[] add metering mode to CLI

1 files changed, 1147 insertions, 0 deletions

diff --git a/contrib/libs/clapack/clatrs.c b/contrib/libs/clapack/clatrs.c
new file mode 100644
index 0000000000..3bf8994483
--- /dev/null
+++ b/contrib/libs/clapack/clatrs.c
@@ -0,0 +1,1147 @@
+/* clatrs.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 clatrs_(char *uplo, char *trans, char *diag, char *
+	normin, integer *n, complex *a, integer *lda, complex *x, real *scale, 
+	 real *cnorm, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+    real r__1, r__2, r__3, r__4;
+    complex q__1, q__2, q__3, q__4;
+
+    /* Builtin functions */
+    double r_imag(complex *);
+    void r_cnjg(complex *, complex *);
+
+    /* Local variables */
+    integer i__, j;
+    real xj, rec, tjj;
+    integer jinc;
+    real xbnd;
+    integer imax;
+    real tmax;
+    complex tjjs;
+    real xmax, grow;
+    extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
+	    *, complex *, integer *);
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
+    real tscal;
+    complex uscal;
+    integer jlast;
+    extern /* Complex */ VOID cdotu_(complex *, integer *, complex *, integer 
+	    *, complex *, integer *);
+    complex csumj;
+    extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, 
+	    integer *, complex *, integer *);
+    logical upper;
+    extern /* Subroutine */ int ctrsv_(char *, char *, char *, integer *, 
+	    complex *, integer *, complex *, integer *), slabad_(real *, real *);
+    extern integer icamax_(integer *, complex *, integer *);
+    extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
+    extern doublereal slamch_(char *);
+    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
+	    *), xerbla_(char *, integer *);
+    real bignum;
+    extern integer isamax_(integer *, real *, integer *);
+    extern doublereal scasum_(integer *, complex *, 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 */
+/*  ======= */
+
+/*  CLATRS solves one of the triangular systems */
+
+/*     A * x = s*b,  A**T * x = s*b,  or  A**H * x = s*b, */
+
+/*  with scaling to prevent overflow.  Here A is an upper or lower */
+/*  triangular matrix, A**T denotes the transpose of A, A**H denotes the */
+/*  conjugate 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 */
+/*  CTRSV 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**T * x = s*b  (Transpose) */
+/*          = 'C':  Solve A**H * x = s*b  (Conjugate 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. */
+
+/*  A       (input) COMPLEX 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). */
+
+/*  X       (input/output) COMPLEX 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,  A**T * x = s*b,  or  A**H * 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, CTRSV */
+/*  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 CTRSV 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**T *x = b  or */
+/*  A**H *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 CTRSV 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 .. */
+/*     .. */
+/*     .. Statement Functions .. */
+/*     .. */
+/*     .. Statement Function definitions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_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 (*lda < max(1,*n)) {
+	*info = -7;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CLATRS", &i__1);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+/*     Determine machine dependent parameters to control overflow. */
+
+    smlnum = slamch_("Safe minimum");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+    smlnum /= 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) {
+		i__2 = j - 1;
+		cnorm[j] = scasum_(&i__2, &a[j * a_dim1 + 1], &c__1);
+/* L10: */
+	    }
+	} else {
+
+/*           A is lower triangular. */
+
+	    i__1 = *n - 1;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *n - j;
+		cnorm[j] = scasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1);
+/* L20: */
+	    }
+	    cnorm[*n] = 0.f;
+	}
+    }
+
+/*     Scale the column norms by TSCAL if the maximum element in CNORM is */
+/*     greater than BIGNUM/2. */
+
+    imax = isamax_(n, &cnorm[1], &c__1);
+    tmax = cnorm[imax];
+    if (tmax <= bignum * .5f) {
+	tscal = 1.f;
+    } else {
+	tscal = .5f / (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 CTRSV can be used. */
+
+    xmax = 0.f;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MAX */
+	i__2 = j;
+	r__3 = xmax, r__4 = (r__1 = x[i__2].r / 2.f, dabs(r__1)) + (r__2 = 
+		r_imag(&x[j]) / 2.f, dabs(r__2));
+	xmax = dmax(r__3,r__4);
+/* L30: */
+    }
+    xbnd = xmax;
+
+    if (notran) {
+
+/*        Compute the growth in A * x = b. */
+
+	if (upper) {
+	    jfirst = *n;
+	    jlast = 1;
+	    jinc = -1;
+	} else {
+	    jfirst = 1;
+	    jlast = *n;
+	    jinc = 1;
+	}
+
+	if (tscal != 1.f) {
+	    grow = 0.f;
+	    goto L60;
+	}
+
+	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 = .5f / 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 L60;
+		}
+
+		i__3 = j + j * a_dim1;
+		tjjs.r = a[i__3].r, tjjs.i = a[i__3].i;
+		tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs), 
+			dabs(r__2));
+
+		if (tjj >= smlnum) {
+
+/*                 M(j) = G(j-1) / abs(A(j,j)) */
+
+/* Computing MIN */
+		    r__1 = xbnd, r__2 = dmin(1.f,tjj) * grow;
+		    xbnd = dmin(r__1,r__2);
+		} else {
+
+/*                 M(j) could overflow, set XBND to 0. */
+
+		    xbnd = 0.f;
+		}
+
+		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;
+		}
+/* L40: */
+	    }
+	    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 = .5f / 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 L60;
+		}
+
+/*              G(j) = G(j-1)*( 1 + CNORM(j) ) */
+
+		grow *= 1.f / (cnorm[j] + 1.f);
+/* L50: */
+	    }
+	}
+L60:
+
+	;
+    } else {
+
+/*        Compute the growth in A**T * x = b  or  A**H * x = b. */
+
+	if (upper) {
+	    jfirst = 1;
+	    jlast = *n;
+	    jinc = 1;
+	} else {
+	    jfirst = *n;
+	    jlast = 1;
+	    jinc = -1;
+	}
+
+	if (tscal != 1.f) {
+	    grow = 0.f;
+	    goto L90;
+	}
+
+	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 = .5f / 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 L90;
+		}
+
+/*              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);
+
+		i__3 = j + j * a_dim1;
+		tjjs.r = a[i__3].r, tjjs.i = a[i__3].i;
+		tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs), 
+			dabs(r__2));
+
+		if (tjj >= smlnum) {
+
+/*                 M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */
+
+		    if (xj > tjj) {
+			xbnd *= tjj / xj;
+		    }
+		} else {
+
+/*                 M(j) could overflow, set XBND to 0. */
+
+		    xbnd = 0.f;
+		}
+/* L70: */
+	    }
+	    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 = .5f / 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 L90;
+		}
+
+/*              G(j) = ( 1 + CNORM(j) )*G(j-1) */
+
+		xj = cnorm[j] + 1.f;
+		grow /= xj;
+/* L80: */
+	    }
+	}
+L90:
+	;
+    }
+
+    if (grow * tscal > smlnum) {
+
+/*        Use the Level 2 BLAS solve if the reciprocal of the bound on */
+/*        elements of X is not too small. */
+
+	ctrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1);
+    } else {
+
+/*        Use a Level 1 BLAS solve, scaling intermediate results. */
+
+	if (xmax > bignum * .5f) {
+
+/*           Scale X so that its components are less than or equal to */
+/*           BIGNUM in absolute value. */
+
+	    *scale = bignum * .5f / xmax;
+	    csscal_(n, scale, &x[1], &c__1);
+	    xmax = bignum;
+	} else {
+	    xmax *= 2.f;
+	}
+
+	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. */
+
+		i__3 = j;
+		xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]), 
+			dabs(r__2));
+		if (nounit) {
+		    i__3 = j + j * a_dim1;
+		    q__1.r = tscal * a[i__3].r, q__1.i = tscal * a[i__3].i;
+		    tjjs.r = q__1.r, tjjs.i = q__1.i;
+		} else {
+		    tjjs.r = tscal, tjjs.i = 0.f;
+		    if (tscal == 1.f) {
+			goto L105;
+		    }
+		}
+		tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs), 
+			dabs(r__2));
+		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;
+			    csscal_(n, &rec, &x[1], &c__1);
+			    *scale *= rec;
+			    xmax *= rec;
+			}
+		    }
+		    i__3 = j;
+		    cladiv_(&q__1, &x[j], &tjjs);
+		    x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    i__3 = j;
+		    xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
+			    ), dabs(r__2));
+		} 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];
+			}
+			csscal_(n, &rec, &x[1], &c__1);
+			*scale *= rec;
+			xmax *= rec;
+		    }
+		    i__3 = j;
+		    cladiv_(&q__1, &x[j], &tjjs);
+		    x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    i__3 = j;
+		    xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
+			    ), dabs(r__2));
+		} 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__) {
+			i__4 = i__;
+			x[i__4].r = 0.f, x[i__4].i = 0.f;
+/* L100: */
+		    }
+		    i__3 = j;
+		    x[i__3].r = 1.f, x[i__3].i = 0.f;
+		    xj = 1.f;
+		    *scale = 0.f;
+		    xmax = 0.f;
+		}
+L105:
+
+/*              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;
+			csscal_(n, &rec, &x[1], &c__1);
+			*scale *= rec;
+		    }
+		} else if (xj * cnorm[j] > bignum - xmax) {
+
+/*                 Scale x by 1/2. */
+
+		    csscal_(n, &c_b36, &x[1], &c__1);
+		    *scale *= .5f;
+		}
+
+		if (upper) {
+		    if (j > 1) {
+
+/*                    Compute the update */
+/*                       x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j) */
+
+			i__3 = j - 1;
+			i__4 = j;
+			q__2.r = -x[i__4].r, q__2.i = -x[i__4].i;
+			q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
+			caxpy_(&i__3, &q__1, &a[j * a_dim1 + 1], &c__1, &x[1], 
+				 &c__1);
+			i__3 = j - 1;
+			i__ = icamax_(&i__3, &x[1], &c__1);
+			i__3 = i__;
+			xmax = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = 
+				r_imag(&x[i__]), dabs(r__2));
+		    }
+		} else {
+		    if (j < *n) {
+
+/*                    Compute the update */
+/*                       x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j) */
+
+			i__3 = *n - j;
+			i__4 = j;
+			q__2.r = -x[i__4].r, q__2.i = -x[i__4].i;
+			q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
+			caxpy_(&i__3, &q__1, &a[j + 1 + j * a_dim1], &c__1, &
+				x[j + 1], &c__1);
+			i__3 = *n - j;
+			i__ = j + icamax_(&i__3, &x[j + 1], &c__1);
+			i__3 = i__;
+			xmax = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = 
+				r_imag(&x[i__]), dabs(r__2));
+		    }
+		}
+/* L110: */
+	    }
+
+	} else if (lsame_(trans, "T")) {
+
+/*           Solve A**T * 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 */
+
+		i__3 = j;
+		xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]), 
+			dabs(r__2));
+		uscal.r = tscal, uscal.i = 0.f;
+		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) {
+			i__3 = j + j * a_dim1;
+			q__1.r = tscal * a[i__3].r, q__1.i = tscal * a[i__3]
+				.i;
+			tjjs.r = q__1.r, tjjs.i = q__1.i;
+		    } else {
+			tjjs.r = tscal, tjjs.i = 0.f;
+		    }
+		    tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
+			     dabs(r__2));
+		    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);
+			cladiv_(&q__1, &uscal, &tjjs);
+			uscal.r = q__1.r, uscal.i = q__1.i;
+		    }
+		    if (rec < 1.f) {
+			csscal_(n, &rec, &x[1], &c__1);
+			*scale *= rec;
+			xmax *= rec;
+		    }
+		}
+
+		csumj.r = 0.f, csumj.i = 0.f;
+		if (uscal.r == 1.f && uscal.i == 0.f) {
+
+/*                 If the scaling needed for A in the dot product is 1, */
+/*                 call CDOTU to perform the dot product. */
+
+		    if (upper) {
+			i__3 = j - 1;
+			cdotu_(&q__1, &i__3, &a[j * a_dim1 + 1], &c__1, &x[1], 
+				 &c__1);
+			csumj.r = q__1.r, csumj.i = q__1.i;
+		    } else if (j < *n) {
+			i__3 = *n - j;
+			cdotu_(&q__1, &i__3, &a[j + 1 + j * a_dim1], &c__1, &
+				x[j + 1], &c__1);
+			csumj.r = q__1.r, csumj.i = q__1.i;
+		    }
+		} else {
+
+/*                 Otherwise, use in-line code for the dot product. */
+
+		    if (upper) {
+			i__3 = j - 1;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    i__4 = i__ + j * a_dim1;
+			    q__3.r = a[i__4].r * uscal.r - a[i__4].i * 
+				    uscal.i, q__3.i = a[i__4].r * uscal.i + a[
+				    i__4].i * uscal.r;
+			    i__5 = i__;
+			    q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i, 
+				    q__2.i = q__3.r * x[i__5].i + q__3.i * x[
+				    i__5].r;
+			    q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + 
+				    q__2.i;
+			    csumj.r = q__1.r, csumj.i = q__1.i;
+/* L120: */
+			}
+		    } else if (j < *n) {
+			i__3 = *n;
+			for (i__ = j + 1; i__ <= i__3; ++i__) {
+			    i__4 = i__ + j * a_dim1;
+			    q__3.r = a[i__4].r * uscal.r - a[i__4].i * 
+				    uscal.i, q__3.i = a[i__4].r * uscal.i + a[
+				    i__4].i * uscal.r;
+			    i__5 = i__;
+			    q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i, 
+				    q__2.i = q__3.r * x[i__5].i + q__3.i * x[
+				    i__5].r;
+			    q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + 
+				    q__2.i;
+			    csumj.r = q__1.r, csumj.i = q__1.i;
+/* L130: */
+			}
+		    }
+		}
+
+		q__1.r = tscal, q__1.i = 0.f;
+		if (uscal.r == q__1.r && uscal.i == q__1.i) {
+
+/*                 Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */
+/*                 was not used to scale the dotproduct. */
+
+		    i__3 = j;
+		    i__4 = j;
+		    q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i - 
+			    csumj.i;
+		    x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    i__3 = j;
+		    xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
+			    ), dabs(r__2));
+		    if (nounit) {
+			i__3 = j + j * a_dim1;
+			q__1.r = tscal * a[i__3].r, q__1.i = tscal * a[i__3]
+				.i;
+			tjjs.r = q__1.r, tjjs.i = q__1.i;
+		    } else {
+			tjjs.r = tscal, tjjs.i = 0.f;
+			if (tscal == 1.f) {
+			    goto L145;
+			}
+		    }
+
+/*                    Compute x(j) = x(j) / A(j,j), scaling if necessary. */
+
+		    tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
+			     dabs(r__2));
+		    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;
+				csscal_(n, &rec, &x[1], &c__1);
+				*scale *= rec;
+				xmax *= rec;
+			    }
+			}
+			i__3 = j;
+			cladiv_(&q__1, &x[j], &tjjs);
+			x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    } 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;
+			    csscal_(n, &rec, &x[1], &c__1);
+			    *scale *= rec;
+			    xmax *= rec;
+			}
+			i__3 = j;
+			cladiv_(&q__1, &x[j], &tjjs);
+			x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    } else {
+
+/*                       A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and */
+/*                       scale = 0 and compute a solution to A**T *x = 0. */
+
+			i__3 = *n;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    i__4 = i__;
+			    x[i__4].r = 0.f, x[i__4].i = 0.f;
+/* L140: */
+			}
+			i__3 = j;
+			x[i__3].r = 1.f, x[i__3].i = 0.f;
+			*scale = 0.f;
+			xmax = 0.f;
+		    }
+L145:
+		    ;
+		} else {
+
+/*                 Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */
+/*                 product has already been divided by 1/A(j,j). */
+
+		    i__3 = j;
+		    cladiv_(&q__2, &x[j], &tjjs);
+		    q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i;
+		    x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		}
+/* Computing MAX */
+		i__3 = j;
+		r__3 = xmax, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = 
+			r_imag(&x[j]), dabs(r__2));
+		xmax = dmax(r__3,r__4);
+/* L150: */
+	    }
+
+	} else {
+
+/*           Solve A**H * 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) - sum A(k,j)*x(k). */
+/*                                    k<>j */
+
+		i__3 = j;
+		xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]), 
+			dabs(r__2));
+		uscal.r = tscal, uscal.i = 0.f;
+		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) {
+			r_cnjg(&q__2, &a[j + j * a_dim1]);
+			q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
+			tjjs.r = q__1.r, tjjs.i = q__1.i;
+		    } else {
+			tjjs.r = tscal, tjjs.i = 0.f;
+		    }
+		    tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
+			     dabs(r__2));
+		    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);
+			cladiv_(&q__1, &uscal, &tjjs);
+			uscal.r = q__1.r, uscal.i = q__1.i;
+		    }
+		    if (rec < 1.f) {
+			csscal_(n, &rec, &x[1], &c__1);
+			*scale *= rec;
+			xmax *= rec;
+		    }
+		}
+
+		csumj.r = 0.f, csumj.i = 0.f;
+		if (uscal.r == 1.f && uscal.i == 0.f) {
+
+/*                 If the scaling needed for A in the dot product is 1, */
+/*                 call CDOTC to perform the dot product. */
+
+		    if (upper) {
+			i__3 = j - 1;
+			cdotc_(&q__1, &i__3, &a[j * a_dim1 + 1], &c__1, &x[1], 
+				 &c__1);
+			csumj.r = q__1.r, csumj.i = q__1.i;
+		    } else if (j < *n) {
+			i__3 = *n - j;
+			cdotc_(&q__1, &i__3, &a[j + 1 + j * a_dim1], &c__1, &
+				x[j + 1], &c__1);
+			csumj.r = q__1.r, csumj.i = q__1.i;
+		    }
+		} else {
+
+/*                 Otherwise, use in-line code for the dot product. */
+
+		    if (upper) {
+			i__3 = j - 1;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    r_cnjg(&q__4, &a[i__ + j * a_dim1]);
+			    q__3.r = q__4.r * uscal.r - q__4.i * uscal.i, 
+				    q__3.i = q__4.r * uscal.i + q__4.i * 
+				    uscal.r;
+			    i__4 = i__;
+			    q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, 
+				    q__2.i = q__3.r * x[i__4].i + q__3.i * x[
+				    i__4].r;
+			    q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + 
+				    q__2.i;
+			    csumj.r = q__1.r, csumj.i = q__1.i;
+/* L160: */
+			}
+		    } else if (j < *n) {
+			i__3 = *n;
+			for (i__ = j + 1; i__ <= i__3; ++i__) {
+			    r_cnjg(&q__4, &a[i__ + j * a_dim1]);
+			    q__3.r = q__4.r * uscal.r - q__4.i * uscal.i, 
+				    q__3.i = q__4.r * uscal.i + q__4.i * 
+				    uscal.r;
+			    i__4 = i__;
+			    q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, 
+				    q__2.i = q__3.r * x[i__4].i + q__3.i * x[
+				    i__4].r;
+			    q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + 
+				    q__2.i;
+			    csumj.r = q__1.r, csumj.i = q__1.i;
+/* L170: */
+			}
+		    }
+		}
+
+		q__1.r = tscal, q__1.i = 0.f;
+		if (uscal.r == q__1.r && uscal.i == q__1.i) {
+
+/*                 Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */
+/*                 was not used to scale the dotproduct. */
+
+		    i__3 = j;
+		    i__4 = j;
+		    q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i - 
+			    csumj.i;
+		    x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    i__3 = j;
+		    xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
+			    ), dabs(r__2));
+		    if (nounit) {
+			r_cnjg(&q__2, &a[j + j * a_dim1]);
+			q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
+			tjjs.r = q__1.r, tjjs.i = q__1.i;
+		    } else {
+			tjjs.r = tscal, tjjs.i = 0.f;
+			if (tscal == 1.f) {
+			    goto L185;
+			}
+		    }
+
+/*                    Compute x(j) = x(j) / A(j,j), scaling if necessary. */
+
+		    tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
+			     dabs(r__2));
+		    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;
+				csscal_(n, &rec, &x[1], &c__1);
+				*scale *= rec;
+				xmax *= rec;
+			    }
+			}
+			i__3 = j;
+			cladiv_(&q__1, &x[j], &tjjs);
+			x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    } 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;
+			    csscal_(n, &rec, &x[1], &c__1);
+			    *scale *= rec;
+			    xmax *= rec;
+			}
+			i__3 = j;
+			cladiv_(&q__1, &x[j], &tjjs);
+			x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		    } else {
+
+/*                       A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and */
+/*                       scale = 0 and compute a solution to A**H *x = 0. */
+
+			i__3 = *n;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    i__4 = i__;
+			    x[i__4].r = 0.f, x[i__4].i = 0.f;
+/* L180: */
+			}
+			i__3 = j;
+			x[i__3].r = 1.f, x[i__3].i = 0.f;
+			*scale = 0.f;
+			xmax = 0.f;
+		    }
+L185:
+		    ;
+		} else {
+
+/*                 Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */
+/*                 product has already been divided by 1/A(j,j). */
+
+		    i__3 = j;
+		    cladiv_(&q__2, &x[j], &tjjs);
+		    q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i;
+		    x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+		}
+/* Computing MAX */
+		i__3 = j;
+		r__3 = xmax, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = 
+			r_imag(&x[j]), dabs(r__2));
+		xmax = dmax(r__3,r__4);
+/* L190: */
+	    }
+	}
+	*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 CLATRS */
+
+} /* clatrs_ */