/* nag_dgeqpf (f08bec) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ double tol; Integer i, j, jpvt_len, k, m, n, nrhs; Integer pda, pdb, pdx, tau_len; Integer exit_status = 0; NagError fail; Nag_OrderType order; /* Arrays */ double *a = 0, *b = 0, *tau = 0, *x = 0; Integer *jpvt = 0; #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 X(I, J) x[(J - 1) * pdx + 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 X(I, J) x[(I - 1) * pdx + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dgeqpf (f08bec) 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; pdx = m; #else pda = n; pdb = nrhs; pdx = nrhs; #endif tau_len = MIN(m, n); jpvt_len = n; /* Allocate memory */ if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(m * nrhs, double)) || !(tau = NAG_ALLOC(tau_len, double)) || !(x = NAG_ALLOC(m * nrhs, double)) || !(jpvt = NAG_ALLOC(jpvt_len, 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", &A(i, j)); } scanf("%*[^\n] "); for (i = 1; i <= m; ++i) { for (j = 1; j <= nrhs; ++j) scanf("%lf", &B(i, j)); } scanf("%*[^\n] "); /* Initialize JPVT to be zero so that all columns are free */ /* nag_iload (f16dbc). * Broadcast scalar into integer vector */ nag_iload(n, 0, jpvt, 1, &fail); /* Compute the QR factorization of A */ /* nag_dgeqpf (f08bec). * QR factorization of real general rectangular matrix with * column pivoting */ nag_dgeqpf(order, m, n, a, pda, jpvt, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgeqpf (f08bec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Choose TOL to reflect the relative accuracy of the input data */ tol = 0.01; /* Determine which columns of R to use */ for (k = 1; k <= n; ++k) { if (ABS(A(k, k)) <= tol * ABS(A(1, 1))) break; } --k; /* Compute C = (Q**T)*B, storing the result in B */ /* nag_dormqr (f08agc). * Apply orthogonal transformation determined by nag_dgeqrf * (f08aec) or nag_dgeqpf (f08bec) */ nag_dormqr(order, Nag_LeftSide, Nag_Trans, m, nrhs, n, a, pda, tau, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dormqr (f08agc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute least-squares solution by backsubstitution in R*B = C */ /* nag_dtrtrs (f07tec). * Solution of real triangular system of linear equations, * multiple right-hand sides */ nag_dtrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k, nrhs, a, pda, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dtrtrs (f07tec).\n%s\n", fail.message); exit_status = 1; goto END; } for (i = k + 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) B(i, j) = 0.0; } /* Unscramble the least-squares solution stored in B */ for (i = 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) X(jpvt[i - 1], j) = B(i, j); } /* Print least-squares solution */ /* nag_gen_real_mat_print (x04cac). * Print real general matrix (easy-to-use) */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, x, pdx, "Least-squares solution", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (tau) NAG_FREE(tau); if (x) NAG_FREE(x); if (jpvt) NAG_FREE(jpvt); return exit_status; }