290 lines
8.7 KiB
C
290 lines
8.7 KiB
C
|
#include "clapack.h"
|
||
|
|
|
||
|
|
/* Table of constant values */
|
||
|
|
|
||
|
|
static integer c__1 = 1;
|
||
|
|
static real c_b8 = 0.f;
|
||
|
|
static real c_b14 = -1.f;
|
||
|
|
|
||
|
|
/* Subroutine */ int ssytd2_(char *uplo, integer *n, real *a, integer *lda,
|
||
|
|
real *d__, real *e, real *tau, integer *info)
|
||
|
|
{
|
||
|
|
/* System generated locals */
|
||
|
|
integer a_dim1, a_offset, i__1, i__2, i__3;
|
||
|
|
|
||
|
|
/* Local variables */
|
||
|
|
integer i__;
|
||
|
|
real taui;
|
||
|
|
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
|
||
|
|
extern /* Subroutine */ int ssyr2_(char *, integer *, real *, real *,
|
||
|
|
integer *, real *, integer *, real *, integer *);
|
||
|
|
real alpha;
|
||
|
|
extern logical lsame_(char *, char *);
|
||
|
|
logical upper;
|
||
|
|
extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
|
||
|
|
real *, integer *), ssymv_(char *, integer *, real *, real *,
|
||
|
|
integer *, real *, integer *, real *, real *, integer *),
|
||
|
|
xerbla_(char *, integer *), slarfg_(integer *, real *,
|
||
|
|
real *, integer *, real *);
|
||
|
|
|
||
|
|
|
||
|
|
/* -- LAPACK routine (version 3.1) -- */
|
||
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
||
|
|
/* November 2006 */
|
||
|
|
|
||
|
|
/* .. Scalar Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Array Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
|
||
|
|
/* Purpose */
|
||
|
|
/* ======= */
|
||
|
|
|
||
|
|
/* SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */
|
||
|
|
/* form T by an orthogonal similarity transformation: Q' * A * Q = T. */
|
||
|
|
|
||
|
|
/* 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. N >= 0. */
|
||
|
|
|
||
|
|
/* 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 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. */
|
||
|
|
|
||
|
|
/* LDA (input) INTEGER */
|
||
|
|
/* The leading dimension of the array A. LDA >= max(1,N). */
|
||
|
|
|
||
|
|
/* D (output) REAL array, dimension (N) */
|
||
|
|
/* The diagonal elements of the tridiagonal matrix T: */
|
||
|
|
/* D(i) = A(i,i). */
|
||
|
|
|
||
|
|
/* E (output) REAL 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'. */
|
||
|
|
|
||
|
|
/* TAU (output) REAL array, dimension (N-1) */
|
||
|
|
/* The scalar factors of the elementary reflectors (see Further */
|
||
|
|
/* Details). */
|
||
|
|
|
||
|
|
/* INFO (output) INTEGER */
|
||
|
|
/* = 0: successful exit */
|
||
|
|
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
|
||
|
|
|
||
|
|
/* Further Details */
|
||
|
|
/* =============== */
|
||
|
|
|
||
|
|
/* 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' */
|
||
|
|
|
||
|
|
/* 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' */
|
||
|
|
|
||
|
|
/* 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). */
|
||
|
|
|
||
|
|
/* ===================================================================== */
|
||
|
|
|
||
|
|
/* .. Parameters .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Local Scalars .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. External Subroutines .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. External Functions .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Intrinsic Functions .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Executable Statements .. */
|
||
|
|
|
||
|
|
/* 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 = lsame_(uplo, "U");
|
||
|
|
if (! upper && ! lsame_(uplo, "L")) {
|
||
|
|
*info = -1;
|
||
|
|
} else if (*n < 0) {
|
||
|
|
*info = -2;
|
||
|
|
} else if (*lda < max(1,*n)) {
|
||
|
|
*info = -4;
|
||
|
|
}
|
||
|
|
if (*info != 0) {
|
||
|
|
i__1 = -(*info);
|
||
|
|
xerbla_("SSYTD2", &i__1);
|
||
|
|
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' */
|
||
|
|
/* to annihilate A(1:i-1,i+1) */
|
||
|
|
|
||
|
|
slarfg_(&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.f) {
|
||
|
|
|
||
|
|
/* Apply H(i) from both sides to A(1:i,1:i) */
|
||
|
|
|
||
|
|
a[i__ + (i__ + 1) * a_dim1] = 1.f;
|
||
|
|
|
||
|
|
/* Compute x := tau * A * v storing x in TAU(1:i) */
|
||
|
|
|
||
|
|
ssymv_(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'*v) * v */
|
||
|
|
|
||
|
|
alpha = taui * -.5f * sdot_(&i__, &tau[1], &c__1, &a[(i__ + 1)
|
||
|
|
* a_dim1 + 1], &c__1);
|
||
|
|
saxpy_(&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' - w * v' */
|
||
|
|
|
||
|
|
ssyr2_(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' */
|
||
|
|
/* 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, &taui);
|
||
|
|
e[i__] = a[i__ + 1 + i__ * a_dim1];
|
||
|
|
|
||
|
|
if (taui != 0.f) {
|
||
|
|
|
||
|
|
/* Apply H(i) from both sides to A(i+1:n,i+1:n) */
|
||
|
|
|
||
|
|
a[i__ + 1 + i__ * a_dim1] = 1.f;
|
||
|
|
|
||
|
|
/* Compute x := tau * A * v storing y in TAU(i:n-1) */
|
||
|
|
|
||
|
|
i__2 = *n - i__;
|
||
|
|
ssymv_(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'*v) * v */
|
||
|
|
|
||
|
|
i__2 = *n - i__;
|
||
|
|
alpha = taui * -.5f * sdot_(&i__2, &tau[i__], &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, &tau[
|
||
|
|
i__], &c__1);
|
||
|
|
|
||
|
|
/* Apply the transformation as a rank-2 update: */
|
||
|
|
/* A := A - v * w' - w * v' */
|
||
|
|
|
||
|
|
i__2 = *n - i__;
|
||
|
|
ssyr2_(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 SSYTD2 */
|
||
|
|
|
||
|
|
} /* ssytd2_ */
|