text: #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  static integer c_n1 = -1;
  static real c_b19 = 1.f;
  
  /* Subroutine */ int ssygvx_(integer *itype, char *jobz, char *range, char *
  	uplo, integer *n, real *a, integer *lda, real *b, integer *ldb, real *
  	vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, 
  	real *w, real *z__, integer *ldz, real *work, integer *lwork, integer 
  	*iwork, integer *ifail, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset, i__1, i__2;
  
      /* Local variables */
      integer nb;
      extern logical lsame_(char *, char *);
      char trans[1];
      logical upper;
      extern /* Subroutine */ int strmm_(char *, char *, char *, char *, 
  	    integer *, integer *, real *, real *, integer *, real *, integer *
  );
      logical wantz;
      extern /* Subroutine */ int strsm_(char *, char *, char *, char *, 
  	    integer *, integer *, real *, real *, integer *, real *, integer *
  );
      logical alleig, indeig, valeig;
      extern /* Subroutine */ int xerbla_(char *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *);
      integer lwkmin;
      extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *, 
  	    integer *);
      integer lwkopt;
      logical lquery;
      extern /* Subroutine */ int ssygst_(integer *, char *, integer *, real *, 
  	    integer *, real *, integer *, integer *), ssyevx_(char *, 
  	    char *, char *, integer *, real *, integer *, real *, real *, 
  	    integer *, integer *, real *, integer *, real *, real *, integer *
  , real *, integer *, integer *, integer *, integer *);
  
  
  /*  -- LAPACK driver routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  SSYGVX computes selected eigenvalues, and optionally, eigenvectors */
  /*  of a real generalized symmetric-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 symmetric and B is also positive definite. */
  /*  Eigenvalues and eigenvectors can be selected by specifying either a */
  /*  range of values or a range of indices for the desired eigenvalues. */
  
  /*  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. */
  
  /*  RANGE   (input) CHARACTER*1 */
  /*          = 'A': all eigenvalues will be found. */
  /*          = 'V': all eigenvalues in the half-open interval (VL,VU] */
  /*                 will be found. */
  /*          = 'I': the IL-th through IU-th eigenvalues will be found. */
  
  /*  UPLO    (input) CHARACTER*1 */
  /*          = 'U':  Upper triangle of A and B are stored; */
  /*          = 'L':  Lower triangle of A and B are stored. */
  
  /*  N       (input) INTEGER */
  /*          The order of the matrix pencil (A,B).  N >= 0. */
  
  /*  A       (input/output) REAL array, dimension (LDA, N) */
  /*          On entry, the symmetric 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, the lower triangle (if UPLO='L') or the upper */
  /*          triangle (if UPLO='U') of A, including the diagonal, is */
  /*          destroyed. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A.  LDA >= max(1,N). */
  
  /*  B       (input/output) REAL array, dimension (LDA, N) */
  /*          On entry, the symmetric 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**T*U or B = L*L**T. */
  
  /*  LDB     (input) INTEGER */
  /*          The leading dimension of the array B.  LDB >= max(1,N). */
  
  /*  VL      (input) REAL */
  /*  VU      (input) REAL */
  /*          If RANGE='V', the lower and upper bounds of the interval to */
  /*          be searched for eigenvalues. VL < VU. */
  /*          Not referenced if RANGE = 'A' or 'I'. */
  
  /*  IL      (input) INTEGER */
  /*  IU      (input) INTEGER */
  /*          If RANGE='I', the indices (in ascending order) of the */
  /*          smallest and largest eigenvalues to be returned. */
  /*          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
  /*          Not referenced if RANGE = 'A' or 'V'. */
  
  /*  ABSTOL  (input) REAL */
  /*          The absolute error tolerance for the eigenvalues. */
  /*          An approximate eigenvalue is accepted as converged */
  /*          when it is determined to lie in an interval [a,b] */
  /*          of width less than or equal to */
  
  /*                  ABSTOL + EPS *   max( |a|,|b| ) , */
  
  /*          where EPS is the machine precision.  If ABSTOL is less than */
  /*          or equal to zero, then  EPS*|T|  will be used in its place, */
  /*          where |T| is the 1-norm of the tridiagonal matrix obtained */
  /*          by reducing A to tridiagonal form. */
  
  /*          Eigenvalues will be computed most accurately when ABSTOL is */
  /*          set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
  /*          If this routine returns with INFO>0, indicating that some */
  /*          eigenvectors did not converge, try setting ABSTOL to */
  /*          2*SLAMCH('S'). */
  
  /*  M       (output) INTEGER */
  /*          The total number of eigenvalues found.  0 <= M <= N. */
  /*          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
  
  /*  W       (output) REAL array, dimension (N) */
  /*          On normal exit, the first M elements contain the selected */
  /*          eigenvalues in ascending order. */
  
  /*  Z       (output) REAL array, dimension (LDZ, max(1,M)) */
  /*          If JOBZ = 'N', then Z is not referenced. */
  /*          If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
  /*          contain the orthonormal eigenvectors of the matrix A */
  /*          corresponding to the selected eigenvalues, with the i-th */
  /*          column of Z holding the eigenvector associated with W(i). */
  /*          The eigenvectors are normalized as follows: */
  /*          if ITYPE = 1 or 2, Z**T*B*Z = I; */
  /*          if ITYPE = 3, Z**T*inv(B)*Z = I. */
  
  /*          If an eigenvector fails to converge, then that column of Z */
  /*          contains the latest approximation to the eigenvector, and the */
  /*          index of the eigenvector is returned in IFAIL. */
  /*          Note: the user must ensure that at least max(1,M) columns are */
  /*          supplied in the array Z; if RANGE = 'V', the exact value of M */
  /*          is not known in advance and an upper bound must be used. */
  
  /*  LDZ     (input) INTEGER */
  /*          The leading dimension of the array Z.  LDZ >= 1, and if */
  /*          JOBZ = 'V', LDZ >= max(1,N). */
  
  /*  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
  /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  
  /*  LWORK   (input) INTEGER */
  /*          The length of the array WORK.  LWORK >= max(1,8*N). */
  /*          For optimal efficiency, LWORK >= (NB+3)*N, */
  /*          where NB is the blocksize for SSYTRD 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. */
  
  /*  IWORK   (workspace) INTEGER array, dimension (5*N) */
  
  /*  IFAIL   (output) INTEGER array, dimension (N) */
  /*          If JOBZ = 'V', then if INFO = 0, the first M elements of */
  /*          IFAIL are zero.  If INFO > 0, then IFAIL contains the */
  /*          indices of the eigenvectors that failed to converge. */
  /*          If JOBZ = 'N', then IFAIL is not referenced. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0:  successful exit */
  /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
  /*          > 0:  SPOTRF or SSYEVX returned an error code: */
  /*             <= N:  if INFO = i, SSYEVX failed to converge; */
  /*                    i eigenvectors failed to converge.  Their indices */
  /*                    are stored in array IFAIL. */
  /*             > 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 */
  
  /* ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1;
      b -= b_offset;
      --w;
      z_dim1 = *ldz;
      z_offset = 1 + z_dim1;
      z__ -= z_offset;
      --work;
      --iwork;
      --ifail;
  
      /* Function Body */
      upper = lsame_(uplo, "U");
      wantz = lsame_(jobz, "V");
      alleig = lsame_(range, "A");
      valeig = lsame_(range, "V");
      indeig = lsame_(range, "I");
      lquery = *lwork == -1;
  
      *info = 0;
      if (*itype < 1 || *itype > 3) {
  	*info = -1;
      } else if (! (wantz || lsame_(jobz, "N"))) {
  	*info = -2;
      } else if (! (alleig || valeig || indeig)) {
  	*info = -3;
      } else if (! (upper || lsame_(uplo, "L"))) {
  	*info = -4;
      } else if (*n < 0) {
  	*info = -5;
      } else if (*lda < max(1,*n)) {
  	*info = -7;
      } else if (*ldb < max(1,*n)) {
  	*info = -9;
      } else {
  	if (valeig) {
  	    if (*n > 0 && *vu <= *vl) {
  		*info = -11;
  	    }
  	} else if (indeig) {
  	    if (*il < 1 || *il > max(1,*n)) {
  		*info = -12;
  	    } else if (*iu < min(*n,*il) || *iu > *n) {
  		*info = -13;
  	    }
  	}
      }
      if (*info == 0) {
  	if (*ldz < 1 || wantz && *ldz < *n) {
  	    *info = -18;
  	}
      }
  
      if (*info == 0) {
  /* Computing MAX */
  	i__1 = 1, i__2 = *n << 3;
  	lwkmin = max(i__1,i__2);
  	nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
  /* Computing MAX */
  	i__1 = lwkmin, i__2 = (nb + 3) * *n;
  	lwkopt = max(i__1,i__2);
  	work[1] = (real) lwkopt;
  
  	if (*lwork < lwkmin && ! lquery) {
  	    *info = -20;
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("SSYGVX", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      *m = 0;
      if (*n == 0) {
  	return 0;
      }
  
  /*     Form a Cholesky factorization of B. */
  
      spotrf_(uplo, n, &b[b_offset], ldb, info);
      if (*info != 0) {
  	*info = *n + *info;
  	return 0;
      }
  
  /*     Transform problem to standard eigenvalue problem and solve. */
  
      ssygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
      ssyevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol, 
  	    m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], &ifail[
  	    1], info);
  
      if (wantz) {
  
  /*        Backtransform eigenvectors to the original problem. */
  
  	if (*info > 0) {
  	    *m = *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 = 'T';
  	    }
  
  	    strsm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
  , ldb, &z__[z_offset], ldz);
  
  	} else if (*itype == 3) {
  
  /*           For B*A*x=(lambda)*x; */
  /*           backtransform eigenvectors: x = L*y or U'*y */
  
  	    if (upper) {
  		*(unsigned char *)trans = 'T';
  	    } else {
  		*(unsigned char *)trans = 'N';
  	    }
  
  	    strmm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
  , ldb, &z__[z_offset], ldz);
  	}
      }
  
  /*     Set WORK(1) to optimal workspace size. */
  
      work[1] = (real) lwkopt;
  
      return 0;
  
  /*     End of SSYGVX */
  
  } /* ssygvx_ */
  