text: #include "blaswrap.h"
  #include "f2c.h"
  
  /* Subroutine */ int chegv_(integer *itype, char *jobz, char *uplo, integer *
  	n, complex *a, integer *lda, complex *b, integer *ldb, real *w, 
  	complex *work, integer *lwork, real *rwork, integer *info)
  {
  /*  -- LAPACK driver routine (version 3.0) --   
         Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
         Courant Institute, Argonne National Lab, and Rice University   
         June 30, 1999   
  
  
      Purpose   
      =======   
  
      CHEGV 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 and B is also   
      positive definite.   
  
      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.   
  
      A       (input/output) COMPLEX array, dimension (LDA, N)   
              On entry, the Hermitian matrix A.  If UPLO = 'U', the   
              leading N-by-N upper triangular part of A contains the   
              upper triangular part of the matrix A.  If UPLO = 'L',   
              the leading N-by-N lower triangular part of A contains   
              the lower triangular part of the matrix A.   
  
              On exit, if JOBZ = 'V', then if INFO = 0, A 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 on exit the upper triangle (if UPLO='U')   
              or the lower triangle (if UPLO='L') of A, including the   
              diagonal, is destroyed.   
  
      LDA     (input) INTEGER   
              The leading dimension of the array A.  LDA >= max(1,N).   
  
      B       (input/output) COMPLEX array, dimension (LDB, N)   
              On entry, the Hermitian positive definite matrix B.   
              If UPLO = 'U', the leading N-by-N upper triangular part of B   
              contains the upper triangular part of the matrix B.   
              If UPLO = 'L', the leading N-by-N lower triangular part of B   
              contains the lower triangular part of the matrix B.   
  
              On exit, if INFO <= N, the part of B containing the matrix is   
              overwritten by the triangular factor U or L from the Cholesky   
              factorization B = U**H*U or B = L*L**H.   
  
      LDB     (input) INTEGER   
              The leading dimension of the array B.  LDB >= max(1,N).   
  
      W       (output) REAL array, dimension (N)   
              If INFO = 0, the eigenvalues in ascending order.   
  
      WORK    (workspace/output) COMPLEX array, dimension (LWORK)   
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   
  
      LWORK   (input) INTEGER   
              The length of the array WORK.  LWORK >= max(1,2*N-1).   
              For optimal efficiency, LWORK >= (NB+1)*N,   
              where NB is the blocksize for CHETRD returned by ILAENV.   
  
              If LWORK = -1, then a workspace query is assumed; the routine   
              only calculates the optimal size of the WORK array, returns   
              this value as the first entry of the WORK array, and no error   
              message related to LWORK is issued by XERBLA.   
  
      RWORK   (workspace) REAL array, dimension (max(1, 3*N-2))   
  
      INFO    (output) INTEGER   
              = 0:  successful exit   
              < 0:  if INFO = -i, the i-th argument had an illegal value   
              > 0:  CPOTRF or CHEEV returned an error code:   
                 <= N:  if INFO = i, CHEEV failed to converge;   
                        i off-diagonal elements of an intermediate   
                        tridiagonal form did not converge to 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.   
  
      =====================================================================   
  
  
         Test the input parameters.   
  
         Parameter adjustments */
      /* Table of constant values */
      static complex c_b1 = {1.f,0.f};
      static integer c__1 = 1;
      static integer c_n1 = -1;
      
      /* System generated locals */
      integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
      /* Local variables */
      static integer neig;
      extern /* Subroutine */ int cheev_(char *, char *, integer *, complex *, 
  	    integer *, real *, complex *, integer *, real *, integer *);
      extern logical lsame_(char *, char *);
      extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, 
  	    integer *, integer *, complex *, complex *, integer *, complex *, 
  	    integer *);
      static char trans[1];
      extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
  	    integer *, integer *, complex *, complex *, integer *, complex *, 
  	    integer *);
      static logical upper, wantz;
      static integer nb;
      extern /* Subroutine */ int chegst_(integer *, char *, integer *, complex 
  	    *, integer *, complex *, integer *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *, ftnlen, ftnlen);
      extern /* Subroutine */ int xerbla_(char *, integer *), cpotrf_(
  	    char *, integer *, complex *, integer *, integer *);
      static integer lwkopt;
      static logical lquery;
  
  
      a_dim1 = *lda;
      a_offset = 1 + a_dim1 * 1;
      a -= a_offset;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1 * 1;
      b -= b_offset;
      --w;
      --work;
      --rwork;
  
      /* Function Body */
      wantz = lsame_(jobz, "V");
      upper = lsame_(uplo, "U");
      lquery = *lwork == -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 (*lda < max(1,*n)) {
  	*info = -6;
      } else if (*ldb < max(1,*n)) {
  	*info = -8;
      } else /* if(complicated condition) */ {
  /* Computing MAX */
  	i__1 = 1, i__2 = (*n << 1) - 1;
  	if (*lwork < max(i__1,i__2) && ! lquery) {
  	    *info = -11;
  	}
      }
  
      if (*info == 0) {
  	nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
  		 (ftnlen)1);
  	lwkopt = (nb + 1) * *n;
  	work[1].r = (real) lwkopt, work[1].i = 0.f;
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("CHEGV ", &i__1);
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*n == 0) {
  	return 0;
      }
  
  /*     Form a Cholesky factorization of B. */
  
      cpotrf_(uplo, n, &b[b_offset], ldb, info);
      if (*info != 0) {
  	*info = *n + *info;
  	return 0;
      }
  
  /*     Transform problem to standard eigenvalue problem and solve. */
  
      chegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
      cheev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[1]
  	    , info);
  
      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';
  	    }
  
  	    ctrsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
  		    b_offset], ldb, &a[a_offset], lda);
  
  	} 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';
  	    }
  
  	    ctrmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
  		    b_offset], ldb, &a[a_offset], lda);
  	}
      }
  
      work[1].r = (real) lwkopt, work[1].i = 0.f;
  
      return 0;
  
  /*     End of CHEGV */
  
  } /* chegv_ */
  
  