text: /* zhpgvd.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;
  
  /* Subroutine */ int zhpgvd_(integer *itype, char *jobz, char *uplo, integer *
  	n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex 
  	*z__, integer *ldz, doublecomplex *work, integer *lwork, doublereal *
  	rwork, integer *lrwork, integer *iwork, integer *liwork, integer *
  	info)
  {
      /* System generated locals */
      integer z_dim1, z_offset, i__1;
      doublereal d__1, d__2;
  
      /* Local variables */
      integer j, neig;
      extern logical lsame_(char *, char *);
      integer lwmin;
      char trans[1];
      logical upper, wantz;
      extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, 
  	    doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex *
  , doublecomplex *, integer *), xerbla_(
  	    char *, integer *);
      integer liwmin;
      extern /* Subroutine */ int zhpevd_(char *, char *, integer *, 
  	    doublecomplex *, doublereal *, doublecomplex *, integer *, 
  	    doublecomplex *, integer *, doublereal *, integer *, integer *, 
  	    integer *, integer *);
      integer lrwmin;
      extern /* Subroutine */ int zhpgst_(integer *, char *, integer *, 
  	    doublecomplex *, doublecomplex *, integer *);
      logical lquery;
      extern /* Subroutine */ int zpptrf_(char *, integer *, doublecomplex *, 
  	    integer *);
  
  
  /*  -- LAPACK driver routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors */
  /*  of a complex generalized Hermitian-definite eigenproblem, of the form */
  /*  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and */
  /*  B are assumed to be Hermitian, stored in packed format, and B is also */
  /*  positive definite. */
  /*  If eigenvectors are desired, it uses a divide and conquer algorithm. */
  
  /*  The divide and conquer algorithm makes very mild assumptions about */
  /*  floating point arithmetic. It will work on machines with a guard */
  /*  digit in add/subtract, or on those binary machines without guard */
  /*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
  /*  Cray-2. It could conceivably fail on hexadecimal or decimal machines */
  /*  without guard digits, but we know of none. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  ITYPE   (input) INTEGER */
  /*          Specifies the problem type to be solved: */
  /*          = 1:  A*x = (lambda)*B*x */
  /*          = 2:  A*B*x = (lambda)*x */
  /*          = 3:  B*A*x = (lambda)*x */
  
  /*  JOBZ    (input) CHARACTER*1 */
  /*          = 'N':  Compute eigenvalues only; */
  /*          = 'V':  Compute eigenvalues and eigenvectors. */
  
  /*  UPLO    (input) CHARACTER*1 */
  /*          = 'U':  Upper triangles of A and B are stored; */
  /*          = 'L':  Lower triangles of A and B are stored. */
  
  /*  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)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
  
  /*          On exit, the contents of AP are destroyed. */
  
  /*  BP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */
  /*          On entry, the upper or lower triangle of the Hermitian matrix */
  /*          B, packed columnwise in a linear array.  The j-th column of B */
  /*          is stored in the array BP as follows: */
  /*          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */
  /*          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */
  
  /*          On exit, the triangular factor U or L from the Cholesky */
  /*          factorization B = U**H*U or B = L*L**H, in the same storage */
  /*          format as B. */
  
  /*  W       (output) DOUBLE PRECISION array, dimension (N) */
  /*          If INFO = 0, the eigenvalues in ascending order. */
  
  /*  Z       (output) COMPLEX*16 array, dimension (LDZ, N) */
  /*          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
  /*          eigenvectors.  The eigenvectors are normalized as follows: */
  /*          if ITYPE = 1 or 2, Z**H*B*Z = I; */
  /*          if ITYPE = 3, Z**H*inv(B)*Z = I. */
  /*          If JOBZ = 'N', then Z is not referenced. */
  
  /*  LDZ     (input) INTEGER */
  /*          The leading dimension of the array Z.  LDZ >= 1, and if */
  /*          JOBZ = 'V', LDZ >= max(1,N). */
  
  /*  WORK    (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
  /*          On exit, if INFO = 0, WORK(1) returns the required LWORK. */
  
  /*  LWORK   (input) INTEGER */
  /*          The dimension of array WORK. */
  /*          If N <= 1,               LWORK >= 1. */
  /*          If JOBZ = 'N' and N > 1, LWORK >= N. */
  /*          If JOBZ = 'V' and N > 1, LWORK >= 2*N. */
  
  /*          If LWORK = -1, then a workspace query is assumed; the routine */
  /*          only calculates the required sizes of the WORK, RWORK and */
  /*          IWORK arrays, returns these values as the first entries of */
  /*          the WORK, RWORK and IWORK arrays, and no error message */
  /*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
  
  /*  RWORK   (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
  /*          On exit, if INFO = 0, RWORK(1) returns the required LRWORK. */
  
  /*  LRWORK  (input) INTEGER */
  /*          The dimension of array RWORK. */
  /*          If N <= 1,               LRWORK >= 1. */
  /*          If JOBZ = 'N' and N > 1, LRWORK >= N. */
  /*          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. */
  
  /*          If LRWORK = -1, then a workspace query is assumed; the */
  /*          routine only calculates the required sizes of the WORK, RWORK */
  /*          and IWORK arrays, returns these values as the first entries */
  /*          of the WORK, RWORK and IWORK arrays, and no error message */
  /*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
  
  /*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
  /*          On exit, if INFO = 0, IWORK(1) returns the required LIWORK. */
  
  /*  LIWORK  (input) INTEGER */
  /*          The dimension of array IWORK. */
  /*          If JOBZ  = 'N' or N <= 1, LIWORK >= 1. */
  /*          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N. */
  
  /*          If LIWORK = -1, then a workspace query is assumed; the */
  /*          routine only calculates the required sizes of the WORK, RWORK */
  /*          and IWORK arrays, returns these values as the first entries */
  /*          of the WORK, RWORK and IWORK arrays, and no error message */
  /*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0:  successful exit */
  /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
  /*          > 0:  ZPPTRF or ZHPEVD returned an error code: */
  /*             <= N:  if INFO = i, ZHPEVD failed to converge; */
  /*                    i off-diagonal elements of an intermediate */
  /*                    tridiagonal form did not convergeto zero; */
  /*             > N:   if INFO = N + i, for 1 <= i <= n, then the leading */
  /*                    minor of order i of B is not positive definite. */
  /*                    The factorization of B could not be completed and */
  /*                    no eigenvalues or eigenvectors were computed. */
  
  /*  Further Details */
  /*  =============== */
  
  /*  Based on contributions by */
  /*     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
  
  /*  ===================================================================== */
  
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      --ap;
      --bp;
      --w;
      z_dim1 = *ldz;
      z_offset = 1 + z_dim1;
      z__ -= z_offset;
      --work;
      --rwork;
      --iwork;
  
      /* Function Body */
      wantz = lsame_(jobz, "V");
      upper = lsame_(uplo, "U");
      lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
  
      *info = 0;
      if (*itype < 1 || *itype > 3) {
  	*info = -1;
      } else if (! (wantz || lsame_(jobz, "N"))) {
  	*info = -2;
      } else if (! (upper || lsame_(uplo, "L"))) {
  	*info = -3;
      } else if (*n < 0) {
  	*info = -4;
      } else if (*ldz < 1 || wantz && *ldz < *n) {
  	*info = -9;
      }
  
      if (*info == 0) {
  	if (*n <= 1) {
  	    lwmin = 1;
  	    liwmin = 1;
  	    lrwmin = 1;
  	} else {
  	    if (wantz) {
  		lwmin = *n << 1;
  /* Computing 2nd power */
  		i__1 = *n;
  		lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
  		liwmin = *n * 5 + 3;
  	    } else {
  		lwmin = *n;
  		lrwmin = *n;
  		liwmin = 1;
  	    }
  	}
  
  	work[1].r = (doublereal) lwmin, work[1].i = 0.;
  	rwork[1] = (doublereal) lrwmin;
  	iwork[1] = liwmin;
  	if (*lwork < lwmin && ! lquery) {
  	    *info = -11;
  	} else if (*lrwork < lrwmin && ! lquery) {
  	    *info = -13;
  	} else if (*liwork < liwmin && ! lquery) {
  	    *info = -15;
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("ZHPGVD", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*n == 0) {
  	return 0;
      }
  
  /*     Form a Cholesky factorization of B. */
  
      zpptrf_(uplo, n, &bp[1], info);
      if (*info != 0) {
  	*info = *n + *info;
  	return 0;
      }
  
  /*     Transform problem to standard eigenvalue problem and solve. */
  
      zhpgst_(itype, uplo, n, &ap[1], &bp[1], info);
      zhpevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], 
  	    lwork, &rwork[1], lrwork, &iwork[1], liwork, info);
  /* Computing MAX */
      d__1 = (doublereal) lwmin, d__2 = work[1].r;
      lwmin = (integer) max(d__1,d__2);
  /* Computing MAX */
      d__1 = (doublereal) lrwmin;
      lrwmin = (integer) max(d__1,rwork[1]);
  /* Computing MAX */
      d__1 = (doublereal) liwmin, d__2 = (doublereal) iwork[1];
      liwmin = (integer) max(d__1,d__2);
  
      if (wantz) {
  
  /*        Backtransform eigenvectors to the original problem. */
  
  	neig = *n;
  	if (*info > 0) {
  	    neig = *info - 1;
  	}
  	if (*itype == 1 || *itype == 2) {
  
  /*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
  /*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
  
  	    if (upper) {
  		*(unsigned char *)trans = 'N';
  	    } else {
  		*(unsigned char *)trans = 'C';
  	    }
  
  	    i__1 = neig;
  	    for (j = 1; j <= i__1; ++j) {
  		ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 
  			1], &c__1);
  /* L10: */
  	    }
  
  	} else if (*itype == 3) {
  
  /*           For B*A*x=(lambda)*x; */
  /*           backtransform eigenvectors: x = L*y or U'*y */
  
  	    if (upper) {
  		*(unsigned char *)trans = 'C';
  	    } else {
  		*(unsigned char *)trans = 'N';
  	    }
  
  	    i__1 = neig;
  	    for (j = 1; j <= i__1; ++j) {
  		ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 
  			1], &c__1);
  /* L20: */
  	    }
  	}
      }
  
      work[1].r = (doublereal) lwmin, work[1].i = 0.;
      rwork[1] = (doublereal) lrwmin;
      iwork[1] = liwmin;
      return 0;
  
  /*     End of ZHPGVD */
  
  } /* zhpgvd_ */
  