/* -- translated by f2c (version 20100827).
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*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b8 = 0.;
static doublereal c_b14 = -1.;
/* > \brief \b DSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarit
y transformation (unblocked algorithm).
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
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Definition:
===========
SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * )
> \par Purpose:
=============
>
> \verbatim
>
> DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
> form T by an orthogonal similarity transformation: Q**T * A * Q = T.
> \endverbatim
Arguments:
==========
> \param[in] UPLO
> \verbatim
> UPLO is CHARACTER*1
> Specifies whether the upper or lower triangular part of the
> symmetric matrix A is stored:
> = 'U': Upper triangular
> = 'L': Lower triangular
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix A. N >= 0.
> \endverbatim
>
> \param[in,out] A
> \verbatim
> A is DOUBLE PRECISION 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 diagonal and first superdiagonal
> of A are overwritten by the corresponding elements of the
> tridiagonal matrix T, and the elements above the first
> superdiagonal, with the array TAU, represent the orthogonal
> matrix Q as a product of elementary reflectors; if UPLO
> = 'L', the diagonal and first subdiagonal of A are over-
> written by the corresponding elements of the tridiagonal
> matrix T, and the elements below the first subdiagonal, with
> the array TAU, represent the orthogonal matrix Q as a product
> of elementary reflectors. See Further Details.
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(1,N).
> \endverbatim
>
> \param[out] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N)
> The diagonal elements of the tridiagonal matrix T:
> D(i) = A(i,i).
> \endverbatim
>
> \param[out] E
> \verbatim
> E is DOUBLE PRECISION array, dimension (N-1)
> The off-diagonal elements of the tridiagonal matrix T:
> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
> \endverbatim
>
> \param[out] TAU
> \verbatim
> TAU is DOUBLE PRECISION array, dimension (N-1)
> The scalar factors of the elementary reflectors (see Further
> Details).
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleSYcomputational
> \par Further Details:
=====================
>
> \verbatim
>
> If UPLO = 'U', the matrix Q is represented as a product of elementary
> reflectors
>
> Q = H(n-1) . . . H(2) H(1).
>
> Each H(i) has the form
>
> H(i) = I - tau * v * v**T
>
> where tau is a real scalar, and v is a real vector with
> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
> A(1:i-1,i+1), and tau in TAU(i).
>
> If UPLO = 'L', the matrix Q is represented as a product of elementary
> reflectors
>
> Q = H(1) H(2) . . . H(n-1).
>
> Each H(i) has the form
>
> H(i) = I - tau * v * v**T
>
> where tau is a real scalar, and v is a real vector with
> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
> and tau in TAU(i).
>
> The contents of A on exit are illustrated by the following examples
> with n = 5:
>
> if UPLO = 'U': if UPLO = 'L':
>
> ( d e v2 v3 v4 ) ( d )
> ( d e v3 v4 ) ( e d )
> ( d e v4 ) ( v1 e d )
> ( d e ) ( v1 v2 e d )
> ( d ) ( v1 v2 v3 e d )
>
> where d and e denote diagonal and off-diagonal elements of T, and vi
> denotes an element of the vector defining H(i).
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdsytd2_(char *uplo, integer *n, doublereal *a, integer *
lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer i__;
extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal taui;
extern /* Subroutine */ int igraphdsyr2_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal alpha;
extern logical igraphlsame_(char *, char *);
extern /* Subroutine */ int igraphdaxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
logical upper;
extern /* Subroutine */ int igraphdsymv_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *), igraphdlarfg_(integer *, doublereal *,
doublereal *, integer *, doublereal *), igraphxerbla_(char *, integer *
, ftnlen);
/* -- LAPACK computational routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
Test the input parameters
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--d__;
--e;
--tau;
/* Function Body */
*info = 0;
upper = igraphlsame_(uplo, "U");
if (! upper && ! igraphlsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DSYTD2", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
return 0;
}
if (upper) {
/* Reduce the upper triangle of A */
for (i__ = *n - 1; i__ >= 1; --i__) {
/* Generate elementary reflector H(i) = I - tau * v * v**T
to annihilate A(1:i-1,i+1) */
igraphdlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1
+ 1], &c__1, &taui);
e[i__] = a[i__ + (i__ + 1) * a_dim1];
if (taui != 0.) {
/* Apply H(i) from both sides to A(1:i,1:i) */
a[i__ + (i__ + 1) * a_dim1] = 1.;
/* Compute x := tau * A * v storing x in TAU(1:i) */
igraphdsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) *
a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1);
/* Compute w := x - 1/2 * tau * (x**T * v) * v */
alpha = taui * -.5 * igraphddot_(&i__, &tau[1], &c__1, &a[(i__ + 1)
* a_dim1 + 1], &c__1);
igraphdaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[
1], &c__1);
/* Apply the transformation as a rank-2 update:
A := A - v * w**T - w * v**T */
igraphdsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1,
&tau[1], &c__1, &a[a_offset], lda);
a[i__ + (i__ + 1) * a_dim1] = e[i__];
}
d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1];
tau[i__] = taui;
/* L10: */
}
d__[1] = a[a_dim1 + 1];
} else {
/* Reduce the lower triangle of A */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector H(i) = I - tau * v * v**T
to annihilate A(i+2:n,i) */
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
igraphdlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ *
a_dim1], &c__1, &taui);
e[i__] = a[i__ + 1 + i__ * a_dim1];
if (taui != 0.) {
/* Apply H(i) from both sides to A(i+1:n,i+1:n) */
a[i__ + 1 + i__ * a_dim1] = 1.;
/* Compute x := tau * A * v storing y in TAU(i:n-1) */
i__2 = *n - i__;
igraphdsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1],
lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[
i__], &c__1);
/* Compute w := x - 1/2 * tau * (x**T * v) * v */
i__2 = *n - i__;
alpha = taui * -.5 * igraphddot_(&i__2, &tau[i__], &c__1, &a[i__ +
1 + i__ * a_dim1], &c__1);
i__2 = *n - i__;
igraphdaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
i__], &c__1);
/* Apply the transformation as a rank-2 update:
A := A - v * w**T - w * v**T */
i__2 = *n - i__;
igraphdsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1,
&tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1],
lda);
a[i__ + 1 + i__ * a_dim1] = e[i__];
}
d__[i__] = a[i__ + i__ * a_dim1];
tau[i__] = taui;
/* L20: */
}
d__[*n] = a[*n + *n * a_dim1];
}
return 0;
/* End of DSYTD2 */
} /* igraphdsytd2_ */