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336 lines
11 KiB
336 lines
11 KiB
/* dgebrd.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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/* Table of constant values */ |
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static integer c__1 = 1; |
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static integer c_n1 = -1; |
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static integer c__3 = 3; |
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static integer c__2 = 2; |
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static doublereal c_b21 = -1.; |
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static doublereal c_b22 = 1.; |
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/* Subroutine */ int dgebrd_(integer *m, integer *n, doublereal *a, integer * |
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lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * |
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taup, doublereal *work, integer *lwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4; |
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/* Local variables */ |
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integer i__, j, nb, nx; |
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doublereal ws; |
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extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, |
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integer *, doublereal *, doublereal *, integer *, doublereal *, |
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integer *, doublereal *, doublereal *, integer *); |
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integer nbmin, iinfo, minmn; |
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extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *, |
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integer *, doublereal *, doublereal *, doublereal *, doublereal *, |
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doublereal *, integer *), dlabrd_(integer *, integer *, integer * |
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, doublereal *, integer *, doublereal *, doublereal *, doublereal |
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*, doublereal *, doublereal *, integer *, doublereal *, integer *) |
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, xerbla_(char *, integer *); |
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
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integer *, integer *); |
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integer ldwrkx, ldwrky, lwkopt; |
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logical lquery; |
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/* -- LAPACK routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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/* Purpose */ |
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/* ======= */ |
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/* DGEBRD reduces a general real M-by-N matrix A to upper or lower */ |
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/* bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */ |
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/* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ |
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/* Arguments */ |
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/* ========= */ |
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/* M (input) INTEGER */ |
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/* The number of rows in the matrix A. M >= 0. */ |
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/* N (input) INTEGER */ |
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/* The number of columns in the matrix A. N >= 0. */ |
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ |
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/* On entry, the M-by-N general matrix to be reduced. */ |
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/* On exit, */ |
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/* if m >= n, the diagonal and the first superdiagonal are */ |
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/* overwritten with the upper bidiagonal matrix B; the */ |
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/* elements below the diagonal, with the array TAUQ, represent */ |
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/* the orthogonal matrix Q as a product of elementary */ |
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/* reflectors, and the elements above the first superdiagonal, */ |
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/* with the array TAUP, represent the orthogonal matrix P as */ |
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/* a product of elementary reflectors; */ |
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/* if m < n, the diagonal and the first subdiagonal are */ |
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/* overwritten with the lower bidiagonal matrix B; the */ |
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/* elements below the first subdiagonal, with the array TAUQ, */ |
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/* represent the orthogonal matrix Q as a product of */ |
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/* elementary reflectors, and the elements above the diagonal, */ |
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/* with the array TAUP, represent the orthogonal matrix P as */ |
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/* a product of elementary reflectors. */ |
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/* See Further Details. */ |
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/* LDA (input) INTEGER */ |
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/* The leading dimension of the array A. LDA >= max(1,M). */ |
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/* D (output) DOUBLE PRECISION array, dimension (min(M,N)) */ |
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/* The diagonal elements of the bidiagonal matrix B: */ |
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/* D(i) = A(i,i). */ |
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/* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */ |
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/* The off-diagonal elements of the bidiagonal matrix B: */ |
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/* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ |
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/* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ |
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/* TAUQ (output) DOUBLE PRECISION array dimension (min(M,N)) */ |
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/* The scalar factors of the elementary reflectors which */ |
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/* represent the orthogonal matrix Q. See Further Details. */ |
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/* TAUP (output) DOUBLE PRECISION array, dimension (min(M,N)) */ |
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/* The scalar factors of the elementary reflectors which */ |
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/* represent the orthogonal matrix P. See Further Details. */ |
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/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ |
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/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ |
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/* LWORK (input) INTEGER */ |
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/* The length of the array WORK. LWORK >= max(1,M,N). */ |
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/* For optimum performance LWORK >= (M+N)*NB, where NB */ |
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/* is the optimal blocksize. */ |
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/* If LWORK = -1, then a workspace query is assumed; the routine */ |
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/* only calculates the optimal size of the WORK array, returns */ |
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/* this value as the first entry of the WORK array, and no error */ |
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/* message related to LWORK is issued by XERBLA. */ |
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/* INFO (output) INTEGER */ |
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/* = 0: successful exit */ |
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */ |
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/* Further Details */ |
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/* =============== */ |
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/* The matrices Q and P are represented as products of elementary */ |
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/* reflectors: */ |
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/* If m >= n, */ |
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/* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ |
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/* Each H(i) and G(i) has the form: */ |
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/* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ |
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/* where tauq and taup are real scalars, and v and u are real vectors; */ |
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/* v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */ |
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/* u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */ |
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/* tauq is stored in TAUQ(i) and taup in TAUP(i). */ |
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/* If m < n, */ |
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/* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ |
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/* Each H(i) and G(i) has the form: */ |
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/* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ |
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/* where tauq and taup are real scalars, and v and u are real vectors; */ |
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/* v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ |
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/* u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ |
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/* tauq is stored in TAUQ(i) and taup in TAUP(i). */ |
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/* The contents of A on exit are illustrated by the following examples: */ |
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/* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ |
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/* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ |
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/* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ |
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/* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ |
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/* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ |
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/* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ |
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/* ( v1 v2 v3 v4 v5 ) */ |
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/* where d and e denote diagonal and off-diagonal elements of B, vi */ |
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/* denotes an element of the vector defining H(i), and ui an element of */ |
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/* the vector defining G(i). */ |
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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters */ |
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/* Parameter adjustments */ |
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a_dim1 = *lda; |
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a_offset = 1 + a_dim1; |
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a -= a_offset; |
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--d__; |
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--e; |
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--tauq; |
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--taup; |
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--work; |
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/* Function Body */ |
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*info = 0; |
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/* Computing MAX */ |
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i__1 = 1, i__2 = ilaenv_(&c__1, "DGEBRD", " ", m, n, &c_n1, &c_n1); |
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nb = max(i__1,i__2); |
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lwkopt = (*m + *n) * nb; |
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work[1] = (doublereal) lwkopt; |
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lquery = *lwork == -1; |
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if (*m < 0) { |
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*info = -1; |
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} else if (*n < 0) { |
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*info = -2; |
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} else if (*lda < max(1,*m)) { |
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*info = -4; |
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} else /* if(complicated condition) */ { |
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/* Computing MAX */ |
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i__1 = max(1,*m); |
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if (*lwork < max(i__1,*n) && ! lquery) { |
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*info = -10; |
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} |
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} |
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if (*info < 0) { |
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i__1 = -(*info); |
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xerbla_("DGEBRD", &i__1); |
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return 0; |
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} else if (lquery) { |
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return 0; |
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} |
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/* Quick return if possible */ |
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minmn = min(*m,*n); |
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if (minmn == 0) { |
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work[1] = 1.; |
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return 0; |
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} |
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ws = (doublereal) max(*m,*n); |
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ldwrkx = *m; |
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ldwrky = *n; |
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if (nb > 1 && nb < minmn) { |
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/* Set the crossover point NX. */ |
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/* Computing MAX */ |
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i__1 = nb, i__2 = ilaenv_(&c__3, "DGEBRD", " ", m, n, &c_n1, &c_n1); |
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nx = max(i__1,i__2); |
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/* Determine when to switch from blocked to unblocked code. */ |
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if (nx < minmn) { |
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ws = (doublereal) ((*m + *n) * nb); |
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if ((doublereal) (*lwork) < ws) { |
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/* Not enough work space for the optimal NB, consider using */ |
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/* a smaller block size. */ |
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nbmin = ilaenv_(&c__2, "DGEBRD", " ", m, n, &c_n1, &c_n1); |
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if (*lwork >= (*m + *n) * nbmin) { |
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nb = *lwork / (*m + *n); |
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} else { |
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nb = 1; |
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nx = minmn; |
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} |
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} |
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} |
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} else { |
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nx = minmn; |
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} |
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i__1 = minmn - nx; |
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i__2 = nb; |
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for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { |
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/* Reduce rows and columns i:i+nb-1 to bidiagonal form and return */ |
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/* the matrices X and Y which are needed to update the unreduced */ |
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/* part of the matrix */ |
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i__3 = *m - i__ + 1; |
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i__4 = *n - i__ + 1; |
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dlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[ |
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i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx |
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* nb + 1], &ldwrky); |
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/* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update */ |
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/* of the form A := A - V*Y' - X*U' */ |
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i__3 = *m - i__ - nb + 1; |
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i__4 = *n - i__ - nb + 1; |
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dgemm_("No transpose", "Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__ |
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+ nb + i__ * a_dim1], lda, &work[ldwrkx * nb + nb + 1], & |
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ldwrky, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda); |
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i__3 = *m - i__ - nb + 1; |
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i__4 = *n - i__ - nb + 1; |
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dgemm_("No transpose", "No transpose", &i__3, &i__4, &nb, &c_b21, & |
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work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, & |
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c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda); |
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/* Copy diagonal and off-diagonal elements of B back into A */ |
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if (*m >= *n) { |
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i__3 = i__ + nb - 1; |
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for (j = i__; j <= i__3; ++j) { |
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a[j + j * a_dim1] = d__[j]; |
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a[j + (j + 1) * a_dim1] = e[j]; |
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/* L10: */ |
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} |
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} else { |
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i__3 = i__ + nb - 1; |
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for (j = i__; j <= i__3; ++j) { |
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a[j + j * a_dim1] = d__[j]; |
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a[j + 1 + j * a_dim1] = e[j]; |
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/* L20: */ |
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} |
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} |
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/* L30: */ |
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} |
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/* Use unblocked code to reduce the remainder of the matrix */ |
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i__2 = *m - i__ + 1; |
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i__1 = *n - i__ + 1; |
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dgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], & |
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tauq[i__], &taup[i__], &work[1], &iinfo); |
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work[1] = ws; |
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return 0; |
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/* End of DGEBRD */ |
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} /* dgebrd_ */
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