/* slatrd.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static real c_b5 = -1.f;
static real c_b6 = 1.f;
static integer c__1 = 1;
static real c_b16 = 0.f;
/* Subroutine */ int slatrd_(char *uplo, integer *n, integer *nb, real *a,
integer *lda, real *e, real *tau, real *w, integer *ldw)
{
/* System generated locals */
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, iw;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
real alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
sgemv_(char *, integer *, integer *, real *, real *, integer *,
real *, integer *, real *, real *, integer *), saxpy_(
integer *, real *, real *, integer *, real *, integer *), ssymv_(
char *, integer *, real *, real *, integer *, real *, integer *,
real *, real *, integer *), slarfg_(integer *, real *,
real *, integer *, real *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLATRD reduces NB rows and columns of a real symmetric matrix A to */
/* symmetric tridiagonal form by an orthogonal similarity */
/* transformation Q' * A * Q, and returns the matrices V and W which are */
/* needed to apply the transformation to the unreduced part of A. */
/* If UPLO = 'U', SLATRD reduces the last NB rows and columns of a */
/* matrix, of which the upper triangle is supplied; */
/* if UPLO = 'L', SLATRD reduces the first NB rows and columns of a */
/* matrix, of which the lower triangle is supplied. */
/* This is an auxiliary routine called by SSYTRD. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* symmetric matrix A is stored: */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* N (input) INTEGER */
/* The order of the matrix A. */
/* NB (input) INTEGER */
/* The number of rows and columns to be reduced. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
/* n-by-n upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading n-by-n lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit: */
/* if UPLO = 'U', the last NB columns have been reduced to */
/* tridiagonal form, with the diagonal elements overwriting */
/* the diagonal elements of A; the elements above the diagonal */
/* with the array TAU, represent the orthogonal matrix Q as a */
/* product of elementary reflectors; */
/* if UPLO = 'L', the first NB columns have been reduced to */
/* tridiagonal form, with the diagonal elements overwriting */
/* the diagonal elements of A; the elements below the diagonal */
/* with the array TAU, represent the orthogonal matrix Q as a */
/* product of elementary reflectors. */
/* See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= (1,N). */
/* E (output) REAL array, dimension (N-1) */
/* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */
/* elements of the last NB columns of the reduced matrix; */
/* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */
/* the first NB columns of the reduced matrix. */
/* TAU (output) REAL array, dimension (N-1) */
/* The scalar factors of the elementary reflectors, stored in */
/* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */
/* See Further Details. */
/* W (output) REAL array, dimension (LDW,NB) */
/* The n-by-nb matrix W required to update the unreduced part */
/* of A. */
/* LDW (input) INTEGER */
/* The leading dimension of the array W. LDW >= max(1,N). */
/* Further Details */
/* =============== */
/* If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* reflectors */
/* Q = H(n) H(n-1) . . . H(n-nb+1). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a real scalar, and v is a real vector with */
/* v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */
/* and tau in TAU(i-1). */
/* If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* reflectors */
/* Q = H(1) H(2) . . . H(nb). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a real scalar, and v is a real vector with */
/* v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
/* and tau in TAU(i). */
/* The elements of the vectors v together form the n-by-nb matrix V */
/* which is needed, with W, to apply the transformation to the unreduced */
/* part of the matrix, using a symmetric rank-2k update of the form: */
/* A := A - V*W' - W*V'. */
/* The contents of A on exit are illustrated by the following examples */
/* with n = 5 and nb = 2: */
/* if UPLO = 'U': if UPLO = 'L': */
/* ( a a a v4 v5 ) ( d ) */
/* ( a a v4 v5 ) ( 1 d ) */
/* ( a 1 v5 ) ( v1 1 a ) */
/* ( d 1 ) ( v1 v2 a a ) */
/* ( d ) ( v1 v2 a a a ) */
/* where d denotes a diagonal element of the reduced matrix, a denotes */
/* an element of the original matrix that is unchanged, and vi denotes */
/* an element of the vector defining H(i). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--e;
--tau;
w_dim1 = *ldw;
w_offset = 1 + w_dim1;
w -= w_offset;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Reduce last NB columns of upper triangle */
i__1 = *n - *nb + 1;
for (i__ = *n; i__ >= i__1; --i__) {
iw = i__ - *n + *nb;
if (i__ < *n) {
/* Update A(1:i,i) */
i__2 = *n - i__;
sgemv_("No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
c_b6, &a[i__ * a_dim1 + 1], &c__1);
i__2 = *n - i__;
sgemv_("No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) *
w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b6, &a[i__ * a_dim1 + 1], &c__1);
}
if (i__ > 1) {
/* Generate elementary reflector H(i) to annihilate */
/* A(1:i-2,i) */
i__2 = i__ - 1;
slarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 +
1], &c__1, &tau[i__ - 1]);
e[i__ - 1] = a[i__ - 1 + i__ * a_dim1];
a[i__ - 1 + i__ * a_dim1] = 1.f;
/* Compute W(1:i-1,i) */
i__2 = i__ - 1;
ssymv_("Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ *
a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], &
c__1);
if (i__ < *n) {
i__2 = i__ - 1;
i__3 = *n - i__;
sgemv_("Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) *
w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, &
c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
sgemv_("Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) *
a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, &
c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
sgemv_("No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) *
w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
}
i__2 = i__ - 1;
sscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
i__2 = i__ - 1;
alpha = tau[i__ - 1] * -.5f * sdot_(&i__2, &w[iw * w_dim1 + 1]
, &c__1, &a[i__ * a_dim1 + 1], &c__1);
i__2 = i__ - 1;
saxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw *
w_dim1 + 1], &c__1);
}
/* L10: */
}
} else {
/* Reduce first NB columns of lower triangle */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i:n,i) */
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda,
&w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
sgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw,
&a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], &
c__1);
if (i__ < *n) {
/* Generate elementary reflector H(i) to annihilate */
/* A(i+2:n,i) */
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n)+
i__ * a_dim1], &c__1, &tau[i__]);
e[i__] = a[i__ + 1 + i__ * a_dim1];
a[i__ + 1 + i__ * a_dim1] = 1.f;
/* Compute W(i+1:n,i) */
i__2 = *n - i__;
ssymv_("Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1]
, lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
sgemv_("Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1],
ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
i__ * w_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 +
a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
sgemv_("Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1],
lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
i__ * w_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
sgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 +
w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
sscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
alpha = tau[i__] * -.5f * sdot_(&i__2, &w[i__ + 1 + i__ *
w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
i__2 = *n - i__;
saxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
i__ + 1 + i__ * w_dim1], &c__1);
}
/* L20: */
}
}
return 0;
/* End of SLATRD */
} /* slatrd_ */