text: #include "blaswrap.h"
  #include "f2c.h"
  
  /* Subroutine */ int dgesvx_(char *fact, char *trans, integer *n, integer *
  	nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, 
  	integer *ipiv, char *equed, doublereal *r__, doublereal *c__, 
  	doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
  	rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
  	iwork, 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   
      =======   
  
      DGESVX uses the LU factorization to compute the solution to a real   
      system of linear equations   
         A * X = B,   
      where A is an N-by-N 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 = 'E', real scaling factors are computed to equilibrate   
         the system:   
            TRANS = 'N':  diag(R)*A*diag(C)     *inv(diag(C))*X = diag(R)*B   
            TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B   
            TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B   
         Whether or not the system will be equilibrated depends on the   
         scaling of the matrix A, but if equilibration is used, A is   
         overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')   
         or diag(C)*B (if TRANS = 'T' or 'C').   
  
      2. If FACT = 'N' or 'E', the LU decomposition is used to factor the   
         matrix A (after equilibration if FACT = 'E') as   
            A = P * L * U,   
         where P is a permutation matrix, L is a unit lower triangular   
         matrix, and U is upper triangular.   
  
      3. If some U(i,i)=0, so that U 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.   
  
      4. The system of equations is solved for X using the factored form   
         of A.   
  
      5. Iterative refinement is applied to improve the computed solution   
         matrix and calculate error bounds and backward error estimates   
         for it.   
  
      6. If equilibration was used, the matrix X is premultiplied by   
         diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so   
         that it solves the original system before equilibration.   
  
      Arguments   
      =========   
  
      FACT    (input) CHARACTER*1   
              Specifies whether or not the factored form of the matrix A is   
              supplied on entry, and if not, whether the matrix A should be   
              equilibrated before it is factored.   
              = 'F':  On entry, AF and IPIV contain the factored form of A.   
                      If EQUED is not 'N', the matrix A has been   
                      equilibrated with scaling factors given by R and C.   
                      A, AF, and IPIV are not modified.   
              = 'N':  The matrix A will be copied to AF and factored.   
              = 'E':  The matrix A will be equilibrated if necessary, then   
                      copied to AF and factored.   
  
      TRANS   (input) CHARACTER*1   
              Specifies the form of the system of equations:   
              = 'N':  A * X = B     (No transpose)   
              = 'T':  A**T * X = B  (Transpose)   
              = 'C':  A**H * X = B  (Transpose)   
  
      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/output) DOUBLE PRECISION array, dimension (LDA,N)   
              On entry, the N-by-N matrix A.  If FACT = 'F' and EQUED is   
              not 'N', then A must have been equilibrated by the scaling   
              factors in R and/or C.  A is not modified if FACT = 'F' or   
              'N', or if FACT = 'E' and EQUED = 'N' on exit.   
  
              On exit, if EQUED .ne. 'N', A is scaled as follows:   
              EQUED = 'R':  A := diag(R) * A   
              EQUED = 'C':  A := A * diag(C)   
              EQUED = 'B':  A := diag(R) * A * diag(C).   
  
      LDA     (input) INTEGER   
              The leading dimension of the array A.  LDA >= max(1,N).   
  
      AF      (input or output) DOUBLE PRECISION array, dimension (LDAF,N)   
              If FACT = 'F', then AF is an input argument and on entry   
              contains the factors L and U from the factorization   
              A = P*L*U as computed by DGETRF.  If EQUED .ne. 'N', then   
              AF is the factored form of the equilibrated matrix A.   
  
              If FACT = 'N', then AF is an output argument and on exit   
              returns the factors L and U from the factorization A = P*L*U   
              of the original matrix A.   
  
              If FACT = 'E', then AF is an output argument and on exit   
              returns the factors L and U from the factorization A = P*L*U   
              of the equilibrated matrix A (see the description of A for   
              the form of the equilibrated matrix).   
  
      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 the pivot indices from the factorization A = P*L*U   
              as computed by DGETRF; row i of the matrix was interchanged   
              with row IPIV(i).   
  
              If FACT = 'N', then IPIV is an output argument and on exit   
              contains the pivot indices from the factorization A = P*L*U   
              of the original matrix A.   
  
              If FACT = 'E', then IPIV is an output argument and on exit   
              contains the pivot indices from the factorization A = P*L*U   
              of the equilibrated matrix A.   
  
      EQUED   (input or output) CHARACTER*1   
              Specifies the form of equilibration that was done.   
              = 'N':  No equilibration (always true if FACT = 'N').   
              = 'R':  Row equilibration, i.e., A has been premultiplied by   
                      diag(R).   
              = 'C':  Column equilibration, i.e., A has been postmultiplied   
                      by diag(C).   
              = 'B':  Both row and column equilibration, i.e., A has been   
                      replaced by diag(R) * A * diag(C).   
              EQUED is an input argument if FACT = 'F'; otherwise, it is an   
              output argument.   
  
      R       (input or output) DOUBLE PRECISION array, dimension (N)   
              The row scale factors for A.  If EQUED = 'R' or 'B', A is   
              multiplied on the left by diag(R); if EQUED = 'N' or 'C', R   
              is not accessed.  R is an input argument if FACT = 'F';   
              otherwise, R is an output argument.  If FACT = 'F' and   
              EQUED = 'R' or 'B', each element of R must be positive.   
  
      C       (input or output) DOUBLE PRECISION array, dimension (N)   
              The column scale factors for A.  If EQUED = 'C' or 'B', A is   
              multiplied on the right by diag(C); if EQUED = 'N' or 'R', C   
              is not accessed.  C is an input argument if FACT = 'F';   
              otherwise, C is an output argument.  If FACT = 'F' and   
              EQUED = 'C' or 'B', each element of C must be positive.   
  
      B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)   
              On entry, the N-by-NRHS right hand side matrix B.   
              On exit,   
              if EQUED = 'N', B is not modified;   
              if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by   
              diag(R)*B;   
              if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is   
              overwritten by diag(C)*B.   
  
      LDB     (input) INTEGER   
              The leading dimension of the array B.  LDB >= max(1,N).   
  
      X       (output) DOUBLE PRECISION array, dimension (LDX,NRHS)   
              If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X   
              to the original system of equations.  Note that A and B are   
              modified on exit if EQUED .ne. 'N', and the solution to the   
              equilibrated system is inv(diag(C))*X if TRANS = 'N' and   
              EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'   
              and EQUED = 'R' or 'B'.   
  
      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 after equilibration (if done).  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) DOUBLE PRECISION array, dimension (4*N)   
              On exit, WORK(1) contains the reciprocal pivot growth   
              factor norm(A)/norm(U). The "max absolute element" norm is   
              used. If WORK(1) is much less than 1, then the stability   
              of the LU factorization of the (equilibrated) matrix A   
              could be poor. This also means that the solution X, condition   
              estimator RCOND, and forward error bound FERR could be   
              unreliable. If factorization fails with 0<INFO<=N, then   
              WORK(1) contains the reciprocal pivot growth factor for the   
              leading INFO columns of A.   
  
      IWORK   (workspace) INTEGER 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:  U(i,i) is exactly zero.  The factorization has   
                           been completed, but the factor U is exactly   
                           singular, so the solution and error bounds   
                           could not be computed. RCOND = 0 is returned.   
                    = N+1: U 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.   
  
      =====================================================================   
  
  
         Parameter adjustments */
      /* System generated locals */
      integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 
  	    x_offset, i__1, i__2;
      doublereal d__1, d__2;
      /* Local variables */
      static doublereal amax;
      static char norm[1];
      static integer i__, j;
      extern logical lsame_(char *, char *);
      static doublereal rcmin, rcmax, anorm;
      static logical equil;
      extern doublereal dlamch_(char *), dlange_(char *, integer *, 
  	    integer *, doublereal *, integer *, doublereal *);
      extern /* Subroutine */ int dlaqge_(integer *, integer *, doublereal *, 
  	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
  	     doublereal *, char *), dgecon_(char *, integer *, 
  	    doublereal *, integer *, doublereal *, doublereal *, doublereal *,
  	     integer *, integer *);
      static doublereal colcnd;
      static logical nofact;
      extern /* Subroutine */ int dgeequ_(integer *, integer *, doublereal *, 
  	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
  	     doublereal *, integer *), dgerfs_(char *, integer *, integer *, 
  	    doublereal *, integer *, doublereal *, integer *, integer *, 
  	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
  	    doublereal *, doublereal *, integer *, integer *), 
  	    dgetrf_(integer *, integer *, doublereal *, integer *, integer *, 
  	    integer *), dlacpy_(char *, integer *, integer *, doublereal *, 
  	    integer *, doublereal *, integer *), xerbla_(char *, 
  	    integer *);
      static doublereal bignum;
      extern doublereal dlantr_(char *, char *, char *, integer *, integer *, 
  	    doublereal *, integer *, doublereal *);
      static integer infequ;
      static logical colequ;
      extern /* Subroutine */ int dgetrs_(char *, integer *, integer *, 
  	    doublereal *, integer *, integer *, doublereal *, integer *, 
  	    integer *);
      static doublereal rowcnd;
      static logical notran;
      static doublereal smlnum;
      static logical rowequ;
      static doublereal rpvgrw;
  #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
  #define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1]
  
      a_dim1 = *lda;
      a_offset = 1 + a_dim1 * 1;
      a -= a_offset;
      af_dim1 = *ldaf;
      af_offset = 1 + af_dim1 * 1;
      af -= af_offset;
      --ipiv;
      --r__;
      --c__;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1 * 1;
      b -= b_offset;
      x_dim1 = *ldx;
      x_offset = 1 + x_dim1 * 1;
      x -= x_offset;
      --ferr;
      --berr;
      --work;
      --iwork;
  
      /* Function Body */
      *info = 0;
      nofact = lsame_(fact, "N");
      equil = lsame_(fact, "E");
      notran = lsame_(trans, "N");
      if (nofact || equil) {
  	*(unsigned char *)equed = 'N';
  	rowequ = FALSE_;
  	colequ = FALSE_;
      } else {
  	rowequ = lsame_(equed, "R") || lsame_(equed, 
  		"B");
  	colequ = lsame_(equed, "C") || lsame_(equed, 
  		"B");
  	smlnum = dlamch_("Safe minimum");
  	bignum = 1. / smlnum;
      }
  
  /*     Test the input parameters. */
  
      if (! nofact && ! equil && ! lsame_(fact, "F")) {
  	*info = -1;
      } else if (! notran && ! lsame_(trans, "T") && ! 
  	    lsame_(trans, "C")) {
  	*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 (lsame_(fact, "F") && ! (rowequ || colequ 
  	    || lsame_(equed, "N"))) {
  	*info = -10;
      } else {
  	if (rowequ) {
  	    rcmin = bignum;
  	    rcmax = 0.;
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  /* Computing MIN */
  		d__1 = rcmin, d__2 = r__[j];
  		rcmin = min(d__1,d__2);
  /* Computing MAX */
  		d__1 = rcmax, d__2 = r__[j];
  		rcmax = max(d__1,d__2);
  /* L10: */
  	    }
  	    if (rcmin <= 0.) {
  		*info = -11;
  	    } else if (*n > 0) {
  		rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
  	    } else {
  		rowcnd = 1.;
  	    }
  	}
  	if (colequ && *info == 0) {
  	    rcmin = bignum;
  	    rcmax = 0.;
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  /* Computing MIN */
  		d__1 = rcmin, d__2 = c__[j];
  		rcmin = min(d__1,d__2);
  /* Computing MAX */
  		d__1 = rcmax, d__2 = c__[j];
  		rcmax = max(d__1,d__2);
  /* L20: */
  	    }
  	    if (rcmin <= 0.) {
  		*info = -12;
  	    } else if (*n > 0) {
  		colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
  	    } else {
  		colcnd = 1.;
  	    }
  	}
  	if (*info == 0) {
  	    if (*ldb < max(1,*n)) {
  		*info = -14;
  	    } else if (*ldx < max(1,*n)) {
  		*info = -16;
  	    }
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DGESVX", &i__1);
  	return 0;
      }
  
      if (equil) {
  
  /*        Compute row and column scalings to equilibrate the matrix A. */
  
  	dgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, &
  		amax, &infequ);
  	if (infequ == 0) {
  
  /*           Equilibrate the matrix. */
  
  	    dlaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &
  		    colcnd, &amax, equed);
  	    rowequ = lsame_(equed, "R") || lsame_(equed,
  		     "B");
  	    colequ = lsame_(equed, "C") || lsame_(equed,
  		     "B");
  	}
      }
  
  /*     Scale the right hand side. */
  
      if (notran) {
  	if (rowequ) {
  	    i__1 = *nrhs;
  	    for (j = 1; j <= i__1; ++j) {
  		i__2 = *n;
  		for (i__ = 1; i__ <= i__2; ++i__) {
  		    b_ref(i__, j) = r__[i__] * b_ref(i__, j);
  /* L30: */
  		}
  /* L40: */
  	    }
  	}
      } else if (colequ) {
  	i__1 = *nrhs;
  	for (j = 1; j <= i__1; ++j) {
  	    i__2 = *n;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		b_ref(i__, j) = c__[i__] * b_ref(i__, j);
  /* L50: */
  	    }
  /* L60: */
  	}
      }
  
      if (nofact || equil) {
  
  /*        Compute the LU factorization of A. */
  
  	dlacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
  	dgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
  
  /*        Return if INFO is non-zero. */
  
  	if (*info != 0) {
  	    if (*info > 0) {
  
  /*              Compute the reciprocal pivot growth factor of the   
                  leading rank-deficient INFO columns of A. */
  
  		rpvgrw = dlantr_("M", "U", "N", info, info, &af[af_offset], 
  			ldaf, &work[1]);
  		if (rpvgrw == 0.) {
  		    rpvgrw = 1.;
  		} else {
  		    rpvgrw = dlange_("M", n, info, &a[a_offset], lda, &work[1]
  			    ) / rpvgrw;
  		}
  		work[1] = rpvgrw;
  		*rcond = 0.;
  	    }
  	    return 0;
  	}
      }
  
  /*     Compute the norm of the matrix A and the   
         reciprocal pivot growth factor RPVGRW. */
  
      if (notran) {
  	*(unsigned char *)norm = '1';
      } else {
  	*(unsigned char *)norm = 'I';
      }
      anorm = dlange_(norm, n, n, &a[a_offset], lda, &work[1]);
      rpvgrw = dlantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &work[1]);
      if (rpvgrw == 0.) {
  	rpvgrw = 1.;
      } else {
  	rpvgrw = dlange_("M", n, n, &a[a_offset], lda, &work[1]) / 
  		rpvgrw;
      }
  
  /*     Compute the reciprocal of the condition number of A. */
  
      dgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
  	     info);
  
  /*     Set INFO = N+1 if the matrix is singular to working precision. */
  
      if (*rcond < dlamch_("Epsilon")) {
  	*info = *n + 1;
      }
  
  /*     Compute the solution matrix X. */
  
      dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
      dgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx,
  	     info);
  
  /*     Use iterative refinement to improve the computed solution and   
         compute error bounds and backward error estimates for it. */
  
      dgerfs_(trans, 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], &iwork[1], info);
  
  /*     Transform the solution matrix X to a solution of the original   
         system. */
  
      if (notran) {
  	if (colequ) {
  	    i__1 = *nrhs;
  	    for (j = 1; j <= i__1; ++j) {
  		i__2 = *n;
  		for (i__ = 1; i__ <= i__2; ++i__) {
  		    x_ref(i__, j) = c__[i__] * x_ref(i__, j);
  /* L70: */
  		}
  /* L80: */
  	    }
  	    i__1 = *nrhs;
  	    for (j = 1; j <= i__1; ++j) {
  		ferr[j] /= colcnd;
  /* L90: */
  	    }
  	}
      } else if (rowequ) {
  	i__1 = *nrhs;
  	for (j = 1; j <= i__1; ++j) {
  	    i__2 = *n;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		x_ref(i__, j) = r__[i__] * x_ref(i__, j);
  /* L100: */
  	    }
  /* L110: */
  	}
  	i__1 = *nrhs;
  	for (j = 1; j <= i__1; ++j) {
  	    ferr[j] /= rowcnd;
  /* L120: */
  	}
      }
  
      work[1] = rpvgrw;
      return 0;
  
  /*     End of DGESVX */
  
  } /* dgesvx_ */
  
  #undef x_ref
  #undef b_ref
  
  
  