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360 lines
11 KiB
360 lines
11 KiB
/* dsytrd.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 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 doublereal c_b22 = -1.; |
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static doublereal c_b23 = 1.; |
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/* Subroutine */ int dsytrd_(char *uplo, integer *n, doublereal *a, integer * |
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lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal * |
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work, integer *lwork, 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__, 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 dsytd2_(char *, integer *, doublereal *, |
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integer *, doublereal *, doublereal *, doublereal *, integer *), dsyr2k_(char *, char *, integer *, integer *, doublereal |
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*, doublereal *, integer *, doublereal *, integer *, doublereal *, |
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doublereal *, integer *), dlatrd_(char *, |
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integer *, integer *, doublereal *, integer *, doublereal *, |
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doublereal *, doublereal *, integer *), xerbla_(char *, |
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integer *); |
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
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integer *, integer *); |
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integer ldwork, lwkopt; |
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logical lquery; |
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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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/* DSYTRD 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1); |
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lwkopt = *n * nb; |
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work[1] = (doublereal) lwkopt; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DSYTRD", &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.; |
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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, "DSYTRD", 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, "DSYTRD", 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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dlatrd_(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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dsyr2k_(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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dsytd2_(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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dlatrd_(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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dsyr2k_(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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dsytd2_(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] = (doublereal) lwkopt; |
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return 0; |
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/* End of DSYTRD */ |
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} /* dsytrd_ */
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