/* nag_zpbrfs (f07hvc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, k, kd, n, nrhs, pdab, pdafb, pdb, pdx; Integer ferr_len, berr_len; Integer exit_status=0; Nag_UploType uplo_enum; NagError fail; Nag_OrderType order; /* Arrays */ char uplo[2]; Complex *ab=0, *afb=0, *b=0, *x=0; double *berr=0, *ferr=0; #ifdef NAG_COLUMN_MAJOR #define AB_UPPER(I,J) ab[(J-1)*pdab + k + I - J - 1] #define AB_LOWER(I,J) ab[(J-1)*pdab + I - J] #define AFB_UPPER(I,J) afb[(J-1)*pdafb + k + I - J - 1] #define AFB_LOWER(I,J) afb[(J-1)*pdafb + I - J] #define B(I,J) b[(J-1)*pdb + I - 1] #define X(I,J) x[(J-1)*pdx + I - 1] order = Nag_ColMajor; #else #define AB_UPPER(I,J) ab[(I-1)*pdab + J - I] #define AB_LOWER(I,J) ab[(I-1)*pdab + k + J - I - 1] #define AFB_UPPER(I,J) afb[(I-1)*pdafb + J - I] #define AFB_LOWER(I,J) afb[(I-1)*pdafb + k + J - I - 1] #define B(I,J) b[(I-1)*pdb + J - 1] #define X(I,J) x[(I-1)*pdx + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); Vprintf("nag_zpbrfs (f07hvc) Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%ld%ld%*[^\n] ", &n, &kd, &nrhs); pdab = kd + 1; pdafb = kd + 1; #ifdef NAG_COLUMN_MAJOR pdb = n; pdx = n; #else pdb = nrhs; pdx = nrhs; #endif ferr_len = nrhs; berr_len = nrhs; /* Allocate memory */ if ( !(berr = NAG_ALLOC(berr_len, double)) || !(ferr = NAG_ALLOC(ferr_len, double)) || !(ab = NAG_ALLOC((kd+1) * n, Complex)) || !(afb = NAG_ALLOC((kd+1) * n, Complex)) || !(b = NAG_ALLOC(n * nrhs, Complex)) || !(x = NAG_ALLOC(n * nrhs, Complex)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A from data file */ 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; } k = kd + 1; if (uplo_enum == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= MIN(i+kd,n); ++j) { Vscanf(" ( %lf , %lf )", &AB_UPPER(i,j).re, &AB_UPPER(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_LOWER(i,j).re, &AB_LOWER(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] "); /* Copy A to AF and B to X */ if (uplo_enum == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= MIN(i+kd,n); ++j) { AFB_UPPER(i,j).re = AB_UPPER(i,j).re; AFB_UPPER(i,j).im = AB_UPPER(i,j).im; } } } else { for (i = 1; i <= n; ++i) { for (j = MAX(1,i-kd); j <= i; ++j) { AFB_LOWER(i,j).re = AB_LOWER(i,j).re; AFB_LOWER(i,j).im = AB_LOWER(i,j).im; } } } for (i = 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) { X(i,j).re = B(i,j).re; X(i,j).im = B(i,j).im; } } /* Factorize A in the array AFP */ /* nag_zpbtrf (f07hrc). * Cholesky factorization of complex Hermitian * positive-definite band matrix */ nag_zpbtrf(order, uplo_enum, n, kd, afb, pdafb, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zpbtrf (f07hrc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute solution in the array X */ /* nag_zpbtrs (f07hsc). * Solution of complex Hermitian positive-definite band * system of linear equations, multiple right-hand sides, * matrix already factorized by nag_zpbtrf (f07hrc) */ nag_zpbtrs(order, uplo_enum, n, kd, nrhs, afb, pdafb, x, pdx, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zpbtrs (f07hsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Improve solution, and compute backward errors and */ /* estimated bounds on the forward errors */ /* nag_zpbrfs (f07hvc). * Refined solution with error bounds of complex Hermitian * positive-definite band system of linear equations, * multiple right-hand sides */ nag_zpbrfs(order, uplo_enum, n, kd, nrhs, ab, pdab, afb, pdafb, b, pdb, x, pdx, ferr, berr, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zpbrfs (f07hvc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print details of solution */ /* 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, x, pdx, Nag_BracketForm, "%7.4f", "Solution(s)", 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("\nBackward errors (machine-dependent)\n"); for (j = 1; j <= nrhs; ++j) Vprintf("%11.1e%s", berr[j-1], j%7==0 ?"\n":" "); Vprintf("\nEstimated forward error bounds (machine-dependent)\n"); for (j = 1; j <= nrhs; ++j) Vprintf("%11.1e%s", ferr[j-1], j%7==0 ?"\n":" "); Vprintf("\n"); END: if (berr) NAG_FREE(berr); if (ferr) NAG_FREE(ferr); if (ab) NAG_FREE(ab); if (afb) NAG_FREE(afb); if (b) NAG_FREE(b); if (x) NAG_FREE(x); return exit_status; }