/* nag_zgeqp3 (f08btc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ Complex one = { 1.0, 0.0 }; Complex zero = { 0.0, 0.0 }; double tol; Integer i, j, k, m, n, nrhs, pda, pdb, pdw; Integer exit_status = 0; /* Arrays */ Complex *a = 0, *b = 0, *tau = 0, *work = 0; double *rnorm = 0; Integer *jpvt = 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] order = Nag_ColMajor; #else #define A(I, J) a[(I - 1) * pda + J - 1] #define B(I, J) b[(I - 1) * pdb + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_zgeqp3 (f08btc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%ld%ld%*[^\n]", &m, &n, &nrhs); #ifdef NAG_COLUMN_MAJOR pda = m; pdb = m; pdw = m; #else pda = n; pdb = nrhs; pdw = 1; #endif /* Allocate memory */ if (!(a = NAG_ALLOC(m * n, Complex)) || !(b = NAG_ALLOC(m * nrhs, Complex)) || !(tau = NAG_ALLOC(n, Complex)) || !(work = NAG_ALLOC(n, Complex)) || !(rnorm = NAG_ALLOC(nrhs, double)) || !(jpvt = NAG_ALLOC(n, Integer))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* 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]"); /* nag_iload (f16dbc). * Initialize jpvt to be zero so that all columns are free. */ nag_iload(n, 0, jpvt, 1, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_iload (f16dbc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zgeqp3 (f08btc). * Compute the QR factorization of A. */ nag_zgeqp3(order, m, n, a, pda, jpvt, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgeqp3 (f08btc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zunmqr (f08auc). * Compute C = (C1) = (Q**H)*B, storing the result in B. * (C2) */ nag_zunmqr(order, Nag_LeftSide, Nag_ConjTrans, m, nrhs, n, a, pda, tau, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zunmqr (f08auc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Choose tol to reflect the relative accuracy of the input data */ tol = 0.01; /* nag_complex_abs (a02dbc). * Determine and print the rank, k, of R relative to tol. */ for (k = 1; k <= n; ++k) if (nag_complex_abs(A(k, k)) <= tol * nag_complex_abs(A(1, 1))) break; --k; printf("Tolerance used to estimate the rank of A\n"); printf("%11.2e\n", tol); printf("Estimated rank of A\n"); printf("%8ld\n\n", k); /* nag_ztrsm (f16zjc). * Compute least-squares solutions by backsubstitution in * R(1:k,1:k)*Y = C1, storing the result in B. */ nag_ztrsm(order, Nag_LeftSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k, nrhs, one, a, pda, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztrsm (f16zjc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zge_norm (f16uac). * Compute estimates of the square roots of the residual sums of * squares (2-norm of each of the columns of C2). */ for (j = 1; j <= nrhs; ++j) { nag_zge_norm(order, Nag_FrobeniusNorm, m - k, 1, &B(k + 1, j), pdb, &rnorm[j - 1], &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message); exit_status = 1; goto END; } } /* nag_zge_load (f16thc). * Set the remaining elements of the solutions to zero (to give * the basic solutions). */ nag_zge_load(order, n - k, nrhs, zero, zero, &B(k + 1, 1), pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zge_load (f16thc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Permute the least-squares solutions stored in B to give X = P*Y */ for (j = 1; j <= nrhs; ++j) { for (i = 1; i <= n; ++i) { work[jpvt[i - 1] - 1].re = B(i, j).re; work[jpvt[i - 1] - 1].im = B(i, j).im; } /* nag_zge_copy (f16tfc). * Copy matrix. */ nag_zge_copy(order, Nag_NoTrans, n, 1, work, pdw, &B(1, j), pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zge_copy (f16tfc).\n%s\n", fail.message); exit_status = 1; goto END; } } /* nag_gen_complx_mat_print_comp (x04dbc). * Print least-squares solutions. */ fflush(stdout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb, Nag_BracketForm, "%7.4f", "Least-squares solution(s)", 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; } /* Print the square roots of the residual sums of squares */ printf("\nSquare root(s) of the residual sum(s) of squares\n"); for (j = 0; j < nrhs; ++j) printf("%11.2e%s", rnorm[j], (j+1)%7 == 0?"\n":" "); END: NAG_FREE(a); NAG_FREE(b); NAG_FREE(tau); NAG_FREE(work); NAG_FREE(rnorm); NAG_FREE(jpvt); return exit_status; } #undef A #undef B