j<=i; ++j) { Vscanf("%lf", &A(i,j)); } } Vscanf("%*[^\n] "); } /* Read B from data file */ for (i=1; i<=n; ++i) { for (j=1; j<=nrhs; ++j) { Vscanf("%lf", &B(i,j)); } } Vscanf("%*[^\n] "); /* Solve the equations AX = B for X */ /* nag_real_sym_lin_solve (f04bhc). * Computes the solution and error-bound to a real symmetric * system of linear equations */ nag_real_sym_lin_solve(order, uplo_enum, n, nrhs, a, pda, ipiv, b, pdb, &rcond, &errbnd, &fail); if (fail.code == NE_NOERROR) { /* Print solution, estimate of condition number and approximate */ /* error bound */ /* nag_gen_real_mat_print (x04cac). * Print real general matrix (easy-to-use) */ nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb, "Solution", 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } Vprintf("\n%s\n%6s%9.1e\n", "Estimate of condition number", "", 1./rcond); Vprintf("\n\n"); Vprintf("%s\n%6s%9.1e\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 */ Vprintf("\n"); Vprintf("%s\n%6s%9.1e\n\n\n", "Estimate of reciprocal of condition number", "", rcond); /* nag_gen_real_mat_print (x04cac), see above. */ nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb, "Solution", 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } } else if (fail.code == NE_SINGULAR) { /* The upper triangular matrix U is exactly singular. Print */ /* details of factorization */ Vprintf("\n"); /* nag_gen_real_mat_print (x04cac), see above. */ nag_gen_real_mat_print(order, Nag_UpperMatrix, Nag_NonUnitDiag, n, n, a, pda, "Details of factorization", 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print pivot indices */ Vprintf("\n%s\n", "Pivot indices"); for (i=1; i<=n; ++i) { Vprintf("%11ld%s", ipiv[i-1], i%7 == 0 || i == n ?"\n":" "); } Vprintf("\n"); } END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (ipiv) NAG_FREE(ipiv); return exit_status; }