/* nag_real_sym_posdef_band_lin_solve (f04bfc) 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, 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); Vprintf("nag_real_sym_posdef_band_lin_solve (f04bfc)" " Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%ld%ld%*[^\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)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } pdab = kd+1; #ifdef NAG_COLUMN_MAJOR pdb = n; #else pdb = nrhs; #endif } else { Vprintf("%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. */ Vscanf("%s%*[^\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) { Vscanf("%lf", &AB_U(i,j)); } Vscanf("%*[^\n] "); } } else { for (i = 1; i <= n; ++i) { for (j = MAX(1,i - kd); j <= i; ++j) { Vscanf("%lf", &AB_L(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_posdef_band_lin_solve (f04bfc). * Computes the solution and error-bound to a real symmetric * positive-definite banded system of linear equations */ nag_real_sym_posdef_band_lin_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_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\n", "Estimate of condition number", "", 1.0/rcond); Vprintf("\n%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%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_POS_DEF) { /* The matrix A is not positive definite to working precision */ Vprintf("%s%3ld%s\n\n", "The leading minor of order ", fail.errnum, " is not positive definite"); } END: if (ab) NAG_FREE(ab); if (b) NAG_FREE(b); return exit_status; } #undef AB #undef B