/* nag_zunmbr (f08kuc) 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, pdph, pdu; Integer d_len, e_len, tau_len, tauq_len, taup_len; Integer exit_status=0; NagError fail; Nag_OrderType order; /* Arrays */ Complex *a=0, *ph=0, *tau=0, *taup=0, *tauq=0, *u=0; double *d=0, *e=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 PH(I,J) ph[(J-1)*pdph + 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 PH(I,J) ph[(I-1)*pdph + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); Vprintf("nag_zunmbr (f08kuc) Example Program Results\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); for (ic = 1; ic <= 2; ++ic) { Vscanf("%ld%ld%*[^\n] ", &m, &n); #ifdef NAG_COLUMN_MAJOR pda = m; pdph = n; pdu = m; #else pda = n; pdph = n; pdu = m; #endif tau_len = n; taup_len = n; tauq_len = n; d_len = n; e_len = n - 1; /* Allocate memory */ if ( !(a = NAG_ALLOC(m * n, Complex)) || !(ph = NAG_ALLOC(n * n, Complex)) || !(tau = NAG_ALLOC(tau_len, Complex)) || !(taup = NAG_ALLOC(taup_len, Complex)) || !(tauq = NAG_ALLOC(tauq_len, Complex)) || !(u = NAG_ALLOC(m * m, Complex)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) ) { Vprintf("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) Vscanf(" ( %lf , %lf )", &A(i,j).re, &A(i,j).im); } Vscanf("%*[^\n] "); if (m >= n) { /* Compute the QR factorization of A */ /* nag_zgeqrf (f08asc). * QR factorization of complex general rectangular matrix */ nag_zgeqrf(order, m, n, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zgeqrf (f08asc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A to U */ for (i = 1; i <= m; ++i) { for (j = 1; j <= n; ++j) { U(i,j).re = A(i,j).re; U(i,j).im = A(i,j).im; } } /* Form Q explicitly, storing the result in U */ /* nag_zungqr (f08atc). * Form all or part of unitary Q from QR factorization * determined by nag_zgeqrf (f08asc) or nag_zgeqpf (f08bsc) */ nag_zungqr(order, m, n, n, u, pdu, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zungqr (f08atc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy R to PH (used as workspace) */ for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) { PH(i,j).re = A(i,j).re; PH(i,j).im = A(i,j).im; } } /* 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) { PH(i,j).re = 0.0; PH(i,j).im = 0.0; } } /* Bidiagonalize R */ /* nag_zgebrd (f08ksc). * Unitary reduction of complex general rectangular matrix * to bidiagonal form */ nag_zgebrd(order, n, n, ph, pdph, d, e, tauq, taup, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zgebrd (f08ksc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Update Q, storing the result in U */ /* nag_zunmbr (f08kuc). * Apply unitary transformations from reduction to * bidiagonal form determined by nag_zgebrd (f08ksc) */ nag_zunmbr(order, Nag_FormQ, Nag_RightSide, Nag_NoTrans, m, n, n, ph, pdph, tauq, u, pdu, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zunmbr (f08kuc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print bidiagonal form and matrix Q */ Vprintf("\nExample 1: bidiagonal matrix B\nDiagonal\n"); for (i = 1; i <= n; ++i) Vprintf("%8.4f%s", d[i-1], i%8==0 ?"\n":" "); Vprintf("\nSuper-diagonal\n"); for (i = 1; i <= n - 1; ++i) Vprintf("%8.4f%s", e[i-1], i%8 == 0 ?"\n":" "); Vprintf("\n\n"); /* nag_gen_complx_mat_print_comp (x04dbc). * Print complex general matrix (comprehensive) */ nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, u, pdu, Nag_BracketForm, "%7.4f", "Example 1: matrix Q", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc)." "\n%s\n", fail.message); exit_status = 1; goto END; } } else { /* Compute the LQ factorization of A */ /* nag_zgelqf (f08avc). * LQ factorization of complex general rectangular matrix */ nag_zgelqf(order, m, n, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zgelqf (f08avc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A to PH */ for (i = 1; i <= m; ++i) { for (j = 1; j <= n; ++j) { PH(i,j).re = A(i,j).re; PH(i,j).im = A(i,j).im; } } /* Form Q explicitly, storing the result in PH */ /* nag_zunglq (f08awc). * Form all or part of unitary Q from LQ factorization * determined by nag_zgelqf (f08avc) */ nag_zunglq(order, m, n, m, ph, pdph, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zunglq (f08awc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy L to U (used as workspace) */ for (i = 1; i <= m; ++i) { for (j = 1; j <= i; ++j) { U(i,j).re = A(i,j).re; U(i,j).im = A(i,j).im; } } /* 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).re = 0.0; U(i,j).im = 0.0; } } /* Bidiagonalize L */ /* nag_zgebrd (f08ksc), see above. */ nag_zgebrd(order, m, m, u, pdu, d, e, tauq, taup, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zgebrd (f08ksc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Update P**H, storing the result in PH */ /* nag_zunmbr (f08kuc), see above. */ nag_zunmbr(order, Nag_FormP, Nag_LeftSide, Nag_ConjTrans, m, n, m, u, pdu, taup, ph, pdph, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zunmbr (f08kuc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print bidiagonal form and matrix P**H */ Vprintf("\nExample 2: bidiagonal matrix B\n%s\n", "Diagonal"); for (i = 1; i <= m; ++i) Vprintf("%8.4f%s", d[i-1], i%8==0 ?"\n":" "); Vprintf("\nSuper-diagonal\n"); for (i = 1; i <= m - 1; ++i) Vprintf("%8.4f%s", e[i-1], i%8==0 ?"\n":" "); Vprintf("\n\n"); /* nag_gen_complx_mat_print_comp (x04dbc), see above. */ nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, ph, pdph, Nag_BracketForm, "%7.4f", "Example 2: matrix P**H", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc)." "\n%s\n", fail.message); exit_status = 1; goto END; } } END: if (a) NAG_FREE(a); if (ph) NAG_FREE(ph); if (tau) NAG_FREE(tau); if (taup) NAG_FREE(taup); if (tauq) NAG_FREE(tauq); if (u) NAG_FREE(u); if (d) NAG_FREE(d); if (e) NAG_FREE(e); } return exit_status; }