[] add metering mode to CLI

1 files changed, 365 insertions, 0 deletions

diff --git a/contrib/libs/clapack/sptrfs.c b/contrib/libs/clapack/sptrfs.c
new file mode 100644
index 00000000000..f6d9adb7e18
--- /dev/null
+++ b/contrib/libs/clapack/sptrfs.c
@@ -0,0 +1,365 @@
+/* sptrfs.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_b11 = 1.f;
+
+/* Subroutine */ int sptrfs_(integer *n, integer *nrhs, real *d__, real *e, 
+	real *df, real *ef, real *b, integer *ldb, real *x, integer *ldx, 
+	real *ferr, real *berr, real *work, integer *info)
+{
+    /* System generated locals */
+    integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2;
+    real r__1, r__2, r__3;
+
+    /* Local variables */
+    integer i__, j;
+    real s, bi, cx, dx, ex;
+    integer ix, nz;
+    real eps, safe1, safe2;
+    integer count;
+    extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 
+	    real *, integer *);
+    extern doublereal slamch_(char *);
+    real safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    extern integer isamax_(integer *, real *, integer *);
+    real lstres;
+    extern /* Subroutine */ int spttrs_(integer *, integer *, real *, real *, 
+	    real *, integer *, integer *);
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  SPTRFS improves the computed solution to a system of linear */
+/*  equations when the coefficient matrix is symmetric positive definite */
+/*  and tridiagonal, and provides error bounds and backward error */
+/*  estimates for the solution. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  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) REAL array, dimension (N) */
+/*          The n diagonal elements of the tridiagonal matrix A. */
+
+/*  E       (input) REAL array, dimension (N-1) */
+/*          The (n-1) subdiagonal elements of the tridiagonal matrix A. */
+
+/*  DF      (input) REAL array, dimension (N) */
+/*          The n diagonal elements of the diagonal matrix D from the */
+/*          factorization computed by SPTTRF. */
+
+/*  EF      (input) REAL array, dimension (N-1) */
+/*          The (n-1) subdiagonal elements of the unit bidiagonal factor */
+/*          L from the factorization computed by SPTTRF. */
+
+/*  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/output) REAL array, dimension (LDX,NRHS) */
+/*          On entry, the solution matrix X, as computed by SPTTRS. */
+/*          On exit, the improved solution matrix X. */
+
+/*  LDX     (input) INTEGER */
+/*          The leading dimension of the array X.  LDX >= max(1,N). */
+
+/*  FERR    (output) REAL 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) 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 (2*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 Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. 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;
+
+    /* Function Body */
+    *info = 0;
+    if (*n < 0) {
+	*info = -1;
+    } else if (*nrhs < 0) {
+	*info = -2;
+    } else if (*ldb < max(1,*n)) {
+	*info = -8;
+    } else if (*ldx < max(1,*n)) {
+	*info = -10;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("SPTRFS", &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;
+    }
+
+/*     NZ = maximum number of nonzero elements in each row of A, plus 1 */
+
+    nz = 4;
+    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) {
+
+	count = 1;
+	lstres = 3.f;
+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 (*n == 1) {
+	    bi = b[j * b_dim1 + 1];
+	    dx = d__[1] * x[j * x_dim1 + 1];
+	    work[*n + 1] = bi - dx;
+	    work[1] = dabs(bi) + dabs(dx);
+	} else {
+	    bi = b[j * b_dim1 + 1];
+	    dx = d__[1] * x[j * x_dim1 + 1];
+	    ex = e[1] * x[j * x_dim1 + 2];
+	    work[*n + 1] = bi - dx - ex;
+	    work[1] = dabs(bi) + dabs(dx) + dabs(ex);
+	    i__2 = *n - 1;
+	    for (i__ = 2; i__ <= i__2; ++i__) {
+		bi = b[i__ + j * b_dim1];
+		cx = e[i__ - 1] * x[i__ - 1 + j * x_dim1];
+		dx = d__[i__] * x[i__ + j * x_dim1];
+		ex = e[i__] * x[i__ + 1 + j * x_dim1];
+		work[*n + i__] = bi - cx - dx - ex;
+		work[i__] = dabs(bi) + dabs(cx) + dabs(dx) + dabs(ex);
+/* L30: */
+	    }
+	    bi = b[*n + j * b_dim1];
+	    cx = e[*n - 1] * x[*n - 1 + j * x_dim1];
+	    dx = d__[*n] * x[*n + j * x_dim1];
+	    work[*n + *n] = bi - cx - dx;
+	    work[*n] = dabs(bi) + dabs(cx) + dabs(dx);
+	}
+
+/*        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.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);
+	    }
+/* L40: */
+	}
+	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.f <= lstres && count <= 5) {
+
+/*           Update solution and try again. */
+
+	    spttrs_(n, &c__1, &df[1], &ef[1], &work[*n + 1], n, info);
+	    saxpy_(n, &c_b11, &work[*n + 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 (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;
+	    }
+/* L50: */
+	}
+	ix = isamax_(n, &work[1], &c__1);
+	ferr[j] = work[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. */
+
+	work[1] = 1.f;
+	i__2 = *n;
+	for (i__ = 2; i__ <= i__2; ++i__) {
+	    work[i__] = work[i__ - 1] * (r__1 = ef[i__ - 1], dabs(r__1)) + 
+		    1.f;
+/* L60: */
+	}
+
+/*        Solve D * M(L)' * x = b. */
+
+	work[*n] /= df[*n];
+	for (i__ = *n - 1; i__ >= 1; --i__) {
+	    work[i__] = work[i__] / df[i__] + work[i__ + 1] * (r__1 = ef[i__],
+		     dabs(r__1));
+/* L70: */
+	}
+
+/*        Compute norm(inv(A)) = max(x(i)), 1<=i<=n. */
+
+	ix = isamax_(n, &work[1], &c__1);
+	ferr[j] *= (r__1 = work[ix], dabs(r__1));
+
+/*        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);
+/* L80: */
+	}
+	if (lstres != 0.f) {
+	    ferr[j] /= lstres;
+	}
+
+/* L90: */
+    }
+
+    return 0;
+
+/*     End of SPTRFS */
+
+} /* sptrfs_ */