/* nag_dormbr (f08kgc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include int main(void) { /* Scalars */ Integer i, ic, j, m, n, pda, pdpt, pdu; Integer d_len, e_len, tau_len, tauq_len, taup_len; Integer exit_status = 0; NagError fail; Nag_OrderType order; /* Arrays */ double *a = 0, *d = 0, *e = 0, *pt = 0, *tau = 0, *taup = 0, *tauq = 0; double *u = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] #define U(I, J) u[(J - 1) * pdu + I - 1] #define PT(I, J) pt[(J - 1) * pdpt + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I - 1) * pda + J - 1] #define U(I, J) u[(I - 1) * pdu + J - 1] #define PT(I, J) pt[(I - 1) * pdpt + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dormbr (f08kgc) Example Program Results\n"); /* Skip heading in data file */ scanf("%*[^\n] "); for (ic = 1; ic <= 2; ++ic) { scanf("%ld%ld%*[^\n] ", &m, &n); #ifdef NAG_COLUMN_MAJOR pda = m; #else pda = n; #endif pdu = m; pdpt = n; taup_len = n; tauq_len = n; tau_len = n; d_len = n; e_len = n - 1; /* Allocate memory */ if (!(a = NAG_ALLOC(m * n, double)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) || !(pt = NAG_ALLOC(n * n, double)) || !(tau = NAG_ALLOC(tau_len, double)) || !(taup = NAG_ALLOC(taup_len, double)) || !(tauq = NAG_ALLOC(tauq_len, double)) || !(u = NAG_ALLOC(m * m, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A from data file */ for (i = 1; i <= m; ++i) { for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j)); } scanf("%*[^\n] "); if (m >= n) { /* Example 1. */ /* nag_dgeqrf (f08aec): Compute the QR factorization of A */ nag_dgeqrf(order, m, n, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgeqrf (f08aec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A to U */ for (i = 1; i <= m; ++i) { for (j = 1; j <= MIN(i, n); ++j) U(i, j) = A(i, j); } /* nag_dorgqr (f08afc): */ /* Form Q explicitly, storing the result in U */ nag_dorgqr(order, m, m, n, u, pdu, tau, &fail); if (fail.code != NE_NOERROR) { printf("order=%d\n", order); printf("Error from nag_dorgqr (f08afc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy R to PT (used as workspace) */ nag_dtr_copy(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, a, pda, pt, pdpt, &fail); /* Set the strictly lower triangular part of R to zero */ for (i = 2; i <= n; ++i) { for (j = 1; j <= MIN(i - 1, n - 1); ++j) PT(i, j) = 0.0; } /* nag_dgebrd (f08kec): Bidiagonalize R. */ nag_dgebrd(order, n, n, pt, pdpt, d, e, tauq, taup, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgebrd (f08kec).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dormbr (f08kgc): Update Q, storing the result in U. */ nag_dormbr(order, Nag_ApplyQ, Nag_RightSide, Nag_NoTrans, m, n, n, pt, pdpt, tauq, u, pdu, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dormbr (f08kgc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print bidiagonal form and matrix Q */ printf("\nExample 1: bidiagonal matrix B\nDiagonal\n"); for (i = 1; i <= n; ++i) printf("%8.4f%s", d[i - 1], i % 8 == 0?"\n":" "); printf("\nSuper-diagonal\n"); for (i = 1; i <= n - 1; ++i) printf("%8.4f%s", e[i - 1], i % 8 == 0?"\n":" "); printf("\n\n"); /* nag_gen_real_mat_print (x04cac): Print Q as stored in u. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, u, pdu, "Example 1: matrix Q", 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; } } else { /* Example 2. */ /* nag_dgelqf (f08ahc): Compute the LQ factorization of A. */ nag_dgelqf(order, m, n, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgelqf (f08ahc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A to PT */ for (i = 1; i <= m; ++i) { for (j = i; j <= n; ++j) PT(i, j) = A(i, j); } /* nag_dorglq (f08ajc): */ /* Form Q explicitly, storing the result in PT. */ nag_dorglq(order, n, n, m, pt, pdpt, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dorglq (f08ajc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy L to U (used as workspace) */ nag_dtr_copy(order, Nag_Lower, Nag_NoTrans, Nag_NonUnitDiag, m, a, pda, u, pdu, &fail); /* Set the strictly upper triangular part of L to zero */ for (i = 1; i <= m - 1; ++i) { for (j = i + 1; j <= m; ++j) U(i, j) = 0.0; } /* nag_dgebrd (f08kec): Bidiagonalize L. */ nag_dgebrd(order, m, m, u, pdu, d, e, tauq, taup, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgebrd (f08kec).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dormbr (f08kgc):Update P**T, storing the result in PT. */ nag_dormbr(order, Nag_ApplyP, Nag_LeftSide, Nag_Trans, m, n, m, u, pdu, taup, pt, pdpt, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dormbr (f08kgc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print bidiagonal form and matrix P**T */ printf("\nExample 2: bidiagonal matrix B\n%s\n", "Diagonal\n"); for (i = 1; i <= m; ++i) printf("%8.4f%s", d[i - 1], i % 8 == 0?"\n":" "); printf("\nSuper-diagonal\n"); for (i = 1; i <= m - 1; ++i) printf("%8.4f%s", e[i - 1], i % 8 == 0?"\n":" "); printf("\n\n"); /* nag_gen_real_mat_print (x04cac), Print pt. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, pt, pdpt, "Example 2: matrix P**T", 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 (d) NAG_FREE(d); if (e) NAG_FREE(e); if (pt) NAG_FREE(pt); if (tau) NAG_FREE(tau); if (taup) NAG_FREE(taup); if (tauq) NAG_FREE(tauq); if (u) NAG_FREE(u); } return exit_status; } #undef A #undef U #undef PT