343 lines
12 KiB
C
343 lines
12 KiB
C
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#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[
|
||
|
|
i__ + 1 + i__ * w_dim1], &c__1);
|
||
|
|
i__2 = *n - i__;
|
||
|
|
dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
|
||
|
|
i__2 = *n - i__;
|
||
|
|
alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ *
|
||
|
|
w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
|
||
|
|
i__2 = *n - i__;
|
||
|
|
daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
|
||
|
|
i__ + 1 + i__ * w_dim1], &c__1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* L20: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
/* End of DLATRD */
|
||
|
|
|
||
|
|
} /* dlatrd_ */
|