text: #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  
  /* Subroutine */ int sgbt05_(char *trans, integer *n, integer *kl, integer *
  	ku, integer *nrhs, real *ab, integer *ldab, real *b, integer *ldb, 
  	real *x, integer *ldx, real *xact, integer *ldxact, real *ferr, real *
  	berr, real *reslts)
  {
      /* System generated locals */
      integer ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, xact_dim1,
  	     xact_offset, i__1, i__2, i__3, i__4, i__5;
      real r__1, r__2, r__3;
  
      /* Local variables */
      integer i__, j, k, nz;
      real eps, tmp, diff, axbi;
      integer imax;
      real unfl, ovfl;
      extern logical lsame_(char *, char *);
      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 */
  /*  ======= */
  
  /*  SGBT05 tests the error bounds from iterative refinement for the */
  /*  computed solution to a system of equations op(A)*X = B, where A is a */
  /*  general band matrix of order n with kl subdiagonals and ku */
  /*  superdiagonals and op(A) = A or A**T, depending on TRANS. */
  
  /*  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 / ( NZ*EPS + (*) ), where */
  /*              (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) */
  /*              and NZ = max. number of nonzeros in any row of A, plus 1 */
  
  /*  Arguments */
  /*  ========= */
  
  /*  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  (Conjugate transpose = Transpose) */
  
  /*  N       (input) INTEGER */
  /*          The number of rows of the matrices X, B, and XACT, and the */
  /*          order of the matrix A.  N >= 0. */
  
  /*  KL      (input) INTEGER */
  /*          The number of subdiagonals within the band of A.  KL >= 0. */
  
  /*  KU      (input) INTEGER */
  /*          The number of superdiagonals within the band of A.  KU >= 0. */
  
  /*  NRHS    (input) INTEGER */
  /*          The number of columns of the matrices X, B, and XACT. */
  /*          NRHS >= 0. */
  
  /*  AB      (input) REAL array, dimension (LDAB,N) */
  /*          The original band matrix A, stored in rows 1 to KL+KU+1. */
  /*          The j-th column of A is stored in the j-th column of the */
  /*          array AB as follows: */
  /*          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). */
  
  /*  LDAB    (input) INTEGER */
  /*          The leading dimension of the array AB.  LDAB >= KL+KU+1. */
  
  /*  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 / ( NZ*EPS + (*) ) */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Quick exit if N = 0 or NRHS = 0. */
  
      /* Parameter adjustments */
      ab_dim1 = *ldab;
      ab_offset = 1 + ab_dim1;
      ab -= ab_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;
      notran = lsame_(trans, "N");
  /* Computing MIN */
      i__1 = *kl + *ku + 2, i__2 = *n + 1;
      nz = min(i__1,i__2);
  
  /*     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 / ( NZ*EPS + (*) ), where */
  /*     (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) */
  
      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 (notran) {
  /* Computing MAX */
  		i__3 = i__ - *kl;
  /* Computing MIN */
  		i__5 = i__ + *ku;
  		i__4 = min(i__5,*n);
  		for (j = max(i__3,1); j <= i__4; ++j) {
  		    tmp += (r__1 = ab[*ku + 1 + i__ - j + j * ab_dim1], dabs(
  			    r__1)) * (r__2 = x[j + k * x_dim1], dabs(r__2));
  /* L40: */
  		}
  	    } else {
  /* Computing MAX */
  		i__4 = i__ - *ku;
  /* Computing MIN */
  		i__5 = i__ + *kl;
  		i__3 = min(i__5,*n);
  		for (j = max(i__4,1); j <= i__3; ++j) {
  		    tmp += (r__1 = ab[*ku + 1 + j - i__ + i__ * ab_dim1], 
  			    dabs(r__1)) * (r__2 = x[j + k * x_dim1], dabs(
  			    r__2));
  /* L50: */
  		}
  	    }
  	    if (i__ == 1) {
  		axbi = tmp;
  	    } else {
  		axbi = dmin(axbi,tmp);
  	    }
  /* L60: */
  	}
  /* Computing MAX */
  	r__1 = axbi, r__2 = nz * unfl;
  	tmp = berr[k] / (nz * eps + nz * unfl / dmax(r__1,r__2));
  	if (k == 1) {
  	    reslts[2] = tmp;
  	} else {
  	    reslts[2] = dmax(reslts[2],tmp);
  	}
  /* L70: */
      }
  
      return 0;
  
  /*     End of SGBT05 */
  
  } /* sgbt05_ */
  