[] add metering mode to CLI

1 files changed, 576 insertions, 0 deletions

diff --git a/contrib/libs/clapack/zptrfs.c b/contrib/libs/clapack/zptrfs.c
new file mode 100644
index 0000000000..b57ae48d65
--- /dev/null
+++ b/contrib/libs/clapack/zptrfs.c
@@ -0,0 +1,576 @@
+/* zptrfs.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 doublecomplex c_b16 = {1.,0.};
+
+/* Subroutine */ int zptrfs_(char *uplo, integer *n, integer *nrhs, 
+	doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef, 
+	doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+	doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *
+	rwork, integer *info)
+{
+    /* System generated locals */
+    integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, 
+	    i__6;
+    doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10, 
+	    d__11, d__12;
+    doublecomplex z__1, z__2, z__3;
+
+    /* Builtin functions */
+    double d_imag(doublecomplex *);
+    void d_cnjg(doublecomplex *, doublecomplex *);
+    double z_abs(doublecomplex *);
+
+    /* Local variables */
+    integer i__, j;
+    doublereal s;
+    doublecomplex bi, cx, dx, ex;
+    integer ix, nz;
+    doublereal eps, safe1, safe2;
+    extern logical lsame_(char *, char *);
+    integer count;
+    logical upper;
+    extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, 
+	    doublecomplex *, integer *, doublecomplex *, integer *);
+    extern doublereal dlamch_(char *);
+    extern integer idamax_(integer *, doublereal *, integer *);
+    doublereal safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    doublereal lstres;
+    extern /* Subroutine */ int zpttrs_(char *, integer *, integer *, 
+	    doublereal *, doublecomplex *, doublecomplex *, integer *, 
+	    integer *);
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  ZPTRFS improves the computed solution to a system of linear */
+/*  equations when the coefficient matrix is Hermitian positive definite */
+/*  and tridiagonal, and provides error bounds and backward error */
+/*  estimates for the solution. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  UPLO    (input) CHARACTER*1 */
+/*          Specifies whether the superdiagonal or the subdiagonal of the */
+/*          tridiagonal matrix A is stored and the form of the */
+/*          factorization: */
+/*          = 'U':  E is the superdiagonal of A, and A = U**H*D*U; */
+/*          = 'L':  E is the subdiagonal of A, and A = L*D*L**H. */
+/*          (The two forms are equivalent if A is real.) */
+
+/*  N       (input) INTEGER */
+/*          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 matrix B.  NRHS >= 0. */
+
+/*  D       (input) DOUBLE PRECISION array, dimension (N) */
+/*          The n real diagonal elements of the tridiagonal matrix A. */
+
+/*  E       (input) COMPLEX*16 array, dimension (N-1) */
+/*          The (n-1) off-diagonal elements of the tridiagonal matrix A */
+/*          (see UPLO). */
+
+/*  DF      (input) DOUBLE PRECISION array, dimension (N) */
+/*          The n diagonal elements of the diagonal matrix D from */
+/*          the factorization computed by ZPTTRF. */
+
+/*  EF      (input) COMPLEX*16 array, dimension (N-1) */
+/*          The (n-1) off-diagonal elements of the unit bidiagonal */
+/*          factor U or L from the factorization computed by ZPTTRF */
+/*          (see UPLO). */
+
+/*  B       (input) COMPLEX*16 array, dimension (LDB,NRHS) */
+/*          The right hand side matrix B. */
+
+/*  LDB     (input) INTEGER */
+/*          The leading dimension of the array B.  LDB >= max(1,N). */
+
+/*  X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS) */
+/*          On entry, the solution matrix X, as computed by ZPTTRS. */
+/*          On exit, the improved solution matrix X. */
+
+/*  LDX     (input) INTEGER */
+/*          The leading dimension of the array X.  LDX >= max(1,N). */
+
+/*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
+/*          The 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). */
+
+/*  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) COMPLEX*16 array, dimension (N) */
+
+/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */
+
+/*  INFO    (output) INTEGER */
+/*          = 0:  successful exit */
+/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
+
+/*  Internal Parameters */
+/*  =================== */
+
+/*  ITMAX is the maximum number of steps of iterative refinement. */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Statement Functions .. */
+/*     .. */
+/*     .. Statement Function definitions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    --d__;
+    --e;
+    --df;
+    --ef;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    x_dim1 = *ldx;
+    x_offset = 1 + x_dim1;
+    x -= x_offset;
+    --ferr;
+    --berr;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    upper = lsame_(uplo, "U");
+    if (! upper && ! lsame_(uplo, "L")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*nrhs < 0) {
+	*info = -3;
+    } else if (*ldb < max(1,*n)) {
+	*info = -9;
+    } else if (*ldx < max(1,*n)) {
+	*info = -11;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("ZPTRFS", &i__1);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0 || *nrhs == 0) {
+	i__1 = *nrhs;
+	for (j = 1; j <= i__1; ++j) {
+	    ferr[j] = 0.;
+	    berr[j] = 0.;
+/* L10: */
+	}
+	return 0;
+    }
+
+/*     NZ = maximum number of nonzero elements in each row of A, plus 1 */
+
+    nz = 4;
+    eps = dlamch_("Epsilon");
+    safmin = dlamch_("Safe minimum");
+    safe1 = nz * safmin;
+    safe2 = safe1 / eps;
+
+/*     Do for each right hand side */
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+
+	count = 1;
+	lstres = 3.;
+L20:
+
+/*        Loop until stopping criterion is satisfied. */
+
+/*        Compute residual R = B - A * X.  Also compute */
+/*        abs(A)*abs(x) + abs(b) for use in the backward error bound. */
+
+	if (upper) {
+	    if (*n == 1) {
+		i__2 = j * b_dim1 + 1;
+		bi.r = b[i__2].r, bi.i = b[i__2].i;
+		i__2 = j * x_dim1 + 1;
+		z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
+		dx.r = z__1.r, dx.i = z__1.i;
+		z__1.r = bi.r - dx.r, z__1.i = bi.i - dx.i;
+		work[1].r = z__1.r, work[1].i = z__1.i;
+		rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), 
+			abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = 
+			d_imag(&dx), abs(d__4)));
+	    } else {
+		i__2 = j * b_dim1 + 1;
+		bi.r = b[i__2].r, bi.i = b[i__2].i;
+		i__2 = j * x_dim1 + 1;
+		z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
+		dx.r = z__1.r, dx.i = z__1.i;
+		i__2 = j * x_dim1 + 2;
+		z__1.r = e[1].r * x[i__2].r - e[1].i * x[i__2].i, z__1.i = e[
+			1].r * x[i__2].i + e[1].i * x[i__2].r;
+		ex.r = z__1.r, ex.i = z__1.i;
+		z__2.r = bi.r - dx.r, z__2.i = bi.i - dx.i;
+		z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
+		work[1].r = z__1.r, work[1].i = z__1.i;
+		i__2 = j * x_dim1 + 2;
+		rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), 
+			abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = 
+			d_imag(&dx), abs(d__4))) + ((d__5 = e[1].r, abs(d__5))
+			 + (d__6 = d_imag(&e[1]), abs(d__6))) * ((d__7 = x[
+			i__2].r, abs(d__7)) + (d__8 = d_imag(&x[j * x_dim1 + 
+			2]), abs(d__8)));
+		i__2 = *n - 1;
+		for (i__ = 2; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * b_dim1;
+		    bi.r = b[i__3].r, bi.i = b[i__3].i;
+		    d_cnjg(&z__2, &e[i__ - 1]);
+		    i__3 = i__ - 1 + j * x_dim1;
+		    z__1.r = z__2.r * x[i__3].r - z__2.i * x[i__3].i, z__1.i =
+			     z__2.r * x[i__3].i + z__2.i * x[i__3].r;
+		    cx.r = z__1.r, cx.i = z__1.i;
+		    i__3 = i__;
+		    i__4 = i__ + j * x_dim1;
+		    z__1.r = d__[i__3] * x[i__4].r, z__1.i = d__[i__3] * x[
+			    i__4].i;
+		    dx.r = z__1.r, dx.i = z__1.i;
+		    i__3 = i__;
+		    i__4 = i__ + 1 + j * x_dim1;
+		    z__1.r = e[i__3].r * x[i__4].r - e[i__3].i * x[i__4].i, 
+			    z__1.i = e[i__3].r * x[i__4].i + e[i__3].i * x[
+			    i__4].r;
+		    ex.r = z__1.r, ex.i = z__1.i;
+		    i__3 = i__;
+		    z__3.r = bi.r - cx.r, z__3.i = bi.i - cx.i;
+		    z__2.r = z__3.r - dx.r, z__2.i = z__3.i - dx.i;
+		    z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
+		    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
+		    i__3 = i__ - 1;
+		    i__4 = i__ - 1 + j * x_dim1;
+		    i__5 = i__;
+		    i__6 = i__ + 1 + j * x_dim1;
+		    rwork[i__] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&
+			    bi), abs(d__2)) + ((d__3 = e[i__3].r, abs(d__3)) 
+			    + (d__4 = d_imag(&e[i__ - 1]), abs(d__4))) * ((
+			    d__5 = x[i__4].r, abs(d__5)) + (d__6 = d_imag(&x[
+			    i__ - 1 + j * x_dim1]), abs(d__6))) + ((d__7 = 
+			    dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8))
+			    ) + ((d__9 = e[i__5].r, abs(d__9)) + (d__10 = 
+			    d_imag(&e[i__]), abs(d__10))) * ((d__11 = x[i__6]
+			    .r, abs(d__11)) + (d__12 = d_imag(&x[i__ + 1 + j *
+			     x_dim1]), abs(d__12)));
+/* L30: */
+		}
+		i__2 = *n + j * b_dim1;
+		bi.r = b[i__2].r, bi.i = b[i__2].i;
+		d_cnjg(&z__2, &e[*n - 1]);
+		i__2 = *n - 1 + j * x_dim1;
+		z__1.r = z__2.r * x[i__2].r - z__2.i * x[i__2].i, z__1.i = 
+			z__2.r * x[i__2].i + z__2.i * x[i__2].r;
+		cx.r = z__1.r, cx.i = z__1.i;
+		i__2 = *n;
+		i__3 = *n + j * x_dim1;
+		z__1.r = d__[i__2] * x[i__3].r, z__1.i = d__[i__2] * x[i__3]
+			.i;
+		dx.r = z__1.r, dx.i = z__1.i;
+		i__2 = *n;
+		z__2.r = bi.r - cx.r, z__2.i = bi.i - cx.i;
+		z__1.r = z__2.r - dx.r, z__1.i = z__2.i - dx.i;
+		work[i__2].r = z__1.r, work[i__2].i = z__1.i;
+		i__2 = *n - 1;
+		i__3 = *n - 1 + j * x_dim1;
+		rwork[*n] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), 
+			abs(d__2)) + ((d__3 = e[i__2].r, abs(d__3)) + (d__4 = 
+			d_imag(&e[*n - 1]), abs(d__4))) * ((d__5 = x[i__3].r, 
+			abs(d__5)) + (d__6 = d_imag(&x[*n - 1 + j * x_dim1]), 
+			abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 = 
+			d_imag(&dx), abs(d__8)));
+	    }
+	} else {
+	    if (*n == 1) {
+		i__2 = j * b_dim1 + 1;
+		bi.r = b[i__2].r, bi.i = b[i__2].i;
+		i__2 = j * x_dim1 + 1;
+		z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
+		dx.r = z__1.r, dx.i = z__1.i;
+		z__1.r = bi.r - dx.r, z__1.i = bi.i - dx.i;
+		work[1].r = z__1.r, work[1].i = z__1.i;
+		rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), 
+			abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = 
+			d_imag(&dx), abs(d__4)));
+	    } else {
+		i__2 = j * b_dim1 + 1;
+		bi.r = b[i__2].r, bi.i = b[i__2].i;
+		i__2 = j * x_dim1 + 1;
+		z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
+		dx.r = z__1.r, dx.i = z__1.i;
+		d_cnjg(&z__2, &e[1]);
+		i__2 = j * x_dim1 + 2;
+		z__1.r = z__2.r * x[i__2].r - z__2.i * x[i__2].i, z__1.i = 
+			z__2.r * x[i__2].i + z__2.i * x[i__2].r;
+		ex.r = z__1.r, ex.i = z__1.i;
+		z__2.r = bi.r - dx.r, z__2.i = bi.i - dx.i;
+		z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
+		work[1].r = z__1.r, work[1].i = z__1.i;
+		i__2 = j * x_dim1 + 2;
+		rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), 
+			abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = 
+			d_imag(&dx), abs(d__4))) + ((d__5 = e[1].r, abs(d__5))
+			 + (d__6 = d_imag(&e[1]), abs(d__6))) * ((d__7 = x[
+			i__2].r, abs(d__7)) + (d__8 = d_imag(&x[j * x_dim1 + 
+			2]), abs(d__8)));
+		i__2 = *n - 1;
+		for (i__ = 2; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * b_dim1;
+		    bi.r = b[i__3].r, bi.i = b[i__3].i;
+		    i__3 = i__ - 1;
+		    i__4 = i__ - 1 + j * x_dim1;
+		    z__1.r = e[i__3].r * x[i__4].r - e[i__3].i * x[i__4].i, 
+			    z__1.i = e[i__3].r * x[i__4].i + e[i__3].i * x[
+			    i__4].r;
+		    cx.r = z__1.r, cx.i = z__1.i;
+		    i__3 = i__;
+		    i__4 = i__ + j * x_dim1;
+		    z__1.r = d__[i__3] * x[i__4].r, z__1.i = d__[i__3] * x[
+			    i__4].i;
+		    dx.r = z__1.r, dx.i = z__1.i;
+		    d_cnjg(&z__2, &e[i__]);
+		    i__3 = i__ + 1 + j * x_dim1;
+		    z__1.r = z__2.r * x[i__3].r - z__2.i * x[i__3].i, z__1.i =
+			     z__2.r * x[i__3].i + z__2.i * x[i__3].r;
+		    ex.r = z__1.r, ex.i = z__1.i;
+		    i__3 = i__;
+		    z__3.r = bi.r - cx.r, z__3.i = bi.i - cx.i;
+		    z__2.r = z__3.r - dx.r, z__2.i = z__3.i - dx.i;
+		    z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
+		    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
+		    i__3 = i__ - 1;
+		    i__4 = i__ - 1 + j * x_dim1;
+		    i__5 = i__;
+		    i__6 = i__ + 1 + j * x_dim1;
+		    rwork[i__] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&
+			    bi), abs(d__2)) + ((d__3 = e[i__3].r, abs(d__3)) 
+			    + (d__4 = d_imag(&e[i__ - 1]), abs(d__4))) * ((
+			    d__5 = x[i__4].r, abs(d__5)) + (d__6 = d_imag(&x[
+			    i__ - 1 + j * x_dim1]), abs(d__6))) + ((d__7 = 
+			    dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8))
+			    ) + ((d__9 = e[i__5].r, abs(d__9)) + (d__10 = 
+			    d_imag(&e[i__]), abs(d__10))) * ((d__11 = x[i__6]
+			    .r, abs(d__11)) + (d__12 = d_imag(&x[i__ + 1 + j *
+			     x_dim1]), abs(d__12)));
+/* L40: */
+		}
+		i__2 = *n + j * b_dim1;
+		bi.r = b[i__2].r, bi.i = b[i__2].i;
+		i__2 = *n - 1;
+		i__3 = *n - 1 + j * x_dim1;
+		z__1.r = e[i__2].r * x[i__3].r - e[i__2].i * x[i__3].i, 
+			z__1.i = e[i__2].r * x[i__3].i + e[i__2].i * x[i__3]
+			.r;
+		cx.r = z__1.r, cx.i = z__1.i;
+		i__2 = *n;
+		i__3 = *n + j * x_dim1;
+		z__1.r = d__[i__2] * x[i__3].r, z__1.i = d__[i__2] * x[i__3]
+			.i;
+		dx.r = z__1.r, dx.i = z__1.i;
+		i__2 = *n;
+		z__2.r = bi.r - cx.r, z__2.i = bi.i - cx.i;
+		z__1.r = z__2.r - dx.r, z__1.i = z__2.i - dx.i;
+		work[i__2].r = z__1.r, work[i__2].i = z__1.i;
+		i__2 = *n - 1;
+		i__3 = *n - 1 + j * x_dim1;
+		rwork[*n] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), 
+			abs(d__2)) + ((d__3 = e[i__2].r, abs(d__3)) + (d__4 = 
+			d_imag(&e[*n - 1]), abs(d__4))) * ((d__5 = x[i__3].r, 
+			abs(d__5)) + (d__6 = d_imag(&x[*n - 1 + j * x_dim1]), 
+			abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 = 
+			d_imag(&dx), abs(d__8)));
+	    }
+	}
+
+/*        Compute componentwise relative backward error from formula */
+
+/*        max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
+
+/*        where abs(Z) is the componentwise absolute value of the matrix */
+/*        or vector Z.  If the i-th component of the denominator is less */
+/*        than SAFE2, then SAFE1 is added to the i-th components of the */
+/*        numerator and denominator before dividing. */
+
+	s = 0.;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+/* Computing MAX */
+		i__3 = i__;
+		d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2))) / rwork[i__];
+		s = max(d__3,d__4);
+	    } else {
+/* Computing MAX */
+		i__3 = i__;
+		d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__] 
+			+ safe1);
+		s = max(d__3,d__4);
+	    }
+/* L50: */
+	}
+	berr[j] = s;
+
+/*        Test stopping criterion. Continue iterating if */
+/*           1) The residual BERR(J) is larger than machine epsilon, and */
+/*           2) BERR(J) decreased by at least a factor of 2 during the */
+/*              last iteration, and */
+/*           3) At most ITMAX iterations tried. */
+
+	if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) {
+
+/*           Update solution and try again. */
+
+	    zpttrs_(uplo, n, &c__1, &df[1], &ef[1], &work[1], n, info);
+	    zaxpy_(n, &c_b16, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
+	    lstres = berr[j];
+	    ++count;
+	    goto L20;
+	}
+
+/*        Bound error from formula */
+
+/*        norm(X - XTRUE) / norm(X) .le. FERR = */
+/*        norm( abs(inv(A))* */
+/*           ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
+
+/*        where */
+/*          norm(Z) is the magnitude of the largest component of Z */
+/*          inv(A) is the inverse of A */
+/*          abs(Z) is the componentwise absolute value of the matrix or */
+/*             vector Z */
+/*          NZ is the maximum number of nonzeros in any row of A, plus 1 */
+/*          EPS is machine epsilon */
+
+/*        The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */
+/*        is incremented by SAFE1 if the i-th component of */
+/*        abs(A)*abs(X) + abs(B) is less than SAFE2. */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+		i__3 = i__;
+		rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
+			;
+	    } else {
+		i__3 = i__;
+		rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
+			 + safe1;
+	    }
+/* L60: */
+	}
+	ix = idamax_(n, &rwork[1], &c__1);
+	ferr[j] = rwork[ix];
+
+/*        Estimate the norm of inv(A). */
+
+/*        Solve M(A) * x = e, where M(A) = (m(i,j)) is given by */
+
+/*           m(i,j) =  abs(A(i,j)), i = j, */
+/*           m(i,j) = -abs(A(i,j)), i .ne. j, */
+
+/*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'. */
+
+/*        Solve M(L) * x = e. */
+
+	rwork[1] = 1.;
+	i__2 = *n;
+	for (i__ = 2; i__ <= i__2; ++i__) {
+	    rwork[i__] = rwork[i__ - 1] * z_abs(&ef[i__ - 1]) + 1.;
+/* L70: */
+	}
+
+/*        Solve D * M(L)' * x = b. */
+
+	rwork[*n] /= df[*n];
+	for (i__ = *n - 1; i__ >= 1; --i__) {
+	    rwork[i__] = rwork[i__] / df[i__] + rwork[i__ + 1] * z_abs(&ef[
+		    i__]);
+/* L80: */
+	}
+
+/*        Compute norm(inv(A)) = max(x(i)), 1<=i<=n. */
+
+	ix = idamax_(n, &rwork[1], &c__1);
+	ferr[j] *= (d__1 = rwork[ix], abs(d__1));
+
+/*        Normalize error. */
+
+	lstres = 0.;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    d__1 = lstres, d__2 = z_abs(&x[i__ + j * x_dim1]);
+	    lstres = max(d__1,d__2);
+/* L90: */
+	}
+	if (lstres != 0.) {
+	    ferr[j] /= lstres;
+	}
+
+/* L100: */
+    }
+
+    return 0;
+
+/*     End of ZPTRFS */
+
+} /* zptrfs_ */