text: /* Copyright (c) 1992-2008 The University of Tennessee.  All rights reserved.
   * See file COPYING in this directory for details. */
  
  #ifdef __cplusplus
  extern "C" {
  #endif
  
  #include "f2c.h"
  #include "hypre_lapack.h"
  
  /* Subroutine */ integer dsygs2_(integer *itype,const char *uplo, integer *n,
  	doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
  	info)
  {
  /*  -- LAPACK routine (version 3.0) --
         Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
         Courant Institute, Argonne National Lab, and Rice University
         February 29, 1992
  
  
      Purpose
      =======
  
      DSYGS2 reduces a real symmetric-definite generalized eigenproblem
      to standard form.
  
      If ITYPE = 1, the problem is A*x = lambda*B*x,
      and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
  
      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` or L'*A*L.
  
      B must have been previously factorized as U'*U or L*L' by DPOTRF.
  
      Arguments
      =========
  
      ITYPE   (input) INTEGER
              = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
              = 2 or 3: compute U*A*U' or L'*A*L.
  
      UPLO    (input) CHARACTER
              Specifies whether the upper or lower triangular part of the
              symmetric matrix A is stored, and how B has been factorized.
              = 'U':  Upper triangular
              = 'L':  Lower triangular
  
      N       (input) INTEGER
              The order of the matrices A and B.  N >= 0.
  
      A       (input/output) DOUBLE PRECISION 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, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading n by n lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
  
              On exit, if INFO = 0, the transformed matrix, stored in the
              same format as A.
  
      LDA     (input) INTEGER
              The leading dimension of the array A.  LDA >= max(1,N).
  
      B       (input) DOUBLE PRECISION array, dimension (LDB,N)
              The triangular factor from the Cholesky factorization of B,
              as returned by DPOTRF.
  
      LDB     (input) INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).
  
      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 */
      doublereal c_b6 = -1.;
      integer c__1 = 1;
      doublereal c_b27 = 1.;
  
      /* System generated locals */
      integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
      doublereal d__1;
      /* Local variables */
      extern /* Subroutine */ integer dsyr2_(const char *, integer *, doublereal *,
  	    doublereal *, integer *, doublereal *, integer *, doublereal *,
  	    integer *);
      integer k;
      extern /* Subroutine */ integer dscal_(integer *, doublereal *, doublereal *,
  	    integer *);
      extern logical lsame_(const char *,const char *);
      extern /* Subroutine */ integer daxpy_(integer *, doublereal *, doublereal *,
  	    integer *, doublereal *, integer *);
      logical upper;
      extern /* Subroutine */ integer dtrmv_(const char *,const char *,const char *, integer *,
  	    doublereal *, integer *, doublereal *, integer *), dtrsv_(const char *,const char *,const char *, integer *, doublereal *,
  	    integer *, doublereal *, integer *);
      doublereal ct;
      extern /* Subroutine */ integer xerbla_(const char *, integer *);
      doublereal akk, bkk;
  #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
  #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
  
  
      a_dim1 = *lda;
      a_offset = 1 + a_dim1 * 1;
      a -= a_offset;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1 * 1;
      b -= b_offset;
  
      /* 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;
      } else if (*lda < max(1,*n)) {
  	*info = -5;
      } else if (*ldb < max(1,*n)) {
  	*info = -7;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DSYGS2", &i__1);
  	return 0;
      }
  
      if (*itype == 1) {
  	if (upper) {
  
  /*           Compute inv(U')*A*inv(U) */
  
  	    i__1 = *n;
  	    for (k = 1; k <= i__1; ++k) {
  
  /*              Update the upper triangle of A(k:n,k:n) */
  
  		akk = a_ref(k, k);
  		bkk = b_ref(k, k);
  /* Computing 2nd power */
  		d__1 = bkk;
  		akk /= d__1 * d__1;
  		a_ref(k, k) = akk;
  		if (k < *n) {
  		    i__2 = *n - k;
  		    d__1 = 1. / bkk;
  		    dscal_(&i__2, &d__1, &a_ref(k, k + 1), lda);
  		    ct = akk * -.5;
  		    i__2 = *n - k;
  		    daxpy_(&i__2, &ct, &b_ref(k, k + 1), ldb, &a_ref(k, k + 1)
  			    , lda);
  		    i__2 = *n - k;
  		    dsyr2_(uplo, &i__2, &c_b6, &a_ref(k, k + 1), lda, &b_ref(
  			    k, k + 1), ldb, &a_ref(k + 1, k + 1), lda);
  		    i__2 = *n - k;
  		    daxpy_(&i__2, &ct, &b_ref(k, k + 1), ldb, &a_ref(k, k + 1)
  			    , lda);
  		    i__2 = *n - k;
  		    dtrsv_(uplo, "Transpose", "Non-unit", &i__2, &b_ref(k + 1,
  			     k + 1), ldb, &a_ref(k, k + 1), lda);
  		}
  /* L10: */
  	    }
  	} else {
  
  /*           Compute inv(L)*A*inv(L') */
  
  	    i__1 = *n;
  	    for (k = 1; k <= i__1; ++k) {
  
  /*              Update the lower triangle of A(k:n,k:n) */
  
  		akk = a_ref(k, k);
  		bkk = b_ref(k, k);
  /* Computing 2nd power */
  		d__1 = bkk;
  		akk /= d__1 * d__1;
  		a_ref(k, k) = akk;
  		if (k < *n) {
  		    i__2 = *n - k;
  		    d__1 = 1. / bkk;
  		    dscal_(&i__2, &d__1, &a_ref(k + 1, k), &c__1);
  		    ct = akk * -.5;
  		    i__2 = *n - k;
  		    daxpy_(&i__2, &ct, &b_ref(k + 1, k), &c__1, &a_ref(k + 1,
  			    k), &c__1);
  		    i__2 = *n - k;
  		    dsyr2_(uplo, &i__2, &c_b6, &a_ref(k + 1, k), &c__1, &
  			    b_ref(k + 1, k), &c__1, &a_ref(k + 1, k + 1), lda);
  		    i__2 = *n - k;
  		    daxpy_(&i__2, &ct, &b_ref(k + 1, k), &c__1, &a_ref(k + 1,
  			    k), &c__1);
  		    i__2 = *n - k;
  		    dtrsv_(uplo, "No transpose", "Non-unit", &i__2, &b_ref(k
  			    + 1, k + 1), ldb, &a_ref(k + 1, k), &c__1);
  		}
  /* L20: */
  	    }
  	}
      } else {
  	if (upper) {
  
  /*           Compute U*A*U' */
  
  	    i__1 = *n;
  	    for (k = 1; k <= i__1; ++k) {
  
  /*              Update the upper triangle of A(1:k,1:k) */
  
  		akk = a_ref(k, k);
  		bkk = b_ref(k, k);
  		i__2 = k - 1;
  		dtrmv_(uplo, "No transpose", "Non-unit", &i__2, &b[b_offset],
  			ldb, &a_ref(1, k), &c__1);
  		ct = akk * .5;
  		i__2 = k - 1;
  		daxpy_(&i__2, &ct, &b_ref(1, k), &c__1, &a_ref(1, k), &c__1);
  		i__2 = k - 1;
  		dsyr2_(uplo, &i__2, &c_b27, &a_ref(1, k), &c__1, &b_ref(1, k),
  			 &c__1, &a[a_offset], lda);
  		i__2 = k - 1;
  		daxpy_(&i__2, &ct, &b_ref(1, k), &c__1, &a_ref(1, k), &c__1);
  		i__2 = k - 1;
  		dscal_(&i__2, &bkk, &a_ref(1, k), &c__1);
  /* Computing 2nd power */
  		d__1 = bkk;
  		a_ref(k, k) = akk * (d__1 * d__1);
  /* L30: */
  	    }
  	} else {
  
  /*           Compute L'*A*L */
  
  	    i__1 = *n;
  	    for (k = 1; k <= i__1; ++k) {
  
  /*              Update the lower triangle of A(1:k,1:k) */
  
  		akk = a_ref(k, k);
  		bkk = b_ref(k, k);
  		i__2 = k - 1;
  		dtrmv_(uplo, "Transpose", "Non-unit", &i__2, &b[b_offset],
  			ldb, &a_ref(k, 1), lda);
  		ct = akk * .5;
  		i__2 = k - 1;
  		daxpy_(&i__2, &ct, &b_ref(k, 1), ldb, &a_ref(k, 1), lda);
  		i__2 = k - 1;
  		dsyr2_(uplo, &i__2, &c_b27, &a_ref(k, 1), lda, &b_ref(k, 1),
  			ldb, &a[a_offset], lda);
  		i__2 = k - 1;
  		daxpy_(&i__2, &ct, &b_ref(k, 1), ldb, &a_ref(k, 1), lda);
  		i__2 = k - 1;
  		dscal_(&i__2, &bkk, &a_ref(k, 1), lda);
  /* Computing 2nd power */
  		d__1 = bkk;
  		a_ref(k, k) = akk * (d__1 * d__1);
  /* L40: */
  	    }
  	}
      }
      return 0;
  
  /*     End of DSYGS2 */
  
  } /* dsygs2_ */
  
  #undef b_ref
  #undef a_ref
  
  #ifdef __cplusplus
  }
  #endif
  