text: /* strt05.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;
  
  /* Subroutine */ int strt05_(char *uplo, char *trans, char *diag, integer *n, 
  	integer *nrhs, real *a, integer *lda, real *b, integer *ldb, real *x, 
  	integer *ldx, real *xact, integer *ldxact, real *ferr, real *berr, 
  	real *reslts)
  {
      /* System generated locals */
      integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, xact_dim1, 
  	    xact_offset, i__1, i__2, i__3;
      real r__1, r__2, r__3;
  
      /* Local variables */
      integer i__, j, k, ifu;
      real eps, tmp, diff, axbi;
      integer imax;
      real unfl, ovfl;
      logical unit;
      extern logical lsame_(char *, char *);
      logical upper;
      real xnorm;
      extern doublereal slamch_(char *);
      real errbnd;
      extern integer isamax_(integer *, real *, integer *);
      logical notran;
  
  
  /*  -- LAPACK test routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  STRT05 tests the error bounds from iterative refinement for the */
  /*  computed solution to a system of equations A*X = B, where A is a */
  /*  triangular n by n matrix. */
  
  /*  RESLTS(1) = test of the error bound */
  /*            = norm(X - XACT) / ( norm(X) * FERR ) */
  
  /*  A large value is returned if this ratio is not less than one. */
  
  /*  RESLTS(2) = residual from the iterative refinement routine */
  /*            = the maximum of BERR / ( (n+1)*EPS + (*) ), where */
  /*              (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) */
  
  /*  Arguments */
  /*  ========= */
  
  /*  UPLO    (input) CHARACTER*1 */
  /*          Specifies whether the matrix A is upper or lower triangular. */
  /*          = 'U':  Upper triangular */
  /*          = 'L':  Lower triangular */
  
  /*  TRANS   (input) CHARACTER*1 */
  /*          Specifies the form of the system of equations. */
  /*          = 'N':  A * X = B  (No transpose) */
  /*          = 'T':  A'* X = B  (Transpose) */
  /*          = 'C':  A'* X = B  (Conjugate transpose = Transpose) */
  
  /*  DIAG    (input) CHARACTER*1 */
  /*          Specifies whether or not the matrix A is unit triangular. */
  /*          = 'N':  Non-unit triangular */
  /*          = 'U':  Unit triangular */
  
  /*  N       (input) INTEGER */
  /*          The number of rows of the matrices X, B, and XACT, and the */
  /*          order of the matrix A.  N >= 0. */
  
  /*  NRHS    (input) INTEGER */
  /*          The number of columns of the matrices X, B, and XACT. */
  /*          NRHS >= 0. */
  
  /*  A       (input) REAL array, dimension (LDA,N) */
  /*          The triangular matrix A.  If UPLO = 'U', the leading n by n */
  /*          upper triangular part of the array A contains the upper */
  /*          triangular matrix, and the strictly lower triangular part of */
  /*          A is not referenced.  If UPLO = 'L', the leading n by n lower */
  /*          triangular part of the array A contains the lower triangular */
  /*          matrix, and the strictly upper triangular part of A is not */
  /*          referenced.  If DIAG = 'U', the diagonal elements of A are */
  /*          also not referenced and are assumed to be 1. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A.  LDA >= max(1,N). */
  
  /*  B       (input) REAL array, dimension (LDB,NRHS) */
  /*          The right hand side vectors for the system of linear */
  /*          equations. */
  
  /*  LDB     (input) INTEGER */
  /*          The leading dimension of the array B.  LDB >= max(1,N). */
  
  /*  X       (input) REAL array, dimension (LDX,NRHS) */
  /*          The computed solution vectors.  Each vector is stored as a */
  /*          column of the matrix X. */
  
  /*  LDX     (input) INTEGER */
  /*          The leading dimension of the array X.  LDX >= max(1,N). */
  
  /*  XACT    (input) REAL array, dimension (LDX,NRHS) */
  /*          The exact solution vectors.  Each vector is stored as a */
  /*          column of the matrix XACT. */
  
  /*  LDXACT  (input) INTEGER */
  /*          The leading dimension of the array XACT.  LDXACT >= max(1,N). */
  
  /*  FERR    (input) REAL array, dimension (NRHS) */
  /*          The estimated forward error bounds for each solution vector */
  /*          X.  If XTRUE is the true solution, FERR bounds the magnitude */
  /*          of the largest entry in (X - XTRUE) divided by the magnitude */
  /*          of the largest entry in X. */
  
  /*  BERR    (input) REAL array, dimension (NRHS) */
  /*          The componentwise relative backward error of each solution */
  /*          vector (i.e., the smallest relative change in any entry of A */
  /*          or B that makes X an exact solution). */
  
  /*  RESLTS  (output) REAL array, dimension (2) */
  /*          The maximum over the NRHS solution vectors of the ratios: */
  /*          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) */
  /*          RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Quick exit if N = 0 or NRHS = 0. */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1;
      b -= b_offset;
      x_dim1 = *ldx;
      x_offset = 1 + x_dim1;
      x -= x_offset;
      xact_dim1 = *ldxact;
      xact_offset = 1 + xact_dim1;
      xact -= xact_offset;
      --ferr;
      --berr;
      --reslts;
  
      /* Function Body */
      if (*n <= 0 || *nrhs <= 0) {
  	reslts[1] = 0.f;
  	reslts[2] = 0.f;
  	return 0;
      }
  
      eps = slamch_("Epsilon");
      unfl = slamch_("Safe minimum");
      ovfl = 1.f / unfl;
      upper = lsame_(uplo, "U");
      notran = lsame_(trans, "N");
      unit = lsame_(diag, "U");
  
  /*     Test 1:  Compute the maximum of */
  /*        norm(X - XACT) / ( norm(X) * FERR ) */
  /*     over all the vectors X and XACT using the infinity-norm. */
  
      errbnd = 0.f;
      i__1 = *nrhs;
      for (j = 1; j <= i__1; ++j) {
  	imax = isamax_(n, &x[j * x_dim1 + 1], &c__1);
  /* Computing MAX */
  	r__2 = (r__1 = x[imax + j * x_dim1], dabs(r__1));
  	xnorm = dmax(r__2,unfl);
  	diff = 0.f;
  	i__2 = *n;
  	for (i__ = 1; i__ <= i__2; ++i__) {
  /* Computing MAX */
  	    r__2 = diff, r__3 = (r__1 = x[i__ + j * x_dim1] - xact[i__ + j * 
  		    xact_dim1], dabs(r__1));
  	    diff = dmax(r__2,r__3);
  /* L10: */
  	}
  
  	if (xnorm > 1.f) {
  	    goto L20;
  	} else if (diff <= ovfl * xnorm) {
  	    goto L20;
  	} else {
  	    errbnd = 1.f / eps;
  	    goto L30;
  	}
  
  L20:
  	if (diff / xnorm <= ferr[j]) {
  /* Computing MAX */
  	    r__1 = errbnd, r__2 = diff / xnorm / ferr[j];
  	    errbnd = dmax(r__1,r__2);
  	} else {
  	    errbnd = 1.f / eps;
  	}
  L30:
  	;
      }
      reslts[1] = errbnd;
  
  /*     Test 2:  Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where */
  /*     (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) */
  
      ifu = 0;
      if (unit) {
  	ifu = 1;
      }
      i__1 = *nrhs;
      for (k = 1; k <= i__1; ++k) {
  	i__2 = *n;
  	for (i__ = 1; i__ <= i__2; ++i__) {
  	    tmp = (r__1 = b[i__ + k * b_dim1], dabs(r__1));
  	    if (upper) {
  		if (! notran) {
  		    i__3 = i__ - ifu;
  		    for (j = 1; j <= i__3; ++j) {
  			tmp += (r__1 = a[j + i__ * a_dim1], dabs(r__1)) * (
  				r__2 = x[j + k * x_dim1], dabs(r__2));
  /* L40: */
  		    }
  		    if (unit) {
  			tmp += (r__1 = x[i__ + k * x_dim1], dabs(r__1));
  		    }
  		} else {
  		    if (unit) {
  			tmp += (r__1 = x[i__ + k * x_dim1], dabs(r__1));
  		    }
  		    i__3 = *n;
  		    for (j = i__ + ifu; j <= i__3; ++j) {
  			tmp += (r__1 = a[i__ + j * a_dim1], dabs(r__1)) * (
  				r__2 = x[j + k * x_dim1], dabs(r__2));
  /* L50: */
  		    }
  		}
  	    } else {
  		if (notran) {
  		    i__3 = i__ - ifu;
  		    for (j = 1; j <= i__3; ++j) {
  			tmp += (r__1 = a[i__ + j * a_dim1], dabs(r__1)) * (
  				r__2 = x[j + k * x_dim1], dabs(r__2));
  /* L60: */
  		    }
  		    if (unit) {
  			tmp += (r__1 = x[i__ + k * x_dim1], dabs(r__1));
  		    }
  		} else {
  		    if (unit) {
  			tmp += (r__1 = x[i__ + k * x_dim1], dabs(r__1));
  		    }
  		    i__3 = *n;
  		    for (j = i__ + ifu; j <= i__3; ++j) {
  			tmp += (r__1 = a[j + i__ * a_dim1], dabs(r__1)) * (
  				r__2 = x[j + k * x_dim1], dabs(r__2));
  /* L70: */
  		    }
  		}
  	    }
  	    if (i__ == 1) {
  		axbi = tmp;
  	    } else {
  		axbi = dmin(axbi,tmp);
  	    }
  /* L80: */
  	}
  /* Computing MAX */
  	r__1 = axbi, r__2 = (*n + 1) * unfl;
  	tmp = berr[k] / ((*n + 1) * eps + (*n + 1) * unfl / dmax(r__1,r__2));
  	if (k == 1) {
  	    reslts[2] = tmp;
  	} else {
  	    reslts[2] = dmax(reslts[2],tmp);
  	}
  /* L90: */
      }
  
      return 0;
  
  /*     End of STRT05 */
  
  } /* strt05_ */
  