348 lines
10 KiB
C
348 lines
10 KiB
C
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#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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static integer c__3 = 3;
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static integer c__2 = 2;
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static real c_b22 = -1.f;
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static real c_b23 = 1.f;
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/* Subroutine */ int ssytrd_(char *uplo, integer *n, real *a, integer *lda,
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real *d__, real *e, real *tau, real *work, integer *lwork, integer *
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info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__, j, nb, kk, nx, iws;
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extern logical lsame_(char *, char *);
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integer nbmin, iinfo;
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logical upper;
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extern /* Subroutine */ int ssytd2_(char *, integer *, real *, integer *,
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real *, real *, real *, integer *), ssyr2k_(char *, char *
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, integer *, integer *, real *, real *, integer *, real *,
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integer *, real *, real *, integer *), xerbla_(
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char *, integer *);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *);
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extern /* Subroutine */ int slatrd_(char *, integer *, integer *, real *,
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integer *, real *, real *, real *, integer *);
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integer ldwork, lwkopt;
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logical lquery;
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/* -- LAPACK 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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/* SSYTRD reduces a real symmetric matrix A to real symmetric */
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/* tridiagonal form T by an orthogonal similarity transformation: */
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/* Q**T * A * Q = T. */
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/* Arguments */
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/* ========= */
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/* UPLO (input) CHARACTER*1 */
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/* = 'U': Upper triangle of A is stored; */
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/* = 'L': Lower triangle of A is stored. */
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/* N (input) INTEGER */
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/* The order of the matrix A. N >= 0. */
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/* A (input/output) REAL 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, if UPLO = 'U', the diagonal and first superdiagonal */
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/* of A are overwritten by the corresponding elements of the */
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/* tridiagonal matrix T, and the elements above the first */
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/* superdiagonal, with the array TAU, represent the orthogonal */
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/* matrix Q as a product of elementary reflectors; if UPLO */
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/* = 'L', the diagonal and first subdiagonal of A are over- */
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/* written by the corresponding elements of the tridiagonal */
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/* matrix T, and the elements below the first subdiagonal, with */
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/* the array TAU, represent the orthogonal matrix Q as a product */
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/* of elementary reflectors. See Further Details. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,N). */
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/* D (output) REAL array, dimension (N) */
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/* The diagonal elements of the tridiagonal matrix T: */
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/* D(i) = A(i,i). */
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/* E (output) REAL array, dimension (N-1) */
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/* The off-diagonal elements of the tridiagonal matrix T: */
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/* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */
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/* TAU (output) REAL array, dimension (N-1) */
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/* The scalar factors of the elementary reflectors (see Further */
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/* Details). */
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/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
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/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* LWORK (input) INTEGER */
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/* The dimension of the array WORK. LWORK >= 1. */
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/* For optimum performance LWORK >= N*NB, where NB is the */
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/* optimal blocksize. */
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/* If LWORK = -1, then a workspace query is assumed; the routine */
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/* only calculates the optimal size of the WORK array, returns */
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/* this value as the first entry of the WORK array, and no error */
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/* message related to LWORK is issued by XERBLA. */
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/* INFO (output) INTEGER */
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/* = 0: successful exit */
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/* < 0: if INFO = -i, the i-th argument had an illegal value */
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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-1) . . . H(2) H(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+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */
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/* A(1:i-1,i+1), and tau in TAU(i). */
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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(n-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(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */
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/* and tau in TAU(i). */
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/* The contents of A on exit are illustrated by the following examples */
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/* with n = 5: */
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/* if UPLO = 'U': if UPLO = 'L': */
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/* ( d e v2 v3 v4 ) ( d ) */
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/* ( d e v3 v4 ) ( e d ) */
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/* ( d e v4 ) ( v1 e d ) */
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/* ( d e ) ( v1 v2 e d ) */
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/* ( d ) ( v1 v2 v3 e d ) */
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/* where d and e denote diagonal and off-diagonal elements of T, and vi */
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/* denotes 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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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters */
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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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--d__;
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--e;
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--tau;
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--work;
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/* Function Body */
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*info = 0;
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upper = lsame_(uplo, "U");
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lquery = *lwork == -1;
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if (! upper && ! lsame_(uplo, "L")) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1,*n)) {
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*info = -4;
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} else if (*lwork < 1 && ! lquery) {
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*info = -9;
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}
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if (*info == 0) {
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/* Determine the block size. */
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nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
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lwkopt = *n * nb;
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work[1] = (real) lwkopt;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SSYTRD", &i__1);
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return 0;
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} else if (lquery) {
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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work[1] = 1.f;
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return 0;
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}
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nx = *n;
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iws = 1;
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if (nb > 1 && nb < *n) {
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/* Determine when to cross over from blocked to unblocked code */
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/* (last block is always handled by unblocked code). */
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/* Computing MAX */
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i__1 = nb, i__2 = ilaenv_(&c__3, "SSYTRD", uplo, n, &c_n1, &c_n1, &
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c_n1);
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nx = max(i__1,i__2);
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if (nx < *n) {
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/* Determine if workspace is large enough for blocked code. */
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ldwork = *n;
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iws = ldwork * nb;
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if (*lwork < iws) {
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/* Not enough workspace to use optimal NB: determine the */
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/* minimum value of NB, and reduce NB or force use of */
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/* unblocked code by setting NX = N. */
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/* Computing MAX */
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i__1 = *lwork / ldwork;
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nb = max(i__1,1);
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nbmin = ilaenv_(&c__2, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
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if (nb < nbmin) {
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nx = *n;
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}
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}
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} else {
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nx = *n;
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}
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} else {
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nb = 1;
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}
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if (upper) {
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/* Reduce the upper triangle of A. */
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/* Columns 1:kk are handled by the unblocked method. */
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kk = *n - (*n - nx + nb - 1) / nb * nb;
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i__1 = kk + 1;
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i__2 = -nb;
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for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
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i__2) {
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/* Reduce columns i:i+nb-1 to tridiagonal form and form the */
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/* matrix W which is needed to update the unreduced part of */
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/* the matrix */
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i__3 = i__ + nb - 1;
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slatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
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work[1], &ldwork);
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/* Update the unreduced submatrix A(1:i-1,1:i-1), using an */
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/* update of the form: A := A - V*W' - W*V' */
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i__3 = i__ - 1;
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ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1
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+ 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda);
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/* Copy superdiagonal elements back into A, and diagonal */
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/* elements into D */
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i__3 = i__ + nb - 1;
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for (j = i__; j <= i__3; ++j) {
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a[j - 1 + j * a_dim1] = e[j - 1];
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d__[j] = a[j + j * a_dim1];
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/* L10: */
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}
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/* L20: */
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}
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/* Use unblocked code to reduce the last or only block */
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ssytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo);
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} else {
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/* Reduce the lower triangle of A */
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i__2 = *n - nx;
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i__1 = nb;
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for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
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/* Reduce columns i:i+nb-1 to tridiagonal form and form the */
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/* matrix W which is needed to update the unreduced part of */
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/* the matrix */
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i__3 = *n - i__ + 1;
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slatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &
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tau[i__], &work[1], &ldwork);
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/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using */
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/* an update of the form: A := A - V*W' - W*V' */
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i__3 = *n - i__ - nb + 1;
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ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ + nb +
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i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[
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i__ + nb + (i__ + nb) * a_dim1], lda);
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/* Copy subdiagonal elements back into A, and diagonal */
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/* elements into D */
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i__3 = i__ + nb - 1;
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for (j = i__; j <= i__3; ++j) {
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a[j + 1 + j * a_dim1] = e[j];
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d__[j] = a[j + j * a_dim1];
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/* L30: */
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}
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/* L40: */
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}
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/* Use unblocked code to reduce the last or only block */
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i__1 = *n - i__ + 1;
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ssytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__],
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&tau[i__], &iinfo);
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}
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work[1] = (real) lwkopt;
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return 0;
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/* End of SSYTRD */
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} /* ssytrd_ */
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