[] add metering mode to CLI

1 files changed, 492 insertions, 0 deletions

diff --git a/contrib/libs/clapack/strrfs.c b/contrib/libs/clapack/strrfs.c
new file mode 100644
index 0000000000..b914b0ec17
--- /dev/null
+++ b/contrib/libs/clapack/strrfs.c
@@ -0,0 +1,492 @@
+/* strrfs.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_b19 = -1.f;
+
+/* Subroutine */ int strrfs_(char *uplo, char *trans, char *diag, integer *n, 
+	integer *nrhs, real *a, integer *lda, real *b, integer *ldb, real *x, 
+	integer *ldx, real *ferr, real *berr, real *work, integer *iwork, 
+	integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, 
+	    i__3;
+    real r__1, r__2, r__3;
+
+    /* Local variables */
+    integer i__, j, k;
+    real s, xk;
+    integer nz;
+    real eps;
+    integer kase;
+    real safe1, safe2;
+    extern logical lsame_(char *, char *);
+    integer isave[3];
+    logical upper;
+    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
+	    integer *), saxpy_(integer *, real *, real *, integer *, real *, 
+	    integer *), strmv_(char *, char *, char *, integer *, real *, 
+	    integer *, real *, integer *), strsv_(
+	    char *, char *, char *, integer *, real *, integer *, real *, 
+	    integer *), slacn2_(integer *, real *, 
+	    real *, integer *, real *, integer *, integer *);
+    extern doublereal slamch_(char *);
+    real safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    logical notran;
+    char transt[1];
+    logical nounit;
+    real lstres;
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH. */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  STRRFS provides error bounds and backward error estimates for the */
+/*  solution to a system of linear equations with a triangular */
+/*  coefficient matrix. */
+
+/*  The solution matrix X must be computed by STRTRS or some other */
+/*  means before entering this routine.  STRRFS does not do iterative */
+/*  refinement because doing so cannot improve the backward error. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  UPLO    (input) CHARACTER*1 */
+/*          = 'U':  A is upper triangular; */
+/*          = 'L':  A is lower triangular. */
+
+/*  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) */
+
+/*  DIAG    (input) CHARACTER*1 */
+/*          = 'N':  A is non-unit triangular; */
+/*          = 'U':  A is unit triangular. */
+
+/*  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 matrices B and X.  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 matrix B. */
+
+/*  LDB     (input) INTEGER */
+/*          The leading dimension of the array B.  LDB >= max(1,N). */
+
+/*  X       (input) REAL array, dimension (LDX,NRHS) */
+/*          The solution matrix X. */
+
+/*  LDX     (input) INTEGER */
+/*          The leading dimension of the array X.  LDX >= max(1,N). */
+
+/*  FERR    (output) REAL array, dimension (NRHS) */
+/*          The estimated 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).  The estimate is as reliable as */
+/*          the estimate for RCOND, and is almost always a slight */
+/*          overestimate of the true error. */
+
+/*  BERR    (output) REAL 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) REAL array, dimension (3*N) */
+
+/*  IWORK   (workspace) INTEGER array, dimension (N) */
+
+/*  INFO    (output) INTEGER */
+/*          = 0:  successful exit */
+/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Test the input parameters. */
+
+    /* 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;
+    --ferr;
+    --berr;
+    --work;
+    --iwork;
+
+    /* Function Body */
+    *info = 0;
+    upper = lsame_(uplo, "U");
+    notran = lsame_(trans, "N");
+    nounit = lsame_(diag, "N");
+
+    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 (*n < 0) {
+	*info = -4;
+    } else if (*nrhs < 0) {
+	*info = -5;
+    } else if (*lda < max(1,*n)) {
+	*info = -7;
+    } else if (*ldb < max(1,*n)) {
+	*info = -9;
+    } else if (*ldx < max(1,*n)) {
+	*info = -11;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("STRRFS", &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.f;
+	    berr[j] = 0.f;
+/* L10: */
+	}
+	return 0;
+    }
+
+    if (notran) {
+	*(unsigned char *)transt = 'T';
+    } else {
+	*(unsigned char *)transt = 'N';
+    }
+
+/*     NZ = maximum number of nonzero elements in each row of A, plus 1 */
+
+    nz = *n + 1;
+    eps = slamch_("Epsilon");
+    safmin = slamch_("Safe minimum");
+    safe1 = nz * safmin;
+    safe2 = safe1 / eps;
+
+/*     Do for each right hand side */
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+
+/*        Compute residual R = B - op(A) * X, */
+/*        where op(A) = A or A', depending on TRANS. */
+
+	scopy_(n, &x[j * x_dim1 + 1], &c__1, &work[*n + 1], &c__1);
+	strmv_(uplo, trans, diag, n, &a[a_offset], lda, &work[*n + 1], &c__1);
+	saxpy_(n, &c_b19, &b[j * b_dim1 + 1], &c__1, &work[*n + 1], &c__1);
+
+/*        Compute componentwise relative backward error from formula */
+
+/*        max(i) ( abs(R(i)) / ( abs(op(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. */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    work[i__] = (r__1 = b[i__ + j * b_dim1], dabs(r__1));
+/* L20: */
+	}
+
+	if (notran) {
+
+/*           Compute abs(A)*abs(X) + abs(B). */
+
+	    if (upper) {
+		if (nounit) {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			xk = (r__1 = x[k + j * x_dim1], dabs(r__1));
+			i__3 = k;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    work[i__] += (r__1 = a[i__ + k * a_dim1], dabs(
+				    r__1)) * xk;
+/* L30: */
+			}
+/* L40: */
+		    }
+		} else {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			xk = (r__1 = x[k + j * x_dim1], dabs(r__1));
+			i__3 = k - 1;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    work[i__] += (r__1 = a[i__ + k * a_dim1], dabs(
+				    r__1)) * xk;
+/* L50: */
+			}
+			work[k] += xk;
+/* L60: */
+		    }
+		}
+	    } else {
+		if (nounit) {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			xk = (r__1 = x[k + j * x_dim1], dabs(r__1));
+			i__3 = *n;
+			for (i__ = k; i__ <= i__3; ++i__) {
+			    work[i__] += (r__1 = a[i__ + k * a_dim1], dabs(
+				    r__1)) * xk;
+/* L70: */
+			}
+/* L80: */
+		    }
+		} else {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			xk = (r__1 = x[k + j * x_dim1], dabs(r__1));
+			i__3 = *n;
+			for (i__ = k + 1; i__ <= i__3; ++i__) {
+			    work[i__] += (r__1 = a[i__ + k * a_dim1], dabs(
+				    r__1)) * xk;
+/* L90: */
+			}
+			work[k] += xk;
+/* L100: */
+		    }
+		}
+	    }
+	} else {
+
+/*           Compute abs(A')*abs(X) + abs(B). */
+
+	    if (upper) {
+		if (nounit) {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			s = 0.f;
+			i__3 = k;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    s += (r__1 = a[i__ + k * a_dim1], dabs(r__1)) * (
+				    r__2 = x[i__ + j * x_dim1], dabs(r__2));
+/* L110: */
+			}
+			work[k] += s;
+/* L120: */
+		    }
+		} else {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			s = (r__1 = x[k + j * x_dim1], dabs(r__1));
+			i__3 = k - 1;
+			for (i__ = 1; i__ <= i__3; ++i__) {
+			    s += (r__1 = a[i__ + k * a_dim1], dabs(r__1)) * (
+				    r__2 = x[i__ + j * x_dim1], dabs(r__2));
+/* L130: */
+			}
+			work[k] += s;
+/* L140: */
+		    }
+		}
+	    } else {
+		if (nounit) {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			s = 0.f;
+			i__3 = *n;
+			for (i__ = k; i__ <= i__3; ++i__) {
+			    s += (r__1 = a[i__ + k * a_dim1], dabs(r__1)) * (
+				    r__2 = x[i__ + j * x_dim1], dabs(r__2));
+/* L150: */
+			}
+			work[k] += s;
+/* L160: */
+		    }
+		} else {
+		    i__2 = *n;
+		    for (k = 1; k <= i__2; ++k) {
+			s = (r__1 = x[k + j * x_dim1], dabs(r__1));
+			i__3 = *n;
+			for (i__ = k + 1; i__ <= i__3; ++i__) {
+			    s += (r__1 = a[i__ + k * a_dim1], dabs(r__1)) * (
+				    r__2 = x[i__ + j * x_dim1], dabs(r__2));
+/* L170: */
+			}
+			work[k] += s;
+/* L180: */
+		    }
+		}
+	    }
+	}
+	s = 0.f;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (work[i__] > safe2) {
+/* Computing MAX */
+		r__2 = s, r__3 = (r__1 = work[*n + i__], dabs(r__1)) / work[
+			i__];
+		s = dmax(r__2,r__3);
+	    } else {
+/* Computing MAX */
+		r__2 = s, r__3 = ((r__1 = work[*n + i__], dabs(r__1)) + safe1)
+			 / (work[i__] + safe1);
+		s = dmax(r__2,r__3);
+	    }
+/* L190: */
+	}
+	berr[j] = s;
+
+/*        Bound error from formula */
+
+/*        norm(X - XTRUE) / norm(X) .le. FERR = */
+/*        norm( abs(inv(op(A)))* */
+/*           ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
+
+/*        where */
+/*          norm(Z) is the magnitude of the largest component of Z */
+/*          inv(op(A)) is the inverse of op(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(op(A))*abs(X)+abs(B)) */
+/*        is incremented by SAFE1 if the i-th component of */
+/*        abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
+
+/*        Use SLACN2 to estimate the infinity-norm of the matrix */
+/*           inv(op(A)) * diag(W), */
+/*        where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (work[i__] > safe2) {
+		work[i__] = (r__1 = work[*n + i__], dabs(r__1)) + nz * eps * 
+			work[i__];
+	    } else {
+		work[i__] = (r__1 = work[*n + i__], dabs(r__1)) + nz * eps * 
+			work[i__] + safe1;
+	    }
+/* L200: */
+	}
+
+	kase = 0;
+L210:
+	slacn2_(n, &work[(*n << 1) + 1], &work[*n + 1], &iwork[1], &ferr[j], &
+		kase, isave);
+	if (kase != 0) {
+	    if (kase == 1) {
+
+/*              Multiply by diag(W)*inv(op(A)'). */
+
+		strsv_(uplo, transt, diag, n, &a[a_offset], lda, &work[*n + 1]
+, &c__1);
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    work[*n + i__] = work[i__] * work[*n + i__];
+/* L220: */
+		}
+	    } else {
+
+/*              Multiply by inv(op(A))*diag(W). */
+
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    work[*n + i__] = work[i__] * work[*n + i__];
+/* L230: */
+		}
+		strsv_(uplo, trans, diag, n, &a[a_offset], lda, &work[*n + 1], 
+			 &c__1);
+	    }
+	    goto L210;
+	}
+
+/*        Normalize error. */
+
+	lstres = 0.f;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    r__2 = lstres, r__3 = (r__1 = x[i__ + j * x_dim1], dabs(r__1));
+	    lstres = dmax(r__2,r__3);
+/* L240: */
+	}
+	if (lstres != 0.f) {
+	    ferr[j] /= lstres;
+	}
+
+/* L250: */
+    }
+
+    return 0;
+
+/*     End of STRRFS */
+
+} /* strrfs_ */