[] add metering mode to CLI

1 files changed, 429 insertions, 0 deletions

diff --git a/contrib/libs/clapack/dsyrfs.c b/contrib/libs/clapack/dsyrfs.c
new file mode 100644
index 0000000000..399d2f56d0
--- /dev/null
+++ b/contrib/libs/clapack/dsyrfs.c
@@ -0,0 +1,429 @@
+/* dsyrfs.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 doublereal c_b12 = -1.;
+static doublereal c_b14 = 1.;
+
+/* Subroutine */ int dsyrfs_(char *uplo, integer *n, integer *nrhs, 
+	doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer *
+	ipiv, doublereal *b, integer *ldb, doublereal *x, integer *ldx, 
+	doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, 
+	integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 
+	    x_offset, i__1, i__2, i__3;
+    doublereal d__1, d__2, d__3;
+
+    /* Local variables */
+    integer i__, j, k;
+    doublereal s, xk;
+    integer nz;
+    doublereal eps;
+    integer kase;
+    doublereal safe1, safe2;
+    extern logical lsame_(char *, char *);
+    integer isave[3];
+    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *), daxpy_(integer *, doublereal *, 
+	    doublereal *, integer *, doublereal *, integer *);
+    integer count;
+    logical upper;
+    extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *, 
+	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
+	    doublereal *, integer *), dlacn2_(integer *, doublereal *, 
+	     doublereal *, integer *, doublereal *, integer *, integer *);
+    extern doublereal dlamch_(char *);
+    doublereal safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    doublereal lstres;
+    extern /* Subroutine */ int dsytrs_(char *, integer *, integer *, 
+	    doublereal *, integer *, integer *, doublereal *, integer *, 
+	    integer *);
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  DSYRFS improves the computed solution to a system of linear */
+/*  equations when the coefficient matrix is symmetric indefinite, and */
+/*  provides error bounds and backward error estimates for the solution. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  UPLO    (input) CHARACTER*1 */
+/*          = 'U':  Upper triangle of A is stored; */
+/*          = 'L':  Lower triangle of A is stored. */
+
+/*  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) DOUBLE PRECISION array, dimension (LDA,N) */
+/*          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N */
+/*          upper triangular part of A contains the upper triangular part */
+/*          of the matrix A, and the strictly lower triangular part of A */
+/*          is not referenced.  If UPLO = 'L', the leading N-by-N lower */
+/*          triangular part of A contains the lower triangular part of */
+/*          the matrix A, and the strictly upper triangular part of A is */
+/*          not referenced. */
+
+/*  LDA     (input) INTEGER */
+/*          The leading dimension of the array A.  LDA >= max(1,N). */
+
+/*  AF      (input) DOUBLE PRECISION array, dimension (LDAF,N) */
+/*          The factored form of the matrix A.  AF contains the block */
+/*          diagonal matrix D and the multipliers used to obtain the */
+/*          factor U or L from the factorization A = U*D*U**T or */
+/*          A = L*D*L**T as computed by DSYTRF. */
+
+/*  LDAF    (input) INTEGER */
+/*          The leading dimension of the array AF.  LDAF >= max(1,N). */
+
+/*  IPIV    (input) INTEGER array, dimension (N) */
+/*          Details of the interchanges and the block structure of D */
+/*          as determined by DSYTRF. */
+
+/*  B       (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS) */
+/*          On entry, the solution matrix X, as computed by DSYTRS. */
+/*          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 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) 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) DOUBLE PRECISION 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 */
+
+/*  Internal Parameters */
+/*  =================== */
+
+/*  ITMAX is the maximum number of steps of iterative refinement. */
+
+/*  ===================================================================== */
+
+/*     .. 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;
+    af_dim1 = *ldaf;
+    af_offset = 1 + af_dim1;
+    af -= af_offset;
+    --ipiv;
+    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");
+    if (! upper && ! lsame_(uplo, "L")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*nrhs < 0) {
+	*info = -3;
+    } else if (*lda < max(1,*n)) {
+	*info = -5;
+    } else if (*ldaf < max(1,*n)) {
+	*info = -7;
+    } else if (*ldb < max(1,*n)) {
+	*info = -10;
+    } else if (*ldx < max(1,*n)) {
+	*info = -12;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DSYRFS", &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 = *n + 1;
+    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 */
+
+	dcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[*n + 1], &c__1);
+	dsymv_(uplo, n, &c_b12, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, 
+		&c_b14, &work[*n + 1], &c__1);
+
+/*        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. */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    work[i__] = (d__1 = b[i__ + j * b_dim1], abs(d__1));
+/* L30: */
+	}
+
+/*        Compute abs(A)*abs(X) + abs(B). */
+
+	if (upper) {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		s = 0.;
+		xk = (d__1 = x[k + j * x_dim1], abs(d__1));
+		i__3 = k - 1;
+		for (i__ = 1; i__ <= i__3; ++i__) {
+		    work[i__] += (d__1 = a[i__ + k * a_dim1], abs(d__1)) * xk;
+		    s += (d__1 = a[i__ + k * a_dim1], abs(d__1)) * (d__2 = x[
+			    i__ + j * x_dim1], abs(d__2));
+/* L40: */
+		}
+		work[k] = work[k] + (d__1 = a[k + k * a_dim1], abs(d__1)) * 
+			xk + s;
+/* L50: */
+	    }
+	} else {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		s = 0.;
+		xk = (d__1 = x[k + j * x_dim1], abs(d__1));
+		work[k] += (d__1 = a[k + k * a_dim1], abs(d__1)) * xk;
+		i__3 = *n;
+		for (i__ = k + 1; i__ <= i__3; ++i__) {
+		    work[i__] += (d__1 = a[i__ + k * a_dim1], abs(d__1)) * xk;
+		    s += (d__1 = a[i__ + k * a_dim1], abs(d__1)) * (d__2 = x[
+			    i__ + j * x_dim1], abs(d__2));
+/* L60: */
+		}
+		work[k] += s;
+/* L70: */
+	    }
+	}
+	s = 0.;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (work[i__] > safe2) {
+/* Computing MAX */
+		d__2 = s, d__3 = (d__1 = work[*n + i__], abs(d__1)) / work[
+			i__];
+		s = max(d__2,d__3);
+	    } else {
+/* Computing MAX */
+		d__2 = s, d__3 = ((d__1 = work[*n + i__], abs(d__1)) + safe1) 
+			/ (work[i__] + safe1);
+		s = max(d__2,d__3);
+	    }
+/* L80: */
+	}
+	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. */
+
+	    dsytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[*n 
+		    + 1], n, info);
+	    daxpy_(n, &c_b14, &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. */
+
+/*        Use DLACN2 to estimate the infinity-norm of the matrix */
+/*           inv(A) * diag(W), */
+/*        where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (work[i__] > safe2) {
+		work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps * 
+			work[i__];
+	    } else {
+		work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps * 
+			work[i__] + safe1;
+	    }
+/* L90: */
+	}
+
+	kase = 0;
+L100:
+	dlacn2_(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(A'). */
+
+		dsytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
+			*n + 1], n, info);
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    work[*n + i__] = work[i__] * work[*n + i__];
+/* L110: */
+		}
+	    } else if (kase == 2) {
+
+/*              Multiply by inv(A)*diag(W). */
+
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    work[*n + i__] = work[i__] * work[*n + i__];
+/* L120: */
+		}
+		dsytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
+			*n + 1], n, info);
+	    }
+	    goto L100;
+	}
+
+/*        Normalize error. */
+
+	lstres = 0.;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    d__2 = lstres, d__3 = (d__1 = x[i__ + j * x_dim1], abs(d__1));
+	    lstres = max(d__2,d__3);
+/* L130: */
+	}
+	if (lstres != 0.) {
+	    ferr[j] /= lstres;
+	}
+
+/* L140: */
+    }
+
+    return 0;
+
+/*     End of DSYRFS */
+
+} /* dsyrfs_ */