zhpgst.c

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/* zhpgst.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 doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;

/* Subroutine */ int zhpgst_(integer *itype, char *uplo, integer *n, 
        doublecomplex *ap, doublecomplex *bp, integer *info)
{
    /* System generated locals */
    integer i__1, i__2, i__3, i__4;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2, z__3;

    /* Local variables */
    integer j, k, j1, k1, jj, kk;
    doublecomplex ct;
    doublereal ajj;
    integer j1j1;
    doublereal akk;
    integer k1k1;
    doublereal bjj, bkk;
    extern /* Subroutine */ int zhpr2_(char *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *);
    extern logical lsame_(char *, char *);
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    logical upper;
    extern /* Subroutine */ int zhpmv_(char *, integer *, doublecomplex *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            doublecomplex *, integer *), zaxpy_(integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *), ztpmv_(char *, char *, char *, integer *, 
            doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex *
, doublecomplex *, integer *), xerbla_(
            char *, integer *), zdscal_(integer *, doublereal *, 
            doublecomplex *, integer *);


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

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

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

/*  ZHPGST reduces a complex Hermitian-definite generalized */
/*  eigenproblem to standard form, using packed storage. */

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

/*  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**H or L**H*A*L. */

/*  B must have been previously factorized as U**H*U or L*L**H by ZPPTRF. */

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

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

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored and B is factored as */
/*                  U**H*U; */
/*          = 'L':  Lower triangle of A is stored and B is factored as */
/*                  L*L**H. */

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

/*  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */
/*          On entry, the upper or lower triangle of the Hermitian matrix */
/*          A, packed columnwise in a linear array.  The j-th column of A */
/*          is stored in the array AP as follows: */
/*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/*          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */

/*          On exit, if INFO = 0, the transformed matrix, stored in the */
/*          same format as A. */

/*  BP      (input) COMPLEX*16 array, dimension (N*(N+1)/2) */
/*          The triangular factor from the Cholesky factorization of B, */
/*          stored in the same format as A, as returned by ZPPTRF. */

/*  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 */
    --bp;
    --ap;

    /* 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;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZHPGST", &i__1);
        return 0;
    }

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

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

/*           J1 and JJ are the indices of A(1,j) and A(j,j) */

            jj = 0;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                j1 = jj + 1;
                jj += j;

/*              Compute the j-th column of the upper triangle of A */

                i__2 = jj;
                i__3 = jj;
                d__1 = ap[i__3].r;
                ap[i__2].r = d__1, ap[i__2].i = 0.;
                i__2 = jj;
                bjj = bp[i__2].r;
                ztpsv_(uplo, "Conjugate transpose", "Non-unit", &j, &bp[1], &
                        ap[j1], &c__1);
                i__2 = j - 1;
                z__1.r = -1., z__1.i = -0.;
                zhpmv_(uplo, &i__2, &z__1, &ap[1], &bp[j1], &c__1, &c_b1, &ap[
                        j1], &c__1);
                i__2 = j - 1;
                d__1 = 1. / bjj;
                zdscal_(&i__2, &d__1, &ap[j1], &c__1);
                i__2 = jj;
                i__3 = jj;
                i__4 = j - 1;
                zdotc_(&z__3, &i__4, &ap[j1], &c__1, &bp[j1], &c__1);
                z__2.r = ap[i__3].r - z__3.r, z__2.i = ap[i__3].i - z__3.i;
                z__1.r = z__2.r / bjj, z__1.i = z__2.i / bjj;
                ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
/* L10: */
            }
        } else {

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

/*           KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) */

            kk = 1;
            i__1 = *n;
            for (k = 1; k <= i__1; ++k) {
                k1k1 = kk + *n - k + 1;

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

                i__2 = kk;
                akk = ap[i__2].r;
                i__2 = kk;
                bkk = bp[i__2].r;
/* Computing 2nd power */
                d__1 = bkk;
                akk /= d__1 * d__1;
                i__2 = kk;
                ap[i__2].r = akk, ap[i__2].i = 0.;
                if (k < *n) {
                    i__2 = *n - k;
                    d__1 = 1. / bkk;
                    zdscal_(&i__2, &d__1, &ap[kk + 1], &c__1);
                    d__1 = akk * -.5;
                    ct.r = d__1, ct.i = 0.;
                    i__2 = *n - k;
                    zaxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
                            ;
                    i__2 = *n - k;
                    z__1.r = -1., z__1.i = -0.;
                    zhpr2_(uplo, &i__2, &z__1, &ap[kk + 1], &c__1, &bp[kk + 1]
, &c__1, &ap[k1k1]);
                    i__2 = *n - k;
                    zaxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
                            ;
                    i__2 = *n - k;
                    ztpsv_(uplo, "No transpose", "Non-unit", &i__2, &bp[k1k1], 
                             &ap[kk + 1], &c__1);
                }
                kk = k1k1;
/* L20: */
            }
        }
    } else {
        if (upper) {

/*           Compute U*A*U' */

/*           K1 and KK are the indices of A(1,k) and A(k,k) */

            kk = 0;
            i__1 = *n;
            for (k = 1; k <= i__1; ++k) {
                k1 = kk + 1;
                kk += k;

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

                i__2 = kk;
                akk = ap[i__2].r;
                i__2 = kk;
                bkk = bp[i__2].r;
                i__2 = k - 1;
                ztpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[
                        k1], &c__1);
                d__1 = akk * .5;
                ct.r = d__1, ct.i = 0.;
                i__2 = k - 1;
                zaxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
                i__2 = k - 1;
                zhpr2_(uplo, &i__2, &c_b1, &ap[k1], &c__1, &bp[k1], &c__1, &
                        ap[1]);
                i__2 = k - 1;
                zaxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
                i__2 = k - 1;
                zdscal_(&i__2, &bkk, &ap[k1], &c__1);
                i__2 = kk;
/* Computing 2nd power */
                d__2 = bkk;
                d__1 = akk * (d__2 * d__2);
                ap[i__2].r = d__1, ap[i__2].i = 0.;
/* L30: */
            }
        } else {

/*           Compute L'*A*L */

/*           JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) */

            jj = 1;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                j1j1 = jj + *n - j + 1;

/*              Compute the j-th column of the lower triangle of A */

                i__2 = jj;
                ajj = ap[i__2].r;
                i__2 = jj;
                bjj = bp[i__2].r;
                i__2 = jj;
                d__1 = ajj * bjj;
                i__3 = *n - j;
                zdotc_(&z__2, &i__3, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1);
                z__1.r = d__1 + z__2.r, z__1.i = z__2.i;
                ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
                i__2 = *n - j;
                zdscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
                i__2 = *n - j;
                zhpmv_(uplo, &i__2, &c_b1, &ap[j1j1], &bp[jj + 1], &c__1, &
                        c_b1, &ap[jj + 1], &c__1);
                i__2 = *n - j + 1;
                ztpmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &bp[jj]
, &ap[jj], &c__1);
                jj = j1j1;
/* L40: */
            }
        }
    }
    return 0;

/*     End of ZHPGST */

} /* zhpgst_ */