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

/* Subroutine */ int zhpgst_(integer *itype, char *uplo, integer *n, 
	doublecomplex *ap, doublecomplex *bp, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    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   
            = '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   

    =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static doublecomplex c_b1 = {1.,0.};
    static integer c__1 = 1;
    
    /* 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 */
    extern /* Subroutine */ int zhpr2_(char *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *);
    static integer j, k;
    extern logical lsame_(char *, char *);
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    static logical upper;
    static integer j1, k1;
    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 *);
    static integer jj, kk;
    static doublecomplex ct;
    extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
	    integer *, doublereal *, doublecomplex *, integer *);
    static doublereal ajj;
    static integer j1j1;
    static doublereal akk;
    static integer k1k1;
    static doublereal bjj, bkk;


    --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_ */

