text: /* 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_ */
  