/* nag_real_sym_posdef_packed_lin_solve (f04bec) 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, pdb; /* Arrays */ char uplo[2]; double *ap=0, *b=0; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_UploType uplo_enum; #ifdef NAG_COLUMN_MAJOR #define A_UPPER(I,J) ap[J*(J-1)/2 + I - 1] #define A_LOWER(I,J) ap[(2*n-J)*(J-1)/2 + I - 1] #define B(I,J) b[(J-1)*pdb + I - 1] order = Nag_ColMajor; #else #define A_LOWER(I,J) ap[I*(I-1)/2 + J - 1] #define A_UPPER(I,J) ap[(2*n-I)*(I-1)/2 + 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_posdef_packed_lin_solve (f04bec) 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 ( !(ap = NAG_ALLOC(n*(n+1)/2, double)) || !(b = NAG_ALLOC(n*nrhs, double)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } #ifdef NAG_COLUMN_MAJOR pdb = n; #else 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; } /* Read the upper or lower triangular part of the matrix A from */ /* data file */ if (uplo_enum == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) { Vscanf("%lf", &A_UPPER(i,j)); } } Vscanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) { Vscanf("%lf", &A_LOWER(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_packed_lin_solve (f04bec). * Computes the solution and error-bound to a real symmetric * positive-definite system of linear equations, packed * storage */ nag_real_sym_posdef_packed_lin_solve(order, uplo_enum, n, nrhs, ap, 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"); Vprintf("%s\n%6s%9.1e\n\n\n", "Estimate of condition number", "", 1.0/rcond); 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%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 (ap) NAG_FREE(ap); if (b) NAG_FREE(b); return exit_status; } #undef B