[] add metering mode to CLI

1 files changed, 849 insertions, 0 deletions

diff --git a/contrib/libs/clapack/slatbs.c b/contrib/libs/clapack/slatbs.c
new file mode 100644
index 0000000000..9a3e867a71
--- /dev/null
+++ b/contrib/libs/clapack/slatbs.c
@@ -0,0 +1,849 @@
+/* slatbs.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 real c_b36 = .5f;
+
+/* Subroutine */ int slatbs_(char *uplo, char *trans, char *diag, char *
+	normin, integer *n, integer *kd, real *ab, integer *ldab, real *x, 
+	real *scale, real *cnorm, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
+    real r__1, r__2, r__3;
+
+    /* Local variables */
+    integer i__, j;
+    real xj, rec, tjj;
+    integer jinc, jlen;
+    real xbnd;
+    integer imax;
+    real tmax, tjjs;
+    extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
+    real xmax, grow, sumj;
+    integer maind;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
+    real tscal, uscal;
+    integer jlast;
+    extern doublereal sasum_(integer *, real *, integer *);
+    logical upper;
+    extern /* Subroutine */ int stbsv_(char *, char *, char *, integer *, 
+	    integer *, real *, integer *, real *, integer *), saxpy_(integer *, real *, real *, integer *, real *, 
+	    integer *);
+    extern doublereal slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    real bignum;
+    extern integer isamax_(integer *, real *, integer *);
+    logical notran;
+    integer jfirst;
+    real smlnum;
+    logical nounit;
+
+
+/*  -- LAPACK auxiliary routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  SLATBS solves one of the triangular systems */
+
+/*     A *x = s*b  or  A'*x = s*b */
+
+/*  with scaling to prevent overflow, where A is an upper or lower */
+/*  triangular band matrix.  Here A' denotes the transpose of A, x and b */
+/*  are n-element vectors, and s is a scaling factor, usually less than */
+/*  or equal to 1, chosen so that the components of x will be less than */
+/*  the overflow threshold.  If the unscaled problem will not cause */
+/*  overflow, the Level 2 BLAS routine STBSV is called.  If the matrix A */
+/*  is singular (A(j,j) = 0 for some j), then s is set to 0 and a */
+/*  non-trivial solution to A*x = 0 is returned. */
+
+/*  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 operation applied to A. */
+/*          = 'N':  Solve A * x = s*b  (No transpose) */
+/*          = 'T':  Solve A'* x = s*b  (Transpose) */
+/*          = 'C':  Solve A'* x = s*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 */
+
+/*  NORMIN  (input) CHARACTER*1 */
+/*          Specifies whether CNORM has been set or not. */
+/*          = 'Y':  CNORM contains the column norms on entry */
+/*          = 'N':  CNORM is not set on entry.  On exit, the norms will */
+/*                  be computed and stored in CNORM. */
+
+/*  N       (input) INTEGER */
+/*          The order of the matrix A.  N >= 0. */
+
+/*  KD      (input) INTEGER */
+/*          The number of subdiagonals or superdiagonals in the */
+/*          triangular matrix A.  KD >= 0. */
+
+/*  AB      (input) REAL array, dimension (LDAB,N) */
+/*          The upper or lower triangular band matrix A, stored in the */
+/*          first KD+1 rows of the array. The j-th column of A is stored */
+/*          in the j-th column of the array AB as follows: */
+/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
+/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */
+
+/*  LDAB    (input) INTEGER */
+/*          The leading dimension of the array AB.  LDAB >= KD+1. */
+
+/*  X       (input/output) REAL array, dimension (N) */
+/*          On entry, the right hand side b of the triangular system. */
+/*          On exit, X is overwritten by the solution vector x. */
+
+/*  SCALE   (output) REAL */
+/*          The scaling factor s for the triangular system */
+/*             A * x = s*b  or  A'* x = s*b. */
+/*          If SCALE = 0, the matrix A is singular or badly scaled, and */
+/*          the vector x is an exact or approximate solution to A*x = 0. */
+
+/*  CNORM   (input or output) REAL array, dimension (N) */
+
+/*          If NORMIN = 'Y', CNORM is an input argument and CNORM(j) */
+/*          contains the norm of the off-diagonal part of the j-th column */
+/*          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal */
+/*          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) */
+/*          must be greater than or equal to the 1-norm. */
+
+/*          If NORMIN = 'N', CNORM is an output argument and CNORM(j) */
+/*          returns the 1-norm of the offdiagonal part of the j-th column */
+/*          of A. */
+
+/*  INFO    (output) INTEGER */
+/*          = 0:  successful exit */
+/*          < 0:  if INFO = -k, the k-th argument had an illegal value */
+
+/*  Further Details */
+/*  ======= ======= */
+
+/*  A rough bound on x is computed; if that is less than overflow, STBSV */
+/*  is called, otherwise, specific code is used which checks for possible */
+/*  overflow or divide-by-zero at every operation. */
+
+/*  A columnwise scheme is used for solving A*x = b.  The basic algorithm */
+/*  if A is lower triangular is */
+
+/*       x[1:n] := b[1:n] */
+/*       for j = 1, ..., n */
+/*            x(j) := x(j) / A(j,j) */
+/*            x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] */
+/*       end */
+
+/*  Define bounds on the components of x after j iterations of the loop: */
+/*     M(j) = bound on x[1:j] */
+/*     G(j) = bound on x[j+1:n] */
+/*  Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}. */
+
+/*  Then for iteration j+1 we have */
+/*     M(j+1) <= G(j) / | A(j+1,j+1) | */
+/*     G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | */
+/*            <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) */
+
+/*  where CNORM(j+1) is greater than or equal to the infinity-norm of */
+/*  column j+1 of A, not counting the diagonal.  Hence */
+
+/*     G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) */
+/*                  1<=i<=j */
+/*  and */
+
+/*     |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) */
+/*                                   1<=i< j */
+
+/*  Since |x(j)| <= M(j), we use the Level 2 BLAS routine STBSV if the */
+/*  reciprocal of the largest M(j), j=1,..,n, is larger than */
+/*  max(underflow, 1/overflow). */
+
+/*  The bound on x(j) is also used to determine when a step in the */
+/*  columnwise method can be performed without fear of overflow.  If */
+/*  the computed bound is greater than a large constant, x is scaled to */
+/*  prevent overflow, but if the bound overflows, x is set to 0, x(j) to */
+/*  1, and scale to 0, and a non-trivial solution to A*x = 0 is found. */
+
+/*  Similarly, a row-wise scheme is used to solve A'*x = b.  The basic */
+/*  algorithm for A upper triangular is */
+
+/*       for j = 1, ..., n */
+/*            x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j) */
+/*       end */
+
+/*  We simultaneously compute two bounds */
+/*       G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j */
+/*       M(j) = bound on x(i), 1<=i<=j */
+
+/*  The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we */
+/*  add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. */
+/*  Then the bound on x(j) is */
+
+/*       M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | */
+
+/*            <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) */
+/*                      1<=i<=j */
+
+/*  and we can safely call STBSV if 1/M(n) and 1/G(n) are both greater */
+/*  than max(underflow, 1/overflow). */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1;
+    ab -= ab_offset;
+    --x;
+    --cnorm;
+
+    /* Function Body */
+    *info = 0;
+    upper = lsame_(uplo, "U");
+    notran = lsame_(trans, "N");
+    nounit = lsame_(diag, "N");
+
+/*     Test the input parameters. */
+
+    if (! upper && ! lsame_(uplo, "L")) {
+	*info = -1;
+    } else if (! notran && ! lsame_(trans, "T") && ! 
+	    lsame_(trans, "C")) {
+	*info = -2;
+    } else if (! nounit && ! lsame_(diag, "U")) {
+	*info = -3;
+    } else if (! lsame_(normin, "Y") && ! lsame_(normin, 
+	     "N")) {
+	*info = -4;
+    } else if (*n < 0) {
+	*info = -5;
+    } else if (*kd < 0) {
+	*info = -6;
+    } else if (*ldab < *kd + 1) {
+	*info = -8;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("SLATBS", &i__1);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+/*     Determine machine dependent parameters to control overflow. */
+
+    smlnum = slamch_("Safe minimum") / slamch_("Precision");
+    bignum = 1.f / smlnum;
+    *scale = 1.f;
+
+    if (lsame_(normin, "N")) {
+
+/*        Compute the 1-norm of each column, not including the diagonal. */
+
+	if (upper) {
+
+/*           A is upper triangular. */
+
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+		i__2 = *kd, i__3 = j - 1;
+		jlen = min(i__2,i__3);
+		cnorm[j] = sasum_(&jlen, &ab[*kd + 1 - jlen + j * ab_dim1], &
+			c__1);
+/* L10: */
+	    }
+	} else {
+
+/*           A is lower triangular. */
+
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+		i__2 = *kd, i__3 = *n - j;
+		jlen = min(i__2,i__3);
+		if (jlen > 0) {
+		    cnorm[j] = sasum_(&jlen, &ab[j * ab_dim1 + 2], &c__1);
+		} else {
+		    cnorm[j] = 0.f;
+		}
+/* L20: */
+	    }
+	}
+    }
+
+/*     Scale the column norms by TSCAL if the maximum element in CNORM is */
+/*     greater than BIGNUM. */
+
+    imax = isamax_(n, &cnorm[1], &c__1);
+    tmax = cnorm[imax];
+    if (tmax <= bignum) {
+	tscal = 1.f;
+    } else {
+	tscal = 1.f / (smlnum * tmax);
+	sscal_(n, &tscal, &cnorm[1], &c__1);
+    }
+
+/*     Compute a bound on the computed solution vector to see if the */
+/*     Level 2 BLAS routine STBSV can be used. */
+
+    j = isamax_(n, &x[1], &c__1);
+    xmax = (r__1 = x[j], dabs(r__1));
+    xbnd = xmax;
+    if (notran) {
+
+/*        Compute the growth in A * x = b. */
+
+	if (upper) {
+	    jfirst = *n;
+	    jlast = 1;
+	    jinc = -1;
+	    maind = *kd + 1;
+	} else {
+	    jfirst = 1;
+	    jlast = *n;
+	    jinc = 1;
+	    maind = 1;
+	}
+
+	if (tscal != 1.f) {
+	    grow = 0.f;
+	    goto L50;
+	}
+
+	if (nounit) {
+
+/*           A is non-unit triangular. */
+
+/*           Compute GROW = 1/G(j) and XBND = 1/M(j). */
+/*           Initially, G(0) = max{x(i), i=1,...,n}. */
+
+	    grow = 1.f / dmax(xbnd,smlnum);
+	    xbnd = grow;
+	    i__1 = jlast;
+	    i__2 = jinc;
+	    for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
+
+/*              Exit the loop if the growth factor is too small. */
+
+		if (grow <= smlnum) {
+		    goto L50;
+		}
+
+/*              M(j) = G(j-1) / abs(A(j,j)) */
+
+		tjj = (r__1 = ab[maind + j * ab_dim1], dabs(r__1));
+/* Computing MIN */
+		r__1 = xbnd, r__2 = dmin(1.f,tjj) * grow;
+		xbnd = dmin(r__1,r__2);
+		if (tjj + cnorm[j] >= smlnum) {
+
+/*                 G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */
+
+		    grow *= tjj / (tjj + cnorm[j]);
+		} else {
+
+/*                 G(j) could overflow, set GROW to 0. */
+
+		    grow = 0.f;
+		}
+/* L30: */
+	    }
+	    grow = xbnd;
+	} else {
+
+/*           A is unit triangular. */
+
+/*           Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */
+
+/* Computing MIN */
+	    r__1 = 1.f, r__2 = 1.f / dmax(xbnd,smlnum);
+	    grow = dmin(r__1,r__2);
+	    i__2 = jlast;
+	    i__1 = jinc;
+	    for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
+
+/*              Exit the loop if the growth factor is too small. */
+
+		if (grow <= smlnum) {
+		    goto L50;
+		}
+
+/*              G(j) = G(j-1)*( 1 + CNORM(j) ) */
+
+		grow *= 1.f / (cnorm[j] + 1.f);
+/* L40: */
+	    }
+	}
+L50:
+
+	;
+    } else {
+
+/*        Compute the growth in A' * x = b. */
+
+	if (upper) {
+	    jfirst = 1;
+	    jlast = *n;
+	    jinc = 1;
+	    maind = *kd + 1;
+	} else {
+	    jfirst = *n;
+	    jlast = 1;
+	    jinc = -1;
+	    maind = 1;
+	}
+
+	if (tscal != 1.f) {
+	    grow = 0.f;
+	    goto L80;
+	}
+
+	if (nounit) {
+
+/*           A is non-unit triangular. */
+
+/*           Compute GROW = 1/G(j) and XBND = 1/M(j). */
+/*           Initially, M(0) = max{x(i), i=1,...,n}. */
+
+	    grow = 1.f / dmax(xbnd,smlnum);
+	    xbnd = grow;
+	    i__1 = jlast;
+	    i__2 = jinc;
+	    for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
+
+/*              Exit the loop if the growth factor is too small. */
+
+		if (grow <= smlnum) {
+		    goto L80;
+		}
+
+/*              G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */
+
+		xj = cnorm[j] + 1.f;
+/* Computing MIN */
+		r__1 = grow, r__2 = xbnd / xj;
+		grow = dmin(r__1,r__2);
+
+/*              M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */
+
+		tjj = (r__1 = ab[maind + j * ab_dim1], dabs(r__1));
+		if (xj > tjj) {
+		    xbnd *= tjj / xj;
+		}
+/* L60: */
+	    }
+	    grow = dmin(grow,xbnd);
+	} else {
+
+/*           A is unit triangular. */
+
+/*           Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */
+
+/* Computing MIN */
+	    r__1 = 1.f, r__2 = 1.f / dmax(xbnd,smlnum);
+	    grow = dmin(r__1,r__2);
+	    i__2 = jlast;
+	    i__1 = jinc;
+	    for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
+
+/*              Exit the loop if the growth factor is too small. */
+
+		if (grow <= smlnum) {
+		    goto L80;
+		}
+
+/*              G(j) = ( 1 + CNORM(j) )*G(j-1) */
+
+		xj = cnorm[j] + 1.f;
+		grow /= xj;
+/* L70: */
+	    }
+	}
+L80:
+	;
+    }
+
+    if (grow * tscal > smlnum) {
+
+/*        Use the Level 2 BLAS solve if the reciprocal of the bound on */
+/*        elements of X is not too small. */
+
+	stbsv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &x[1], &c__1);
+    } else {
+
+/*        Use a Level 1 BLAS solve, scaling intermediate results. */
+
+	if (xmax > bignum) {
+
+/*           Scale X so that its components are less than or equal to */
+/*           BIGNUM in absolute value. */
+
+	    *scale = bignum / xmax;
+	    sscal_(n, scale, &x[1], &c__1);
+	    xmax = bignum;
+	}
+
+	if (notran) {
+
+/*           Solve A * x = b */
+
+	    i__1 = jlast;
+	    i__2 = jinc;
+	    for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
+
+/*              Compute x(j) = b(j) / A(j,j), scaling x if necessary. */
+
+		xj = (r__1 = x[j], dabs(r__1));
+		if (nounit) {
+		    tjjs = ab[maind + j * ab_dim1] * tscal;
+		} else {
+		    tjjs = tscal;
+		    if (tscal == 1.f) {
+			goto L95;
+		    }
+		}
+		tjj = dabs(tjjs);
+		if (tjj > smlnum) {
+
+/*                    abs(A(j,j)) > SMLNUM: */
+
+		    if (tjj < 1.f) {
+			if (xj > tjj * bignum) {
+
+/*                          Scale x by 1/b(j). */
+
+			    rec = 1.f / xj;
+			    sscal_(n, &rec, &x[1], &c__1);
+			    *scale *= rec;
+			    xmax *= rec;
+			}
+		    }
+		    x[j] /= tjjs;
+		    xj = (r__1 = x[j], dabs(r__1));
+		} else if (tjj > 0.f) {
+
+/*                    0 < abs(A(j,j)) <= SMLNUM: */
+
+		    if (xj > tjj * bignum) {
+
+/*                       Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */
+/*                       to avoid overflow when dividing by A(j,j). */
+
+			rec = tjj * bignum / xj;
+			if (cnorm[j] > 1.f) {
+
+/*                          Scale by 1/CNORM(j) to avoid overflow when */
+/*                          multiplying x(j) times column j. */
+
+			    rec /= cnorm[j];
+			}
+			sscal_(n, &rec, &x[1], &c__1);
+			*scale *= rec;
+			xmax *= rec;
+		    }
+		    x[j] /= tjjs;
+		    xj = (r__1 = x[j], dabs(r__1));
+		} else {
+
+/*                    A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and */
+/*                    scale = 0, and compute a solution to A*x = 0. */
+
+		    i__3 = *n;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			x[i__] = 0.f;
+/* L90: */
+		    }
+		    x[j] = 1.f;
+		    xj = 1.f;
+		    *scale = 0.f;
+		    xmax = 0.f;
+		}
+L95:
+
+/*              Scale x if necessary to avoid overflow when adding a */
+/*              multiple of column j of A. */
+
+		if (xj > 1.f) {
+		    rec = 1.f / xj;
+		    if (cnorm[j] > (bignum - xmax) * rec) {
+
+/*                    Scale x by 1/(2*abs(x(j))). */
+
+			rec *= .5f;
+			sscal_(n, &rec, &x[1], &c__1);
+			*scale *= rec;
+		    }
+		} else if (xj * cnorm[j] > bignum - xmax) {
+
+/*                 Scale x by 1/2. */
+
+		    sscal_(n, &c_b36, &x[1], &c__1);
+		    *scale *= .5f;
+		}
+
+		if (upper) {
+		    if (j > 1) {
+
+/*                    Compute the update */
+/*                       x(max(1,j-kd):j-1) := x(max(1,j-kd):j-1) - */
+/*                                             x(j)* A(max(1,j-kd):j-1,j) */
+
+/* Computing MIN */
+			i__3 = *kd, i__4 = j - 1;
+			jlen = min(i__3,i__4);
+			r__1 = -x[j] * tscal;
+			saxpy_(&jlen, &r__1, &ab[*kd + 1 - jlen + j * ab_dim1]
+, &c__1, &x[j - jlen], &c__1);
+			i__3 = j - 1;
+			i__ = isamax_(&i__3, &x[1], &c__1);
+			xmax = (r__1 = x[i__], dabs(r__1));
+		    }
+		} else if (j < *n) {
+
+/*                 Compute the update */
+/*                    x(j+1:min(j+kd,n)) := x(j+1:min(j+kd,n)) - */
+/*                                          x(j) * A(j+1:min(j+kd,n),j) */
+
+/* Computing MIN */
+		    i__3 = *kd, i__4 = *n - j;
+		    jlen = min(i__3,i__4);
+		    if (jlen > 0) {
+			r__1 = -x[j] * tscal;
+			saxpy_(&jlen, &r__1, &ab[j * ab_dim1 + 2], &c__1, &x[
+				j + 1], &c__1);
+		    }
+		    i__3 = *n - j;
+		    i__ = j + isamax_(&i__3, &x[j + 1], &c__1);
+		    xmax = (r__1 = x[i__], dabs(r__1));
+		}
+/* L100: */
+	    }
+
+	} else {
+
+/*           Solve A' * x = b */
+
+	    i__2 = jlast;
+	    i__1 = jinc;
+	    for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
+
+/*              Compute x(j) = b(j) - sum A(k,j)*x(k). */
+/*                                    k<>j */
+
+		xj = (r__1 = x[j], dabs(r__1));
+		uscal = tscal;
+		rec = 1.f / dmax(xmax,1.f);
+		if (cnorm[j] > (bignum - xj) * rec) {
+
+/*                 If x(j) could overflow, scale x by 1/(2*XMAX). */
+
+		    rec *= .5f;
+		    if (nounit) {
+			tjjs = ab[maind + j * ab_dim1] * tscal;
+		    } else {
+			tjjs = tscal;
+		    }
+		    tjj = dabs(tjjs);
+		    if (tjj > 1.f) {
+
+/*                       Divide by A(j,j) when scaling x if A(j,j) > 1. */
+
+/* Computing MIN */
+			r__1 = 1.f, r__2 = rec * tjj;
+			rec = dmin(r__1,r__2);
+			uscal /= tjjs;
+		    }
+		    if (rec < 1.f) {
+			sscal_(n, &rec, &x[1], &c__1);
+			*scale *= rec;
+			xmax *= rec;
+		    }
+		}
+
+		sumj = 0.f;
+		if (uscal == 1.f) {
+
+/*                 If the scaling needed for A in the dot product is 1, */
+/*                 call SDOT to perform the dot product. */
+
+		    if (upper) {
+/* Computing MIN */
+			i__3 = *kd, i__4 = j - 1;
+			jlen = min(i__3,i__4);
+			sumj = sdot_(&jlen, &ab[*kd + 1 - jlen + j * ab_dim1], 
+				 &c__1, &x[j - jlen], &c__1);
+		    } else {
+/* Computing MIN */
+			i__3 = *kd, i__4 = *n - j;
+			jlen = min(i__3,i__4);
+			if (jlen > 0) {
+			    sumj = sdot_(&jlen, &ab[j * ab_dim1 + 2], &c__1, &
+				    x[j + 1], &c__1);
+			}
+		    }
+		} else {
+
+/*                 Otherwise, use in-line code for the dot product. */
+
+		    if (upper) {
+/* Computing MIN */
+			i__3 = *kd, i__4 = j - 1;
+			jlen = min(i__3,i__4);
+			i__3 = jlen;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    sumj += ab[*kd + i__ - jlen + j * ab_dim1] * 
+				    uscal * x[j - jlen - 1 + i__];
+/* L110: */
+			}
+		    } else {
+/* Computing MIN */
+			i__3 = *kd, i__4 = *n - j;
+			jlen = min(i__3,i__4);
+			i__3 = jlen;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    sumj += ab[i__ + 1 + j * ab_dim1] * uscal * x[j + 
+				    i__];
+/* L120: */
+			}
+		    }
+		}
+
+		if (uscal == tscal) {
+
+/*                 Compute x(j) := ( x(j) - sumj ) / A(j,j) if 1/A(j,j) */
+/*                 was not used to scale the dotproduct. */
+
+		    x[j] -= sumj;
+		    xj = (r__1 = x[j], dabs(r__1));
+		    if (nounit) {
+
+/*                    Compute x(j) = x(j) / A(j,j), scaling if necessary. */
+
+			tjjs = ab[maind + j * ab_dim1] * tscal;
+		    } else {
+			tjjs = tscal;
+			if (tscal == 1.f) {
+			    goto L135;
+			}
+		    }
+		    tjj = dabs(tjjs);
+		    if (tjj > smlnum) {
+
+/*                       abs(A(j,j)) > SMLNUM: */
+
+			if (tjj < 1.f) {
+			    if (xj > tjj * bignum) {
+
+/*                             Scale X by 1/abs(x(j)). */
+
+				rec = 1.f / xj;
+				sscal_(n, &rec, &x[1], &c__1);
+				*scale *= rec;
+				xmax *= rec;
+			    }
+			}
+			x[j] /= tjjs;
+		    } else if (tjj > 0.f) {
+
+/*                       0 < abs(A(j,j)) <= SMLNUM: */
+
+			if (xj > tjj * bignum) {
+
+/*                          Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
+
+			    rec = tjj * bignum / xj;
+			    sscal_(n, &rec, &x[1], &c__1);
+			    *scale *= rec;
+			    xmax *= rec;
+			}
+			x[j] /= tjjs;
+		    } else {
+
+/*                       A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and */
+/*                       scale = 0, and compute a solution to A'*x = 0. */
+
+			i__3 = *n;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    x[i__] = 0.f;
+/* L130: */
+			}
+			x[j] = 1.f;
+			*scale = 0.f;
+			xmax = 0.f;
+		    }
+L135:
+		    ;
+		} else {
+
+/*                 Compute x(j) := x(j) / A(j,j) - sumj if the dot */
+/*                 product has already been divided by 1/A(j,j). */
+
+		    x[j] = x[j] / tjjs - sumj;
+		}
+/* Computing MAX */
+		r__2 = xmax, r__3 = (r__1 = x[j], dabs(r__1));
+		xmax = dmax(r__2,r__3);
+/* L140: */
+	    }
+	}
+	*scale /= tscal;
+    }
+
+/*     Scale the column norms by 1/TSCAL for return. */
+
+    if (tscal != 1.f) {
+	r__1 = 1.f / tscal;
+	sscal_(n, &r__1, &cnorm[1], &c__1);
+    }
+
+    return 0;
+
+/*     End of SLATBS */
+
+} /* slatbs_ */