/* nag_dtzrzf (f08bhc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ double d, f, tol; Integer i, j, k, m, n, nrhs, pda, pdb; Integer exit_status = 0; /* Arrays */ double *a = 0, *b = 0, *rnorm = 0, *tau = 0, *work = 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_dtzrzf (f08bhc) 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; #else pda = n; pdb = nrhs; #endif /* Allocate memory */ if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(m * nrhs, double)) || !(rnorm = NAG_ALLOC(nrhs, double)) || !(tau = NAG_ALLOC(n, double)) || !(work = NAG_ALLOC(n, 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", &A(i, j)); scanf("%*[^\n]"); for (i = 1; i <= m; ++i) for (j = 1; j <= nrhs; ++j) scanf("%lf", &B(i, j)); 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_dgeqp3 (f08bfc). * Compute the QR factorization of A with column pivoting as * A = Q*(R11 R12)*(P**T) * ( 0 R22) */ nag_dgeqp3(order, m, n, a, pda, jpvt, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgeqp3 (f08bfc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dormqr (f08ckc). * Compute C = (C1) = (Q**T)*B, storing the result in b. * (C2) */ 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 (f08ckc).\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 and print the rank, k, of R relative to tol */ for (k = 1; k <= n; ++k) if ((f = A(k, k), fabs(f)) <= tol * (d = A(1, 1), fabs(d))) 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_dtzrzf (f08bhc). * Compute the RZ factorization of the k by k part of R as * (R11 R12) = (T 0)*Z */ nag_dtzrzf(order, k, n, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dtzrzf (f08bhc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dtrsm (f16yjc). * Compute least-squares solutions of triangular problems by * back substitution in T*Y1 = C1, storing the result in b. */ nag_dtrsm(order, Nag_LeftSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k, nrhs, 1.0, a, pda, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dtrsm (f16yjc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dge_norm (f16rac). * 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_dge_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_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } } /* nag_dge_load (f16qhc). * Set the remaining elements of the solutions to zero (to give * the minimum-norm solutions), Y2 = 0. */ nag_dge_load(order, n - k, nrhs, 0.0, 0.0, &B(k + 1, 1), pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_load (f16qhc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dormrz (f08bkc). * Form W = (Z**T)*Y. */ nag_dormrz(order, Nag_LeftSide, Nag_Trans, n, nrhs, k, n - k, a, pda, tau, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dormrz (f08bkc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Permute the least-squares solutions stored in B to give X = P*W */ for (j = 1; j <= nrhs; ++j) { for (i = 1; i <= n; ++i) work[jpvt[i - 1] - 1] = B(i, j); for (i = 1; i <= n; ++i) B(i, j) = work[i - 1]; } /* nag_gen_real_mat_print (x04cac). * Print least-squares solutions. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb, "Least-squares solution(s)", 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; } /* 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%6 == 5?"\n":" "); END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (rnorm) NAG_FREE(rnorm); if (tau) NAG_FREE(tau); if (work) NAG_FREE(work); if (jpvt) NAG_FREE(jpvt); return exit_status; } #undef A #undef B