/* nag_herm_posdef_band_lin_solve (f04cfc) Example Program. * * Copyright 2004 Numerical Algorithms Group. * * Mark 8, 2004. */ #include #include #include #include #include int main(void) { double errbnd, rcond; Integer exit_status, i, j, kd, n, nrhs, pdab, pdb; /* Arrays */ char nag_enum_arg[20]; char *clabs=0, *rlabs=0; Complex *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_herm_posdef_band_lin_solve (f04cfc)" " 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 ( !(clabs = NAG_ALLOC(2, char)) || !(rlabs = NAG_ALLOC(2, char)) || !(ab = NAG_ALLOC((kd+1)*n, Complex)) || !(b = NAG_ALLOC(n*nrhs, Complex)) ) { 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); /* Read the upper or lower triangular part of the band matrix A */ /* from data file */ if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= MIN(n,i + kd); ++j) { Vscanf(" ( %lf , %lf )", &AB_U(i,j).re, &AB_U(i,j).im); } Vscanf("%*[^\n] "); } } else { for (i = 1; i <= n; ++i) { for (j = MAX(1,i - kd); j <= i; ++j) { Vscanf(" ( %lf , %lf )", &AB_L(i,j).re, &AB_L(i,j).im); } Vscanf("%*[^\n] "); } } /* Read B from data file */ for (i = 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) { Vscanf(" ( %lf , %lf )", &B(i,j).re, &B(i,j).im); } } Vscanf("%*[^\n] "); /* Solve the equations AX = B for X */ /* nag_herm_posdef_band_lin_solve (f04cfc). * Computes the solution and error-bound to a complex * Hermitian positive-definite banded system of linear * equations */ nag_herm_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_complx_mat_print_comp (x04dbc). * Print complex general matrix (comprehensive) */ nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb, Nag_BracketForm, "%7.4f", "Solution", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } Vprintf("\n%s\n%4s%9.1e\n\n", "Estimate of condition number", "", 1.0/rcond); Vprintf("\n%s\n%4s%9.1e\n\n", "Estimate of error bound for computed solutions", "", errbnd); } if (fail.code == NE_RCOND) { /* Matrix A is numerically singular. Print estimate of */ /* reciprocal of condition number and solution. */ Vprintf("\n"); Vprintf("%s\n%4s%9.1e\n\n\n", "Estimate of reciprocal of condition number", "", rcond); /* nag_gen_complx_mat_print_comp (x04dbc), see above. */ nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb, Nag_BracketForm, "%7.4f", "Solution", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } } 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 (clabs) NAG_FREE(clabs); if (rlabs) NAG_FREE(rlabs); if (ab) NAG_FREE(ab); if (b) NAG_FREE(b); return exit_status; } #undef AB #undef B