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419 lines
14 KiB
419 lines
14 KiB
#include "clapack.h" |
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/* Table of constant values */ |
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static real c_b4 = -1.f; |
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static real c_b5 = 1.f; |
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static integer c__1 = 1; |
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static real c_b16 = 0.f; |
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/* Subroutine */ int slabrd_(integer *m, integer *n, integer *nb, real *a, |
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integer *lda, real *d__, real *e, real *tauq, real *taup, real *x, |
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integer *ldx, real *y, integer *ldy) |
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{ |
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/* System generated locals */ |
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integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, |
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i__3; |
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/* Local variables */ |
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integer i__; |
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extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), |
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sgemv_(char *, integer *, integer *, real *, real *, integer *, |
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real *, integer *, real *, real *, integer *), slarfg_( |
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integer *, real *, real *, integer *, real *); |
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/* -- LAPACK auxiliary 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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|
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/* Purpose */ |
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/* ======= */ |
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/* SLABRD reduces the first NB rows and columns of a real general */ |
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/* m by n matrix A to upper or lower bidiagonal form by an orthogonal */ |
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/* transformation Q' * A * P, and returns the matrices X and Y which */ |
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/* are needed to apply the transformation to the unreduced part of A. */ |
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/* If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */ |
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/* bidiagonal form. */ |
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/* This is an auxiliary routine called by SGEBRD */ |
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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. */ |
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/* N (input) INTEGER */ |
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/* The number of columns in the matrix A. */ |
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/* NB (input) INTEGER */ |
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/* The number of leading rows and columns of A to be reduced. */ |
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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, the first NB rows and columns of the matrix are */ |
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/* overwritten; the rest of the array is unchanged. */ |
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/* If m >= n, elements on and below the diagonal in the first NB */ |
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/* columns, with the array TAUQ, represent the orthogonal */ |
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/* matrix Q as a product of elementary reflectors; and */ |
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/* elements above the diagonal in the first NB rows, with the */ |
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/* array TAUP, represent the orthogonal matrix P as a product */ |
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/* of elementary reflectors. */ |
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/* If m < n, elements below the diagonal in the first NB */ |
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/* columns, with the array TAUQ, represent the orthogonal */ |
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/* matrix Q as a product of elementary reflectors, and */ |
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/* elements on and above the diagonal in the first NB rows, */ |
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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 (NB) */ |
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/* The diagonal elements of the first NB rows and columns of */ |
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/* the reduced matrix. D(i) = A(i,i). */ |
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/* E (output) REAL array, dimension (NB) */ |
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/* The off-diagonal elements of the first NB rows and columns of */ |
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/* the reduced matrix. */ |
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/* TAUQ (output) REAL array dimension (NB) */ |
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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 (NB) */ |
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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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/* X (output) REAL array, dimension (LDX,NB) */ |
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/* The m-by-nb matrix X required to update the unreduced part */ |
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/* of A. */ |
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/* LDX (input) INTEGER */ |
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/* The leading dimension of the array X. LDX >= M. */ |
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/* Y (output) REAL array, dimension (LDY,NB) */ |
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/* The n-by-nb matrix Y required to update the unreduced part */ |
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/* of A. */ |
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/* LDY (input) INTEGER */ |
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/* The leading dimension of the array Y. LDY >= N. */ |
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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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/* Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) */ |
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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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/* If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */ |
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/* A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */ |
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/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ |
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/* If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */ |
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/* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */ |
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/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ |
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/* The elements of the vectors v and u together form the m-by-nb matrix */ |
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/* V and the nb-by-n matrix U' which are needed, with X and Y, to apply */ |
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/* the transformation to the unreduced part of the matrix, using a block */ |
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/* update of the form: A := A - V*Y' - X*U'. */ |
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/* The contents of A on exit are illustrated by the following examples */ |
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/* with nb = 2: */ |
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/* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ |
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/* ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) */ |
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/* ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) */ |
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/* ( v1 v2 a a a ) ( v1 1 a a a a ) */ |
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/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */ |
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/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */ |
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/* ( v1 v2 a a a ) */ |
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/* where a denotes an element of the original matrix which is unchanged, */ |
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/* vi denotes an element of the vector defining H(i), and ui an element */ |
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/* of 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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/* Quick return if possible */ |
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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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x_dim1 = *ldx; |
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x_offset = 1 + x_dim1; |
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x -= x_offset; |
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y_dim1 = *ldy; |
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y_offset = 1 + y_dim1; |
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y -= y_offset; |
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/* Function Body */ |
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if (*m <= 0 || *n <= 0) { |
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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 = *nb; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Update A(i:m,i) */ |
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i__2 = *m - i__ + 1; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda, |
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&y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], & |
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c__1); |
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i__2 = *m - i__ + 1; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx, |
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&a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * |
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a_dim1], &c__1); |
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/* Generate reflection Q(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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if (i__ < *n) { |
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a[i__ + i__ * a_dim1] = 1.f; |
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/* Compute Y(i+1:n,i) */ |
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i__2 = *m - i__ + 1; |
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i__3 = *n - i__; |
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sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * |
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a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, & |
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y[i__ + 1 + i__ * y_dim1], &c__1); |
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i__2 = *m - i__ + 1; |
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i__3 = i__ - 1; |
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sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], |
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lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * |
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y_dim1 + 1], &c__1); |
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i__2 = *n - i__; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + |
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y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ |
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i__ + 1 + i__ * y_dim1], &c__1); |
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i__2 = *m - i__ + 1; |
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i__3 = i__ - 1; |
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sgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], |
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ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * |
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y_dim1 + 1], &c__1); |
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i__2 = i__ - 1; |
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i__3 = *n - i__; |
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sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * |
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a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, |
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&y[i__ + 1 + i__ * y_dim1], &c__1); |
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i__2 = *n - i__; |
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sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); |
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/* Update A(i,i+1:n) */ |
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i__2 = *n - i__; |
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sgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + |
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y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + ( |
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i__ + 1) * a_dim1], lda); |
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i__2 = i__ - 1; |
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i__3 = *n - i__; |
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sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * |
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a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[ |
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i__ + (i__ + 1) * a_dim1], lda); |
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/* Generate reflection P(i) to annihilate 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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/* Compute X(i+1:m,i) */ |
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i__2 = *m - i__; |
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i__3 = *n - i__; |
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sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ |
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+ 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], |
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lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1); |
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i__2 = *n - i__; |
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sgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], |
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ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[ |
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i__ * x_dim1 + 1], &c__1); |
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i__2 = *m - i__; |
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sgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + |
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a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ |
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i__ + 1 + i__ * x_dim1], &c__1); |
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i__2 = i__ - 1; |
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i__3 = *n - i__; |
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sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * |
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a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, & |
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c_b16, &x[i__ * x_dim1 + 1], &c__1); |
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i__2 = *m - i__; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + |
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x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ |
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i__ + 1 + i__ * x_dim1], &c__1); |
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i__2 = *m - i__; |
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sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); |
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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 = *nb; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Update A(i,i:n) */ |
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i__2 = *n - i__ + 1; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy, |
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&a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], |
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lda); |
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i__2 = i__ - 1; |
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i__3 = *n - i__ + 1; |
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sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], |
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lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1], |
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lda); |
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/* Generate reflection P(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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if (i__ < *m) { |
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a[i__ + i__ * a_dim1] = 1.f; |
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/* Compute X(i+1:m,i) */ |
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i__2 = *m - i__; |
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i__3 = *n - i__ + 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ * |
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a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, & |
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x[i__ + 1 + i__ * x_dim1], &c__1); |
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i__2 = *n - i__ + 1; |
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i__3 = i__ - 1; |
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sgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], |
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ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * |
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x_dim1 + 1], &c__1); |
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i__2 = *m - i__; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + |
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a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ |
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i__ + 1 + i__ * x_dim1], &c__1); |
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i__2 = i__ - 1; |
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i__3 = *n - i__ + 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + |
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1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * |
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x_dim1 + 1], &c__1); |
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i__2 = *m - i__; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + |
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x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ |
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i__ + 1 + i__ * x_dim1], &c__1); |
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i__2 = *m - i__; |
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sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); |
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/* Update A(i+1:m,i) */ |
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i__2 = *m - i__; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + |
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a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + |
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1 + i__ * a_dim1], &c__1); |
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i__2 = *m - i__; |
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sgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + |
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x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[ |
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i__ + 1 + i__ * a_dim1], &c__1); |
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/* Generate reflection Q(i) to annihilate 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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/* Compute Y(i+1:n,i) */ |
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i__2 = *m - i__; |
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i__3 = *n - i__; |
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sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + |
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1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, |
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&c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1); |
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i__2 = *m - i__; |
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i__3 = i__ - 1; |
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sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], |
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lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ |
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i__ * y_dim1 + 1], &c__1); |
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i__2 = *n - i__; |
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i__3 = i__ - 1; |
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sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + |
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y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ |
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i__ + 1 + i__ * y_dim1], &c__1); |
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i__2 = *m - i__; |
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sgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], |
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ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ |
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i__ * y_dim1 + 1], &c__1); |
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i__2 = *n - i__; |
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sgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 |
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+ 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ |
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+ 1 + i__ * y_dim1], &c__1); |
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i__2 = *n - i__; |
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sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); |
|
} |
|
/* L20: */ |
|
} |
|
} |
|
return 0; |
|
|
|
/* End of SLABRD */ |
|
|
|
} /* slabrd_ */
|
|
|