text: /* zsysvx.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;
  static integer c_n1 = -1;
  
  /* Subroutine */ int zsysvx_(char *fact, char *uplo, integer *n, integer *
  	nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
  	ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, 
  	 integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, 
  	doublecomplex *work, integer *lwork, doublereal *rwork, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 
  	    x_offset, i__1, i__2;
  
      /* Local variables */
      integer nb;
      extern logical lsame_(char *, char *);
      doublereal anorm;
      extern doublereal dlamch_(char *);
      logical nofact;
      extern /* Subroutine */ int xerbla_(char *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *);
      extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
  	    doublecomplex *, integer *, doublecomplex *, integer *);
      integer lwkopt;
      logical lquery;
      extern doublereal zlansy_(char *, char *, integer *, doublecomplex *, 
  	    integer *, doublereal *);
      extern /* Subroutine */ int zsycon_(char *, integer *, doublecomplex *, 
  	    integer *, integer *, doublereal *, doublereal *, doublecomplex *, 
  	     integer *), zsyrfs_(char *, integer *, integer *, 
  	    doublecomplex *, integer *, doublecomplex *, integer *, integer *, 
  	     doublecomplex *, integer *, doublecomplex *, integer *, 
  	    doublereal *, doublereal *, doublecomplex *, doublereal *, 
  	    integer *), zsytrf_(char *, integer *, doublecomplex *, 
  	    integer *, integer *, doublecomplex *, integer *, integer *), zsytrs_(char *, integer *, integer *, doublecomplex *, 
  	    integer *, integer *, doublecomplex *, integer *, integer *);
  
  
  /*  -- LAPACK driver routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  ZSYSVX uses the diagonal pivoting factorization to compute the */
  /*  solution to a complex system of linear equations A * X = B, */
  /*  where A is an N-by-N symmetric matrix and X and B are N-by-NRHS */
  /*  matrices. */
  
  /*  Error bounds on the solution and a condition estimate are also */
  /*  provided. */
  
  /*  Description */
  /*  =========== */
  
  /*  The following steps are performed: */
  
  /*  1. If FACT = 'N', the diagonal pivoting method is used to factor A. */
  /*     The form of the factorization is */
  /*        A = U * D * U**T,  if UPLO = 'U', or */
  /*        A = L * D * L**T,  if UPLO = 'L', */
  /*     where U (or L) is a product of permutation and unit upper (lower) */
  /*     triangular matrices, and D is symmetric and block diagonal with */
  /*     1-by-1 and 2-by-2 diagonal blocks. */
  
  /*  2. If some D(i,i)=0, so that D is exactly singular, then the routine */
  /*     returns with INFO = i. Otherwise, the factored form of A is used */
  /*     to estimate the condition number of the matrix A.  If the */
  /*     reciprocal of the condition number is less than machine precision, */
  /*     INFO = N+1 is returned as a warning, but the routine still goes on */
  /*     to solve for X and compute error bounds as described below. */
  
  /*  3. The system of equations is solved for X using the factored form */
  /*     of A. */
  
  /*  4. Iterative refinement is applied to improve the computed solution */
  /*     matrix and calculate error bounds and backward error estimates */
  /*     for it. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  FACT    (input) CHARACTER*1 */
  /*          Specifies whether or not the factored form of A has been */
  /*          supplied on entry. */
  /*          = 'F':  On entry, AF and IPIV contain the factored form */
  /*                  of A.  A, AF and IPIV will not be modified. */
  /*          = 'N':  The matrix A will be copied to AF and factored. */
  
  /*  UPLO    (input) CHARACTER*1 */
  /*          = 'U':  Upper triangle of A is stored; */
  /*          = 'L':  Lower triangle of A is stored. */
  
  /*  N       (input) INTEGER */
  /*          The number of linear equations, i.e., the order of the */
  /*          matrix A.  N >= 0. */
  
  /*  NRHS    (input) INTEGER */
  /*          The number of right hand sides, i.e., the number of columns */
  /*          of the matrices B and X.  NRHS >= 0. */
  
  /*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
  /*          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. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A.  LDA >= max(1,N). */
  
  /*  AF      (input or output) COMPLEX*16 array, dimension (LDAF,N) */
  /*          If FACT = 'F', then AF is an input argument and on entry */
  /*          contains the block diagonal matrix D and the multipliers used */
  /*          to obtain the factor U or L from the factorization */
  /*          A = U*D*U**T or A = L*D*L**T as computed by ZSYTRF. */
  
  /*          If FACT = 'N', then AF is an output argument and on exit */
  /*          returns the block diagonal matrix D and the multipliers used */
  /*          to obtain the factor U or L from the factorization */
  /*          A = U*D*U**T or A = L*D*L**T. */
  
  /*  LDAF    (input) INTEGER */
  /*          The leading dimension of the array AF.  LDAF >= max(1,N). */
  
  /*  IPIV    (input or output) INTEGER array, dimension (N) */
  /*          If FACT = 'F', then IPIV is an input argument and on entry */
  /*          contains details of the interchanges and the block structure */
  /*          of D, as determined by ZSYTRF. */
  /*          If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
  /*          interchanged and D(k,k) is a 1-by-1 diagonal block. */
  /*          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
  /*          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
  /*          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = */
  /*          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
  /*          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
  
  /*          If FACT = 'N', then IPIV is an output argument and on exit */
  /*          contains details of the interchanges and the block structure */
  /*          of D, as determined by ZSYTRF. */
  
  /*  B       (input) COMPLEX*16 array, dimension (LDB,NRHS) */
  /*          The N-by-NRHS right hand side matrix B. */
  
  /*  LDB     (input) INTEGER */
  /*          The leading dimension of the array B.  LDB >= max(1,N). */
  
  /*  X       (output) COMPLEX*16 array, dimension (LDX,NRHS) */
  /*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */
  
  /*  LDX     (input) INTEGER */
  /*          The leading dimension of the array X.  LDX >= max(1,N). */
  
  /*  RCOND   (output) DOUBLE PRECISION */
  /*          The estimate of the reciprocal condition number of the matrix */
  /*          A.  If RCOND is less than the machine precision (in */
  /*          particular, if RCOND = 0), the matrix is singular to working */
  /*          precision.  This condition is indicated by a return code of */
  /*          INFO > 0. */
  
  /*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
  /*          The estimated forward error bound for each solution vector */
  /*          X(j) (the j-th column of the solution matrix X). */
  /*          If XTRUE is the true solution corresponding to X(j), FERR(j) */
  /*          is an estimated upper bound for the magnitude of the largest */
  /*          element in (X(j) - XTRUE) divided by the magnitude of the */
  /*          largest element in X(j).  The estimate is as reliable as */
  /*          the estimate for RCOND, and is almost always a slight */
  /*          overestimate of the true error. */
  
  /*  BERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
  /*          The componentwise relative backward error of each solution */
  /*          vector X(j) (i.e., the smallest relative change in */
  /*          any element of A or B that makes X(j) an exact solution). */
  
  /*  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
  /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  
  /*  LWORK   (input) INTEGER */
  /*          The length of WORK.  LWORK >= max(1,2*N), and for best */
  /*          performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where */
  /*          NB is the optimal blocksize for ZSYTRF. */
  
  /*          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) DOUBLE PRECISION array, dimension (N) */
  
  /*  INFO    (output) INTEGER */
  /*          = 0: successful exit */
  /*          < 0: if INFO = -i, the i-th argument had an illegal value */
  /*          > 0: if INFO = i, and i is */
  /*                <= N:  D(i,i) is exactly zero.  The factorization */
  /*                       has been completed but the factor D is exactly */
  /*                       singular, so the solution and error bounds could */
  /*                       not be computed. RCOND = 0 is returned. */
  /*                = N+1: D is nonsingular, but RCOND is less than machine */
  /*                       precision, meaning that the matrix is singular */
  /*                       to working precision.  Nevertheless, the */
  /*                       solution and error bounds are computed because */
  /*                       there are a number of situations where the */
  /*                       computed solution can be more accurate than the */
  /*                       value of RCOND would suggest. */
  
  /*  ===================================================================== */
  
  /*     .. 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;
      af_dim1 = *ldaf;
      af_offset = 1 + af_dim1;
      af -= af_offset;
      --ipiv;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1;
      b -= b_offset;
      x_dim1 = *ldx;
      x_offset = 1 + x_dim1;
      x -= x_offset;
      --ferr;
      --berr;
      --work;
      --rwork;
  
      /* Function Body */
      *info = 0;
      nofact = lsame_(fact, "N");
      lquery = *lwork == -1;
      if (! nofact && ! lsame_(fact, "F")) {
  	*info = -1;
      } else if (! lsame_(uplo, "U") && ! lsame_(uplo, 
  	    "L")) {
  	*info = -2;
      } else if (*n < 0) {
  	*info = -3;
      } else if (*nrhs < 0) {
  	*info = -4;
      } else if (*lda < max(1,*n)) {
  	*info = -6;
      } else if (*ldaf < max(1,*n)) {
  	*info = -8;
      } else if (*ldb < max(1,*n)) {
  	*info = -11;
      } else if (*ldx < max(1,*n)) {
  	*info = -13;
      } else /* if(complicated condition) */ {
  /* Computing MAX */
  	i__1 = 1, i__2 = *n << 1;
  	if (*lwork < max(i__1,i__2) && ! lquery) {
  	    *info = -18;
  	}
      }
  
      if (*info == 0) {
  /* Computing MAX */
  	i__1 = 1, i__2 = *n << 1;
  	lwkopt = max(i__1,i__2);
  	if (nofact) {
  	    nb = ilaenv_(&c__1, "ZSYTRF", uplo, n, &c_n1, &c_n1, &c_n1);
  /* Computing MAX */
  	    i__1 = lwkopt, i__2 = *n * nb;
  	    lwkopt = max(i__1,i__2);
  	}
  	work[1].r = (doublereal) lwkopt, work[1].i = 0.;
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("ZSYSVX", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
      if (nofact) {
  
  /*        Compute the factorization A = U*D*U' or A = L*D*L'. */
  
  	zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
  	zsytrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork, 
  		info);
  
  /*        Return if INFO is non-zero. */
  
  	if (*info > 0) {
  	    *rcond = 0.;
  	    return 0;
  	}
      }
  
  /*     Compute the norm of the matrix A. */
  
      anorm = zlansy_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
  
  /*     Compute the reciprocal of the condition number of A. */
  
      zsycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], 
  	    info);
  
  /*     Compute the solution vectors X. */
  
      zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
      zsytrs_(uplo, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, 
  	    info);
  
  /*     Use iterative refinement to improve the computed solutions and */
  /*     compute error bounds and backward error estimates for them. */
  
      zsyrfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], 
  	    &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1]
  , &rwork[1], info);
  
  /*     Set INFO = N+1 if the matrix is singular to working precision. */
  
      if (*rcond < dlamch_("Epsilon")) {
  	*info = *n + 1;
      }
  
      work[1].r = (doublereal) lwkopt, work[1].i = 0.;
  
      return 0;
  
  /*     End of ZSYSVX */
  
  } /* zsysvx_ */
  