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342 lines
12 KiB
342 lines
12 KiB
#include "clapack.h" |
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/* Table of constant values */ |
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static doublereal c_b5 = -1.; |
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static doublereal c_b6 = 1.; |
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static integer c__1 = 1; |
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static doublereal c_b16 = 0.; |
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/* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal * |
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a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, |
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integer *ldw) |
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{ |
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/* System generated locals */ |
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integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; |
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/* Local variables */ |
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integer i__, iw; |
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extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, |
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integer *); |
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doublereal alpha; |
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, |
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integer *); |
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extern logical lsame_(char *, char *); |
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *, |
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doublereal *, doublereal *, integer *, doublereal *, integer *, |
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doublereal *, doublereal *, integer *), daxpy_(integer *, |
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doublereal *, doublereal *, integer *, doublereal *, integer *), |
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dsymv_(char *, integer *, doublereal *, doublereal *, integer *, |
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doublereal *, integer *, doublereal *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *, |
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doublereal *); |
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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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/* Purpose */ |
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/* ======= */ |
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/* DLATRD reduces NB rows and columns of a real symmetric matrix A to */ |
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/* symmetric tridiagonal form by an orthogonal similarity */ |
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/* transformation Q' * A * Q, and returns the matrices V and W which are */ |
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/* needed to apply the transformation to the unreduced part of A. */ |
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/* If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */ |
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/* matrix, of which the upper triangle is supplied; */ |
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/* if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */ |
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/* matrix, of which the lower triangle is supplied. */ |
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/* This is an auxiliary routine called by DSYTRD. */ |
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/* Arguments */ |
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/* ========= */ |
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/* UPLO (input) CHARACTER*1 */ |
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/* Specifies whether the upper or lower triangular part of the */ |
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/* symmetric matrix A is stored: */ |
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/* = 'U': Upper triangular */ |
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/* = 'L': Lower triangular */ |
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/* N (input) INTEGER */ |
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/* The order of the matrix A. */ |
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/* NB (input) INTEGER */ |
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/* The number of rows and columns to be reduced. */ |
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ |
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/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ |
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/* n-by-n upper triangular part of A contains the upper */ |
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/* triangular part of the matrix A, and the strictly lower */ |
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/* triangular part of A is not referenced. If UPLO = 'L', the */ |
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/* leading n-by-n lower triangular part of A contains the lower */ |
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/* triangular part of the matrix A, and the strictly upper */ |
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/* triangular part of A is not referenced. */ |
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/* On exit: */ |
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/* if UPLO = 'U', the last NB columns have been reduced to */ |
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/* tridiagonal form, with the diagonal elements overwriting */ |
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/* the diagonal elements of A; the elements above the diagonal */ |
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/* with the array TAU, represent the orthogonal matrix Q as a */ |
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/* product of elementary reflectors; */ |
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/* if UPLO = 'L', the first NB columns have been reduced to */ |
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/* tridiagonal form, with the diagonal elements overwriting */ |
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/* the diagonal elements of A; the elements below the diagonal */ |
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/* with the array TAU, represent the orthogonal matrix Q as a */ |
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/* 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 >= (1,N). */ |
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/* E (output) DOUBLE PRECISION array, dimension (N-1) */ |
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/* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */ |
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/* elements of the last NB columns of the reduced matrix; */ |
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/* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */ |
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/* the first NB columns of the reduced matrix. */ |
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/* TAU (output) DOUBLE PRECISION array, dimension (N-1) */ |
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/* The scalar factors of the elementary reflectors, stored in */ |
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/* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */ |
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/* See Further Details. */ |
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/* W (output) DOUBLE PRECISION array, dimension (LDW,NB) */ |
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/* The n-by-nb matrix W required to update the unreduced part */ |
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/* of A. */ |
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/* LDW (input) INTEGER */ |
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/* The leading dimension of the array W. LDW >= max(1,N). */ |
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/* Further Details */ |
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/* =============== */ |
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/* If UPLO = 'U', the matrix Q is represented as a product of elementary */ |
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/* reflectors */ |
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/* Q = H(n) H(n-1) . . . H(n-nb+1). */ |
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/* Each H(i) has the form */ |
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/* H(i) = I - tau * v * v' */ |
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/* where tau is a real scalar, and v is a real vector with */ |
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/* v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */ |
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/* and tau in TAU(i-1). */ |
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/* If UPLO = 'L', the matrix Q is represented as a product of elementary */ |
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/* reflectors */ |
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/* Q = H(1) H(2) . . . H(nb). */ |
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/* Each H(i) has the form */ |
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/* H(i) = I - tau * v * v' */ |
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/* where tau is a real scalar, and v is a real vector with */ |
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/* v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */ |
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/* and tau in TAU(i). */ |
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/* The elements of the vectors v together form the n-by-nb matrix V */ |
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/* which is needed, with W, to apply the transformation to the unreduced */ |
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/* part of the matrix, using a symmetric rank-2k update of the form: */ |
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/* A := A - V*W' - W*V'. */ |
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/* The contents of A on exit are illustrated by the following examples */ |
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/* with n = 5 and nb = 2: */ |
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/* if UPLO = 'U': if UPLO = 'L': */ |
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/* ( a a a v4 v5 ) ( d ) */ |
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/* ( a a v4 v5 ) ( 1 d ) */ |
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/* ( a 1 v5 ) ( v1 1 a ) */ |
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/* ( d 1 ) ( v1 v2 a a ) */ |
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/* ( d ) ( v1 v2 a a a ) */ |
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/* where d denotes a diagonal element of the reduced matrix, a denotes */ |
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/* an element of the original matrix that is unchanged, and vi denotes */ |
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/* an element of the vector defining H(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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/* .. External Functions .. */ |
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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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--e; |
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--tau; |
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w_dim1 = *ldw; |
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w_offset = 1 + w_dim1; |
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w -= w_offset; |
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/* Function Body */ |
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if (*n <= 0) { |
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return 0; |
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} |
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if (lsame_(uplo, "U")) { |
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/* Reduce last NB columns of upper triangle */ |
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i__1 = *n - *nb + 1; |
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for (i__ = *n; i__ >= i__1; --i__) { |
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iw = i__ - *n + *nb; |
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if (i__ < *n) { |
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/* Update A(1:i,i) */ |
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i__2 = *n - i__; |
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dgemv_("No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * |
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a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & |
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c_b6, &a[i__ * a_dim1 + 1], &c__1); |
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i__2 = *n - i__; |
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dgemv_("No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * |
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w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & |
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c_b6, &a[i__ * a_dim1 + 1], &c__1); |
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} |
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if (i__ > 1) { |
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/* Generate elementary reflector H(i) to annihilate */ |
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/* A(1:i-2,i) */ |
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i__2 = i__ - 1; |
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dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + |
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1], &c__1, &tau[i__ - 1]); |
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e[i__ - 1] = a[i__ - 1 + i__ * a_dim1]; |
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a[i__ - 1 + i__ * a_dim1] = 1.; |
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/* Compute W(1:i-1,i) */ |
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i__2 = i__ - 1; |
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dsymv_("Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * |
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a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], & |
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c__1); |
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if (i__ < *n) { |
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i__2 = i__ - 1; |
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i__3 = *n - i__; |
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dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * |
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w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, & |
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c_b16, &w[i__ + 1 + iw * w_dim1], &c__1); |
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i__2 = i__ - 1; |
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i__3 = *n - i__; |
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * |
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a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & |
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c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1); |
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i__2 = i__ - 1; |
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i__3 = *n - i__; |
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dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * |
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a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, & |
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c_b16, &w[i__ + 1 + iw * w_dim1], &c__1); |
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i__2 = i__ - 1; |
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i__3 = *n - i__; |
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * |
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w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & |
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c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1); |
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} |
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i__2 = i__ - 1; |
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dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); |
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i__2 = i__ - 1; |
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alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1], |
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&c__1, &a[i__ * a_dim1 + 1], &c__1); |
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i__2 = i__ - 1; |
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daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * |
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w_dim1 + 1], &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 first NB columns of lower triangle */ |
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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:n,i) */ |
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i__2 = *n - i__ + 1; |
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i__3 = i__ - 1; |
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, |
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&w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], & |
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c__1); |
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i__2 = *n - i__ + 1; |
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i__3 = i__ - 1; |
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw, |
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&a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], & |
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c__1); |
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if (i__ < *n) { |
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/* Generate elementary reflector H(i) to annihilate */ |
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/* A(i+2:n,i) */ |
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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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dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n)+ |
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i__ * a_dim1], &c__1, &tau[i__]); |
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e[i__] = a[i__ + 1 + i__ * a_dim1]; |
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a[i__ + 1 + i__ * a_dim1] = 1.; |
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/* Compute W(i+1:n,i) */ |
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i__2 = *n - i__; |
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dsymv_("Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1] |
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, lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ |
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i__ + 1 + i__ * w_dim1], &c__1); |
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i__2 = *n - i__; |
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i__3 = i__ - 1; |
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dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1], |
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ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ |
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i__ * w_dim1 + 1], &c__1); |
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i__2 = *n - i__; |
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i__3 = i__ - 1; |
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + |
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a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ |
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i__ + 1 + i__ * w_dim1], &c__1); |
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i__2 = *n - i__; |
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i__3 = i__ - 1; |
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dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1], |
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lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ |
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i__ * w_dim1 + 1], &c__1); |
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i__2 = *n - i__; |
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i__3 = i__ - 1; |
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + |
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w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ |
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i__ + 1 + i__ * w_dim1], &c__1); |
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i__2 = *n - i__; |
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dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); |
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i__2 = *n - i__; |
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alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ * |
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w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); |
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i__2 = *n - i__; |
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daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ |
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i__ + 1 + i__ * w_dim1], &c__1); |
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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 DLATRD */ |
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} /* dlatrd_ */
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