/* nag_ztpqrt (f08bpc) Example Program. * * Copyright 2013, Numerical Algorithms Group. * * Mark 24, 2013. */ #include #include #include #include #include #include int main(void) { /* Scalars */ double rnorm; Integer exit_status = 0; Integer pda, pdb, pdt; Integer i, j, m, n, nb, nrhs; /* Arrays */ Complex *a = 0, *b = 0, *c = 0, *t = 0; /* Nag Types */ Nag_OrderType order; NagError fail; #ifdef NAG_COLUMN_MAJOR #define A(I,J) a[(J-1)*pda + I-1] #define B(I,J) b[(J-1)*pdb + I-1] #define C(I,J) c[(J-1)*pdb + I-1] #define T(I,J) t[(J-1)*pdt + 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] #define C(I,J) c[(I-1)*pdb + J-1] #define T(I,J) t[(I-1)*pdt + J-1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_ztpqrt (f08bpc) Example Program Results\n\n"); fflush(stdout); /* Skip heading in data file*/ scanf("%*[^\n]"); scanf("%ld%ld%ld%*[^\n]", &m, &n, &nrhs); nb = MIN(m, n); if (!(a = NAG_ALLOC(m*n, Complex))|| !(b = NAG_ALLOC(m*nrhs, Complex))|| !(c = NAG_ALLOC(m*nrhs, Complex))|| !(t = NAG_ALLOC(nb*MIN(m, n), Complex))) { printf("Allocation failure\n"); exit_status = -1; goto END; } #ifdef NAG_COLUMN_MAJOR pda = m; pdb = m; pdt = nb; #else pda = n; pdb = nrhs; pdt = MIN(m, n); #endif /* Read A and B from data file */ for (i = 1; i <= m; ++i) for (j = 1; j <= n; ++j) scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im); scanf("%*[^\n]"); for (i = 1; i <= m; ++i) for (j = 1; j <= nrhs; ++j) scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im); scanf("%*[^\n]"); for (i = 1; i <= m; ++i) for (j = 1; j <= nrhs; ++j) C(i, j) = B(i, j); /* nag_zgeqrt (f08apc). * Compute the QR factorization of first n rows of A by recursive algorithm. */ nag_zgeqrt(order, n, n, nb, a, pda, t, pdt, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgeqrt (f08apc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zgemqrt (f08aqc). * Compute C = (C1) = (Q^H)*B, storing the result in C * (C2) * by applying Q^H from left. */ nag_zgemqrt(order, Nag_LeftSide, Nag_ConjTrans, n, nrhs, n, nb, a, pda, t, pdt, c, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgemqrt (f08aqc).\n%s\n", fail.message); exit_status = 1; goto END; } for (i = 1; i <= n; ++i) for (j = 1; j <= nrhs; ++j) B(i, j) = C(i, j); /* nag_ztrtrs (f07tsc). * Compute least-squares solutions for first n rows * by backsubstitution in R*X = C1. */ nag_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs, a, pda, c, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztrtrs (f07tsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_gen_complx_mat_print_comp (x04dbc). * Print least-squares solutions using first n rows. */ nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, c, pdb, Nag_BracketForm, "%7.4f", "Solution(s) for n rows", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_ztpqrt (f08bpc). * Now add the remaining rows and perform QR update. */ nag_ztpqrt(order, m - n, n, 0, nb, a, pda, &A(n + 1, 1), pda, t, pdt, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztpqrt (f08bpc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_ztpmqrt (f08bqc). * Apply orthogonal transformations to C. */ nag_ztpmqrt(order, Nag_LeftSide, Nag_ConjTrans, m - n, nrhs, n, 0, nb, &A(n + 1, 1), pda, t, pdt, b, pdb, &B(5, 1),pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztpmqrt (f08bqc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_ztrtrs (f07tsc). * Compute least-squares solutions for first n rows * by backsubstitution in R*X = C1. */ nag_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs, a, pda, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztrtrs (f07tsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_gen_complx_mat_print_comp (x04dbc). * Print least-squares solutions. */ printf("\n"); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb, Nag_BracketForm, "%7.4f", "Least-squares solution(s) for all rows", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n Square root(s) of the residual sum(s) of squares\n"); for ( j=1; j<=nrhs; j++) { /* nag_zge_norm (f16uac). * Compute and print estimate of the square root of the residual * sum of squares. */ nag_zge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1,j), pdb, &rnorm, &fail); if (fail.code != NE_NOERROR) { printf("\nError from nag_zge_norm (f16uac).\n%s\n", fail.message); exit_status = 1; goto END; } printf(" %11.2e ", rnorm); } printf("\n"); END: NAG_FREE(a); NAG_FREE(b); NAG_FREE(c); NAG_FREE(t); return exit_status; }