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290 lines
8.8 KiB
290 lines
8.8 KiB
#include "clapack.h" |
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/* Table of constant values */ |
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static integer c__1 = 1; |
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/* Subroutine */ int sgebd2_(integer *m, integer *n, real *a, integer *lda, |
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real *d__, real *e, real *tauq, real *taup, real *work, 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; |
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/* Local variables */ |
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integer i__; |
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extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *, |
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integer *, real *, real *, integer *, real *), xerbla_( |
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char *, integer *), slarfg_(integer *, real *, real *, |
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integer *, real *); |
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/* -- LAPACK routine (version 3.1) -- */ |
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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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/* SGEBD2 reduces a real general m by n matrix A to upper or lower */ |
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/* bidiagonal form B by an orthogonal transformation: Q' * 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL array, dimension (max(M,N)) */ |
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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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/* .. 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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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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} |
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if (*info < 0) { |
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i__1 = -(*info); |
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xerbla_("SGEBD2", &i__1); |
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return 0; |
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} |
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if (*m >= *n) { |
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/* Reduce to upper bidiagonal form */ |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ |
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i__2 = *m - i__ + 1; |
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/* Computing MIN */ |
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i__3 = i__ + 1; |
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slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ * |
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a_dim1], &c__1, &tauq[i__]); |
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d__[i__] = a[i__ + i__ * a_dim1]; |
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a[i__ + i__ * a_dim1] = 1.f; |
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/* Apply H(i) to A(i:m,i+1:n) from the left */ |
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if (i__ < *n) { |
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i__2 = *m - i__ + 1; |
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i__3 = *n - i__; |
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slarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & |
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tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1] |
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); |
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} |
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a[i__ + i__ * a_dim1] = d__[i__]; |
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if (i__ < *n) { |
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/* Generate elementary reflector G(i) to annihilate */ |
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/* A(i,i+2:n) */ |
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i__2 = *n - i__; |
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/* Computing MIN */ |
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i__3 = i__ + 2; |
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slarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( |
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i__3, *n)* a_dim1], lda, &taup[i__]); |
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e[i__] = a[i__ + (i__ + 1) * a_dim1]; |
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a[i__ + (i__ + 1) * a_dim1] = 1.f; |
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/* Apply G(i) to A(i+1:m,i+1:n) from the right */ |
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i__2 = *m - i__; |
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i__3 = *n - i__; |
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slarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], |
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lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], |
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lda, &work[1]); |
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a[i__ + (i__ + 1) * a_dim1] = e[i__]; |
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} else { |
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taup[i__] = 0.f; |
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} |
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/* L10: */ |
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} |
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} else { |
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/* Reduce to lower bidiagonal form */ |
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i__1 = *m; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */ |
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i__2 = *n - i__ + 1; |
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/* Computing MIN */ |
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i__3 = i__ + 1; |
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slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)* |
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a_dim1], lda, &taup[i__]); |
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d__[i__] = a[i__ + i__ * a_dim1]; |
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a[i__ + i__ * a_dim1] = 1.f; |
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/* Apply G(i) to A(i+1:m,i:n) from the right */ |
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if (i__ < *m) { |
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i__2 = *m - i__; |
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i__3 = *n - i__ + 1; |
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slarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & |
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taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]); |
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} |
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a[i__ + i__ * a_dim1] = d__[i__]; |
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if (i__ < *m) { |
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/* Generate elementary reflector H(i) to annihilate */ |
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/* A(i+2:m,i) */ |
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i__2 = *m - i__; |
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/* Computing MIN */ |
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i__3 = i__ + 2; |
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slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+ |
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i__ * a_dim1], &c__1, &tauq[i__]); |
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e[i__] = a[i__ + 1 + i__ * a_dim1]; |
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a[i__ + 1 + i__ * a_dim1] = 1.f; |
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/* Apply H(i) to A(i+1:m,i+1:n) from the left */ |
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i__2 = *m - i__; |
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i__3 = *n - i__; |
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slarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & |
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c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], |
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lda, &work[1]); |
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a[i__ + 1 + i__ * a_dim1] = e[i__]; |
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} else { |
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tauq[i__] = 0.f; |
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} |
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/* L20: */ |
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} |
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} |
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return 0; |
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/* End of SGEBD2 */ |
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} /* sgebd2_ */
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