dsygst.c

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/* dsygst.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b14 = 1.;
static doublereal c_b16 = -.5;
static doublereal c_b19 = -1.;
static doublereal c_b52 = .5;

/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n, 
        doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
        info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;

    /* Local variables */
    integer k, kb, nb;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, 
            integer *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *, integer *), dsymm_(
            char *, char *, integer *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *);
    logical upper;
    extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, 
            integer *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *, integer *), dsygs2_(
            integer *, char *, integer *, doublereal *, integer *, doublereal 
            *, integer *, integer *), dsyr2k_(char *, char *, integer 
            *, integer *, doublereal *, doublereal *, integer *, doublereal *, 
             integer *, doublereal *, doublereal *, integer *)
            , xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DSYGST reduces a real symmetric-definite generalized eigenproblem */
/*  to standard form. */

/*  If ITYPE = 1, the problem is A*x = lambda*B*x, */
/*  and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) */

/*  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */
/*  B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. */

/*  B must have been previously factorized as U**T*U or L*L**T by DPOTRF. */

/*  Arguments */
/*  ========= */

/*  ITYPE   (input) INTEGER */
/*          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */
/*          = 2 or 3: compute U*A*U**T or L**T*A*L. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored and B is factored as */
/*                  U**T*U; */
/*          = 'L':  Lower triangle of A is stored and B is factored as */
/*                  L*L**T. */

/*  N       (input) INTEGER */
/*          The order of the matrices A and B.  N >= 0. */

/*  A       (input/output) 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 INFO = 0, the transformed matrix, stored in the */
/*          same format as A. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  B       (input) DOUBLE PRECISION array, dimension (LDB,N) */
/*          The triangular factor from the Cholesky factorization of B, */
/*          as returned by DPOTRF. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  LDB >= max(1,N). */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (*itype < 1 || *itype > 3) {
        *info = -1;
    } else if (! upper && ! lsame_(uplo, "L")) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    } else if (*ldb < max(1,*n)) {
        *info = -7;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DSYGST", &i__1);
        return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }

/*     Determine the block size for this environment. */

    nb = ilaenv_(&c__1, "DSYGST", uplo, n, &c_n1, &c_n1, &c_n1);

    if (nb <= 1 || nb >= *n) {

/*        Use unblocked code */

        dsygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    } else {

/*        Use blocked code */

        if (*itype == 1) {
            if (upper) {

/*              Compute inv(U')*A*inv(U) */

                i__1 = *n;
                i__2 = nb;
                for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
                    i__3 = *n - k + 1;
                    kb = min(i__3,nb);

/*                 Update the upper triangle of A(k:n,k:n) */

                    dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + 
                            k * b_dim1], ldb, info);
                    if (k + kb <= *n) {
                        i__3 = *n - k - kb + 1;
                        dtrsm_("Left", uplo, "Transpose", "Non-unit", &kb, &
                                i__3, &c_b14, &b[k + k * b_dim1], ldb, &a[k + 
                                (k + kb) * a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dsymm_("Left", uplo, &kb, &i__3, &c_b16, &a[k + k * 
                                a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, 
                                &c_b14, &a[k + (k + kb) * a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dsyr2k_(uplo, "Transpose", &i__3, &kb, &c_b19, &a[k + 
                                (k + kb) * a_dim1], lda, &b[k + (k + kb) * 
                                b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * 
                                a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dsymm_("Left", uplo, &kb, &i__3, &c_b16, &a[k + k * 
                                a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, 
                                &c_b14, &a[k + (k + kb) * a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dtrsm_("Right", uplo, "No transpose", "Non-unit", &kb, 
                                 &i__3, &c_b14, &b[k + kb + (k + kb) * b_dim1]
, ldb, &a[k + (k + kb) * a_dim1], lda);
                    }
/* L10: */
                }
            } else {

/*              Compute inv(L)*A*inv(L') */

                i__2 = *n;
                i__1 = nb;
                for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
                    i__3 = *n - k + 1;
                    kb = min(i__3,nb);

/*                 Update the lower triangle of A(k:n,k:n) */

                    dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + 
                            k * b_dim1], ldb, info);
                    if (k + kb <= *n) {
                        i__3 = *n - k - kb + 1;
                        dtrsm_("Right", uplo, "Transpose", "Non-unit", &i__3, 
                                &kb, &c_b14, &b[k + k * b_dim1], ldb, &a[k + 
                                kb + k * a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dsymm_("Right", uplo, &i__3, &kb, &c_b16, &a[k + k * 
                                a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
                                c_b14, &a[k + kb + k * a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dsyr2k_(uplo, "No transpose", &i__3, &kb, &c_b19, &a[
                                k + kb + k * a_dim1], lda, &b[k + kb + k * 
                                b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * 
                                a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dsymm_("Right", uplo, &i__3, &kb, &c_b16, &a[k + k * 
                                a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
                                c_b14, &a[k + kb + k * a_dim1], lda);
                        i__3 = *n - k - kb + 1;
                        dtrsm_("Left", uplo, "No transpose", "Non-unit", &
                                i__3, &kb, &c_b14, &b[k + kb + (k + kb) * 
                                b_dim1], ldb, &a[k + kb + k * a_dim1], lda);
                    }
/* L20: */
                }
            }
        } else {
            if (upper) {

/*              Compute U*A*U' */

                i__1 = *n;
                i__2 = nb;
                for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
                    i__3 = *n - k + 1;
                    kb = min(i__3,nb);

/*                 Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */

                    i__3 = k - 1;
                    dtrmm_("Left", uplo, "No transpose", "Non-unit", &i__3, &
                            kb, &c_b14, &b[b_offset], ldb, &a[k * a_dim1 + 1], 
                             lda)
                            ;
                    i__3 = k - 1;
                    dsymm_("Right", uplo, &i__3, &kb, &c_b52, &a[k + k * 
                            a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[
                            k * a_dim1 + 1], lda);
                    i__3 = k - 1;
                    dsyr2k_(uplo, "No transpose", &i__3, &kb, &c_b14, &a[k * 
                            a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, 
                             &a[a_offset], lda);
                    i__3 = k - 1;
                    dsymm_("Right", uplo, &i__3, &kb, &c_b52, &a[k + k * 
                            a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[
                            k * a_dim1 + 1], lda);
                    i__3 = k - 1;
                    dtrmm_("Right", uplo, "Transpose", "Non-unit", &i__3, &kb, 
                             &c_b14, &b[k + k * b_dim1], ldb, &a[k * a_dim1 + 
                            1], lda);
                    dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + 
                            k * b_dim1], ldb, info);
/* L30: */
                }
            } else {

/*              Compute L'*A*L */

                i__2 = *n;
                i__1 = nb;
                for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
                    i__3 = *n - k + 1;
                    kb = min(i__3,nb);

/*                 Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */

                    i__3 = k - 1;
                    dtrmm_("Right", uplo, "No transpose", "Non-unit", &kb, &
                            i__3, &c_b14, &b[b_offset], ldb, &a[k + a_dim1], 
                            lda);
                    i__3 = k - 1;
                    dsymm_("Left", uplo, &kb, &i__3, &c_b52, &a[k + k * 
                            a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + 
                            a_dim1], lda);
                    i__3 = k - 1;
                    dsyr2k_(uplo, "Transpose", &i__3, &kb, &c_b14, &a[k + 
                            a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[
                            a_offset], lda);
                    i__3 = k - 1;
                    dsymm_("Left", uplo, &kb, &i__3, &c_b52, &a[k + k * 
                            a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + 
                            a_dim1], lda);
                    i__3 = k - 1;
                    dtrmm_("Left", uplo, "Transpose", "Non-unit", &kb, &i__3, 
                            &c_b14, &b[k + k * b_dim1], ldb, &a[k + a_dim1], 
                            lda);
                    dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + 
                            k * b_dim1], ldb, info);
/* L40: */
                }
            }
        }
    }
    return 0;

/*     End of DSYGST */

} /* dsygst_ */