chpgst.c

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/* chpgst.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 complex c_b1 = {1.f,0.f};
static integer c__1 = 1;

/* Subroutine */ int chpgst_(integer *itype, char *uplo, integer *n, complex *
        ap, complex *bp, integer *info)
{
    /* System generated locals */
    integer i__1, i__2, i__3, i__4;
    real r__1, r__2;
    complex q__1, q__2, q__3;

    /* Local variables */
    integer j, k, j1, k1, jj, kk;
    complex ct;
    real ajj;
    integer j1j1;
    real akk;
    integer k1k1;
    real bjj, bkk;
    extern /* Subroutine */ int chpr2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *);
    extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
            *, complex *, integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int chpmv_(char *, integer *, complex *, complex *
, complex *, integer *, complex *, complex *, integer *), 
            caxpy_(integer *, complex *, complex *, integer *, complex *, 
            integer *), ctpmv_(char *, char *, char *, integer *, complex *, 
            complex *, integer *);
    logical upper;
    extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *, 
            complex *, complex *, integer *), csscal_(
            integer *, real *, complex *, integer *), xerbla_(char *, integer 
            *);


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

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

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

/*  CHPGST 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 CPPTRF. */

/*  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 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 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 CPPTRF. */

/*  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_("CHPGST", &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;
                r__1 = ap[i__3].r;
                ap[i__2].r = r__1, ap[i__2].i = 0.f;
                i__2 = jj;
                bjj = bp[i__2].r;
                ctpsv_(uplo, "Conjugate transpose", "Non-unit", &j, &bp[1], &
                        ap[j1], &c__1);
                i__2 = j - 1;
                q__1.r = -1.f, q__1.i = -0.f;
                chpmv_(uplo, &i__2, &q__1, &ap[1], &bp[j1], &c__1, &c_b1, &ap[
                        j1], &c__1);
                i__2 = j - 1;
                r__1 = 1.f / bjj;
                csscal_(&i__2, &r__1, &ap[j1], &c__1);
                i__2 = jj;
                i__3 = jj;
                i__4 = j - 1;
                cdotc_(&q__3, &i__4, &ap[j1], &c__1, &bp[j1], &c__1);
                q__2.r = ap[i__3].r - q__3.r, q__2.i = ap[i__3].i - q__3.i;
                q__1.r = q__2.r / bjj, q__1.i = q__2.i / bjj;
                ap[i__2].r = q__1.r, ap[i__2].i = q__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 */
                r__1 = bkk;
                akk /= r__1 * r__1;
                i__2 = kk;
                ap[i__2].r = akk, ap[i__2].i = 0.f;
                if (k < *n) {
                    i__2 = *n - k;
                    r__1 = 1.f / bkk;
                    csscal_(&i__2, &r__1, &ap[kk + 1], &c__1);
                    r__1 = akk * -.5f;
                    ct.r = r__1, ct.i = 0.f;
                    i__2 = *n - k;
                    caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
                            ;
                    i__2 = *n - k;
                    q__1.r = -1.f, q__1.i = -0.f;
                    chpr2_(uplo, &i__2, &q__1, &ap[kk + 1], &c__1, &bp[kk + 1]
, &c__1, &ap[k1k1]);
                    i__2 = *n - k;
                    caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
                            ;
                    i__2 = *n - k;
                    ctpsv_(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;
                ctpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[
                        k1], &c__1);
                r__1 = akk * .5f;
                ct.r = r__1, ct.i = 0.f;
                i__2 = k - 1;
                caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
                i__2 = k - 1;
                chpr2_(uplo, &i__2, &c_b1, &ap[k1], &c__1, &bp[k1], &c__1, &
                        ap[1]);
                i__2 = k - 1;
                caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
                i__2 = k - 1;
                csscal_(&i__2, &bkk, &ap[k1], &c__1);
                i__2 = kk;
/* Computing 2nd power */
                r__2 = bkk;
                r__1 = akk * (r__2 * r__2);
                ap[i__2].r = r__1, ap[i__2].i = 0.f;
/* 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;
                r__1 = ajj * bjj;
                i__3 = *n - j;
                cdotc_(&q__2, &i__3, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1);
                q__1.r = r__1 + q__2.r, q__1.i = q__2.i;
                ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
                i__2 = *n - j;
                csscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
                i__2 = *n - j;
                chpmv_(uplo, &i__2, &c_b1, &ap[j1j1], &bp[jj + 1], &c__1, &
                        c_b1, &ap[jj + 1], &c__1);
                i__2 = *n - j + 1;
                ctpmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &bp[jj]
, &ap[jj], &c__1);
                jj = j1j1;
/* L40: */
            }
        }
    }
    return 0;

/*     End of CHPGST */

} /* chpgst_ */