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302 lines
9.2 KiB
302 lines
9.2 KiB
/* ssytd2.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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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 real c_b8 = 0.f; |
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static real c_b14 = -1.f; |
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/* Subroutine */ int ssytd2_(char *uplo, integer *n, real *a, integer *lda, |
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real *d__, real *e, real *tau, integer *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__; |
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real taui; |
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extern doublereal sdot_(integer *, real *, integer *, real *, integer *); |
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extern /* Subroutine */ int ssyr2_(char *, integer *, real *, real *, |
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integer *, real *, integer *, real *, integer *); |
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real alpha; |
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extern logical lsame_(char *, char *); |
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logical upper; |
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extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, |
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real *, integer *), ssymv_(char *, integer *, real *, real *, |
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integer *, real *, integer *, real *, real *, integer *), |
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xerbla_(char *, integer *), slarfg_(integer *, real *, |
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real *, integer *, real *); |
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/* -- LAPACK routine (version 3.2) -- */ |
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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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/* SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */ |
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/* form T by an orthogonal similarity transformation: Q' * A * Q = T. */ |
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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. 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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/* 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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/* .. 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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/* 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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/* Function Body */ |
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*info = 0; |
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upper = lsame_(uplo, "U"); |
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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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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SSYTD2", &i__1); |
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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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return 0; |
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} |
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if (upper) { |
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/* Reduce the upper triangle of A */ |
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for (i__ = *n - 1; i__ >= 1; --i__) { |
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/* Generate elementary reflector H(i) = I - tau * v * v' */ |
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/* to annihilate A(1:i-1,i+1) */ |
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slarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 |
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+ 1], &c__1, &taui); |
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e[i__] = a[i__ + (i__ + 1) * a_dim1]; |
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if (taui != 0.f) { |
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/* Apply H(i) from both sides to A(1:i,1:i) */ |
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a[i__ + (i__ + 1) * a_dim1] = 1.f; |
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/* Compute x := tau * A * v storing x in TAU(1:i) */ |
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ssymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * |
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a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1); |
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/* Compute w := x - 1/2 * tau * (x'*v) * v */ |
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alpha = taui * -.5f * sdot_(&i__, &tau[1], &c__1, &a[(i__ + 1) |
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* a_dim1 + 1], &c__1); |
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saxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ |
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1], &c__1); |
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/* Apply the transformation as a rank-2 update: */ |
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/* A := A - v * w' - w * v' */ |
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ssyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, |
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&tau[1], &c__1, &a[a_offset], lda); |
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a[i__ + (i__ + 1) * a_dim1] = e[i__]; |
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} |
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d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1]; |
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tau[i__] = taui; |
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/* L10: */ |
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} |
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d__[1] = a[a_dim1 + 1]; |
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} else { |
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/* Reduce the lower triangle of A */ |
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i__1 = *n - 1; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Generate elementary reflector H(i) = I - tau * v * v' */ |
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/* to annihilate 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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slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n)+ i__ * |
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a_dim1], &c__1, &taui); |
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e[i__] = a[i__ + 1 + i__ * a_dim1]; |
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if (taui != 0.f) { |
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/* Apply H(i) from both sides to A(i+1:n,i+1:n) */ |
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a[i__ + 1 + i__ * a_dim1] = 1.f; |
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/* Compute x := tau * A * v storing y in TAU(i:n-1) */ |
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i__2 = *n - i__; |
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ssymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], |
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lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ |
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i__], &c__1); |
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/* Compute w := x - 1/2 * tau * (x'*v) * v */ |
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i__2 = *n - i__; |
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alpha = taui * -.5f * sdot_(&i__2, &tau[i__], &c__1, &a[i__ + |
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1 + i__ * a_dim1], &c__1); |
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i__2 = *n - i__; |
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saxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ |
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i__], &c__1); |
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/* Apply the transformation as a rank-2 update: */ |
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/* A := A - v * w' - w * v' */ |
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i__2 = *n - i__; |
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ssyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, |
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&tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], |
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lda); |
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a[i__ + 1 + i__ * a_dim1] = e[i__]; |
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} |
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d__[i__] = a[i__ + i__ * a_dim1]; |
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tau[i__] = taui; |
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/* L20: */ |
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} |
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d__[*n] = a[*n + *n * a_dim1]; |
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} |
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return 0; |
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/* End of SSYTD2 */ |
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} /* ssytd2_ */
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