[] add metering mode to CLI

1 files changed, 530 insertions, 0 deletions

diff --git a/contrib/libs/clapack/slaed2.c b/contrib/libs/clapack/slaed2.c
new file mode 100644
index 0000000000..ad04cf5b03
--- /dev/null
+++ b/contrib/libs/clapack/slaed2.c
@@ -0,0 +1,530 @@
+/* slaed2.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 real c_b3 = -1.f;
+static integer c__1 = 1;
+
+/* Subroutine */ int slaed2_(integer *k, integer *n, integer *n1, real *d__, 
+	real *q, integer *ldq, integer *indxq, real *rho, real *z__, real *
+	dlamda, real *w, real *q2, integer *indx, integer *indxc, integer *
+	indxp, integer *coltyp, integer *info)
+{
+    /* System generated locals */
+    integer q_dim1, q_offset, i__1, i__2;
+    real r__1, r__2, r__3, r__4;
+
+    /* Builtin functions */
+    double sqrt(doublereal);
+
+    /* Local variables */
+    real c__;
+    integer i__, j;
+    real s, t;
+    integer k2, n2, ct, nj, pj, js, iq1, iq2, n1p1;
+    real eps, tau, tol;
+    integer psm[4], imax, jmax, ctot[4];
+    extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, 
+	    integer *, real *, real *), sscal_(integer *, real *, real *, 
+	    integer *), scopy_(integer *, real *, integer *, real *, integer *
+);
+    extern doublereal slapy2_(real *, real *), slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    extern integer isamax_(integer *, real *, integer *);
+    extern /* Subroutine */ int slamrg_(integer *, integer *, real *, integer 
+	    *, integer *, integer *), slacpy_(char *, integer *, integer *, 
+	    real *, integer *, real *, integer *);
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  SLAED2 merges the two sets of eigenvalues together into a single */
+/*  sorted set.  Then it tries to deflate the size of the problem. */
+/*  There are two ways in which deflation can occur:  when two or more */
+/*  eigenvalues are close together or if there is a tiny entry in the */
+/*  Z vector.  For each such occurrence the order of the related secular */
+/*  equation problem is reduced by one. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  K      (output) INTEGER */
+/*         The number of non-deflated eigenvalues, and the order of the */
+/*         related secular equation. 0 <= K <=N. */
+
+/*  N      (input) INTEGER */
+/*         The dimension of the symmetric tridiagonal matrix.  N >= 0. */
+
+/*  N1     (input) INTEGER */
+/*         The location of the last eigenvalue in the leading sub-matrix. */
+/*         min(1,N) <= N1 <= N/2. */
+
+/*  D      (input/output) REAL array, dimension (N) */
+/*         On entry, D contains the eigenvalues of the two submatrices to */
+/*         be combined. */
+/*         On exit, D contains the trailing (N-K) updated eigenvalues */
+/*         (those which were deflated) sorted into increasing order. */
+
+/*  Q      (input/output) REAL array, dimension (LDQ, N) */
+/*         On entry, Q contains the eigenvectors of two submatrices in */
+/*         the two square blocks with corners at (1,1), (N1,N1) */
+/*         and (N1+1, N1+1), (N,N). */
+/*         On exit, Q contains the trailing (N-K) updated eigenvectors */
+/*         (those which were deflated) in its last N-K columns. */
+
+/*  LDQ    (input) INTEGER */
+/*         The leading dimension of the array Q.  LDQ >= max(1,N). */
+
+/*  INDXQ  (input/output) INTEGER array, dimension (N) */
+/*         The permutation which separately sorts the two sub-problems */
+/*         in D into ascending order.  Note that elements in the second */
+/*         half of this permutation must first have N1 added to their */
+/*         values. Destroyed on exit. */
+
+/*  RHO    (input/output) REAL */
+/*         On entry, the off-diagonal element associated with the rank-1 */
+/*         cut which originally split the two submatrices which are now */
+/*         being recombined. */
+/*         On exit, RHO has been modified to the value required by */
+/*         SLAED3. */
+
+/*  Z      (input) REAL array, dimension (N) */
+/*         On entry, Z contains the updating vector (the last */
+/*         row of the first sub-eigenvector matrix and the first row of */
+/*         the second sub-eigenvector matrix). */
+/*         On exit, the contents of Z have been destroyed by the updating */
+/*         process. */
+
+/*  DLAMDA (output) REAL array, dimension (N) */
+/*         A copy of the first K eigenvalues which will be used by */
+/*         SLAED3 to form the secular equation. */
+
+/*  W      (output) REAL array, dimension (N) */
+/*         The first k values of the final deflation-altered z-vector */
+/*         which will be passed to SLAED3. */
+
+/*  Q2     (output) REAL array, dimension (N1**2+(N-N1)**2) */
+/*         A copy of the first K eigenvectors which will be used by */
+/*         SLAED3 in a matrix multiply (SGEMM) to solve for the new */
+/*         eigenvectors. */
+
+/*  INDX   (workspace) INTEGER array, dimension (N) */
+/*         The permutation used to sort the contents of DLAMDA into */
+/*         ascending order. */
+
+/*  INDXC  (output) INTEGER array, dimension (N) */
+/*         The permutation used to arrange the columns of the deflated */
+/*         Q matrix into three groups:  the first group contains non-zero */
+/*         elements only at and above N1, the second contains */
+/*         non-zero elements only below N1, and the third is dense. */
+
+/*  INDXP  (workspace) INTEGER array, dimension (N) */
+/*         The permutation used to place deflated values of D at the end */
+/*         of the array.  INDXP(1:K) points to the nondeflated D-values */
+/*         and INDXP(K+1:N) points to the deflated eigenvalues. */
+
+/*  COLTYP (workspace/output) INTEGER array, dimension (N) */
+/*         During execution, a label which will indicate which of the */
+/*         following types a column in the Q2 matrix is: */
+/*         1 : non-zero in the upper half only; */
+/*         2 : dense; */
+/*         3 : non-zero in the lower half only; */
+/*         4 : deflated. */
+/*         On exit, COLTYP(i) is the number of columns of type i, */
+/*         for i=1 to 4 only. */
+
+/*  INFO   (output) INTEGER */
+/*          = 0:  successful exit. */
+/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+
+/*  Further Details */
+/*  =============== */
+
+/*  Based on contributions by */
+/*     Jeff Rutter, Computer Science Division, University of California */
+/*     at Berkeley, USA */
+/*  Modified by Francoise Tisseur, University of Tennessee. */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    --d__;
+    q_dim1 = *ldq;
+    q_offset = 1 + q_dim1;
+    q -= q_offset;
+    --indxq;
+    --z__;
+    --dlamda;
+    --w;
+    --q2;
+    --indx;
+    --indxc;
+    --indxp;
+    --coltyp;
+
+    /* Function Body */
+    *info = 0;
+
+    if (*n < 0) {
+	*info = -2;
+    } else if (*ldq < max(1,*n)) {
+	*info = -6;
+    } else /* if(complicated condition) */ {
+/* Computing MIN */
+	i__1 = 1, i__2 = *n / 2;
+	if (min(i__1,i__2) > *n1 || *n / 2 < *n1) {
+	    *info = -3;
+	}
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("SLAED2", &i__1);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+    n2 = *n - *n1;
+    n1p1 = *n1 + 1;
+
+    if (*rho < 0.f) {
+	sscal_(&n2, &c_b3, &z__[n1p1], &c__1);
+    }
+
+/*     Normalize z so that norm(z) = 1.  Since z is the concatenation of */
+/*     two normalized vectors, norm2(z) = sqrt(2). */
+
+    t = 1.f / sqrt(2.f);
+    sscal_(n, &t, &z__[1], &c__1);
+
+/*     RHO = ABS( norm(z)**2 * RHO ) */
+
+    *rho = (r__1 = *rho * 2.f, dabs(r__1));
+
+/*     Sort the eigenvalues into increasing order */
+
+    i__1 = *n;
+    for (i__ = n1p1; i__ <= i__1; ++i__) {
+	indxq[i__] += *n1;
+/* L10: */
+    }
+
+/*     re-integrate the deflated parts from the last pass */
+
+    i__1 = *n;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	dlamda[i__] = d__[indxq[i__]];
+/* L20: */
+    }
+    slamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]);
+    i__1 = *n;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	indx[i__] = indxq[indxc[i__]];
+/* L30: */
+    }
+
+/*     Calculate the allowable deflation tolerance */
+
+    imax = isamax_(n, &z__[1], &c__1);
+    jmax = isamax_(n, &d__[1], &c__1);
+    eps = slamch_("Epsilon");
+/* Computing MAX */
+    r__3 = (r__1 = d__[jmax], dabs(r__1)), r__4 = (r__2 = z__[imax], dabs(
+	    r__2));
+    tol = eps * 8.f * dmax(r__3,r__4);
+
+/*     If the rank-1 modifier is small enough, no more needs to be done */
+/*     except to reorganize Q so that its columns correspond with the */
+/*     elements in D. */
+
+    if (*rho * (r__1 = z__[imax], dabs(r__1)) <= tol) {
+	*k = 0;
+	iq2 = 1;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__ = indx[j];
+	    scopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1);
+	    dlamda[j] = d__[i__];
+	    iq2 += *n;
+/* L40: */
+	}
+	slacpy_("A", n, n, &q2[1], n, &q[q_offset], ldq);
+	scopy_(n, &dlamda[1], &c__1, &d__[1], &c__1);
+	goto L190;
+    }
+
+/*     If there are multiple eigenvalues then the problem deflates.  Here */
+/*     the number of equal eigenvalues are found.  As each equal */
+/*     eigenvalue is found, an elementary reflector is computed to rotate */
+/*     the corresponding eigensubspace so that the corresponding */
+/*     components of Z are zero in this new basis. */
+
+    i__1 = *n1;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	coltyp[i__] = 1;
+/* L50: */
+    }
+    i__1 = *n;
+    for (i__ = n1p1; i__ <= i__1; ++i__) {
+	coltyp[i__] = 3;
+/* L60: */
+    }
+
+
+    *k = 0;
+    k2 = *n + 1;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	nj = indx[j];
+	if (*rho * (r__1 = z__[nj], dabs(r__1)) <= tol) {
+
+/*           Deflate due to small z component. */
+
+	    --k2;
+	    coltyp[nj] = 4;
+	    indxp[k2] = nj;
+	    if (j == *n) {
+		goto L100;
+	    }
+	} else {
+	    pj = nj;
+	    goto L80;
+	}
+/* L70: */
+    }
+L80:
+    ++j;
+    nj = indx[j];
+    if (j > *n) {
+	goto L100;
+    }
+    if (*rho * (r__1 = z__[nj], dabs(r__1)) <= tol) {
+
+/*        Deflate due to small z component. */
+
+	--k2;
+	coltyp[nj] = 4;
+	indxp[k2] = nj;
+    } else {
+
+/*        Check if eigenvalues are close enough to allow deflation. */
+
+	s = z__[pj];
+	c__ = z__[nj];
+
+/*        Find sqrt(a**2+b**2) without overflow or */
+/*        destructive underflow. */
+
+	tau = slapy2_(&c__, &s);
+	t = d__[nj] - d__[pj];
+	c__ /= tau;
+	s = -s / tau;
+	if ((r__1 = t * c__ * s, dabs(r__1)) <= tol) {
+
+/*           Deflation is possible. */
+
+	    z__[nj] = tau;
+	    z__[pj] = 0.f;
+	    if (coltyp[nj] != coltyp[pj]) {
+		coltyp[nj] = 2;
+	    }
+	    coltyp[pj] = 4;
+	    srot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, &
+		    c__, &s);
+/* Computing 2nd power */
+	    r__1 = c__;
+/* Computing 2nd power */
+	    r__2 = s;
+	    t = d__[pj] * (r__1 * r__1) + d__[nj] * (r__2 * r__2);
+/* Computing 2nd power */
+	    r__1 = s;
+/* Computing 2nd power */
+	    r__2 = c__;
+	    d__[nj] = d__[pj] * (r__1 * r__1) + d__[nj] * (r__2 * r__2);
+	    d__[pj] = t;
+	    --k2;
+	    i__ = 1;
+L90:
+	    if (k2 + i__ <= *n) {
+		if (d__[pj] < d__[indxp[k2 + i__]]) {
+		    indxp[k2 + i__ - 1] = indxp[k2 + i__];
+		    indxp[k2 + i__] = pj;
+		    ++i__;
+		    goto L90;
+		} else {
+		    indxp[k2 + i__ - 1] = pj;
+		}
+	    } else {
+		indxp[k2 + i__ - 1] = pj;
+	    }
+	    pj = nj;
+	} else {
+	    ++(*k);
+	    dlamda[*k] = d__[pj];
+	    w[*k] = z__[pj];
+	    indxp[*k] = pj;
+	    pj = nj;
+	}
+    }
+    goto L80;
+L100:
+
+/*     Record the last eigenvalue. */
+
+    ++(*k);
+    dlamda[*k] = d__[pj];
+    w[*k] = z__[pj];
+    indxp[*k] = pj;
+
+/*     Count up the total number of the various types of columns, then */
+/*     form a permutation which positions the four column types into */
+/*     four uniform groups (although one or more of these groups may be */
+/*     empty). */
+
+    for (j = 1; j <= 4; ++j) {
+	ctot[j - 1] = 0;
+/* L110: */
+    }
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	ct = coltyp[j];
+	++ctot[ct - 1];
+/* L120: */
+    }
+
+/*     PSM(*) = Position in SubMatrix (of types 1 through 4) */
+
+    psm[0] = 1;
+    psm[1] = ctot[0] + 1;
+    psm[2] = psm[1] + ctot[1];
+    psm[3] = psm[2] + ctot[2];
+    *k = *n - ctot[3];
+
+/*     Fill out the INDXC array so that the permutation which it induces */
+/*     will place all type-1 columns first, all type-2 columns next, */
+/*     then all type-3's, and finally all type-4's. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	js = indxp[j];
+	ct = coltyp[js];
+	indx[psm[ct - 1]] = js;
+	indxc[psm[ct - 1]] = j;
+	++psm[ct - 1];
+/* L130: */
+    }
+
+/*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA */
+/*     and Q2 respectively.  The eigenvalues/vectors which were not */
+/*     deflated go into the first K slots of DLAMDA and Q2 respectively, */
+/*     while those which were deflated go into the last N - K slots. */
+
+    i__ = 1;
+    iq1 = 1;
+    iq2 = (ctot[0] + ctot[1]) * *n1 + 1;
+    i__1 = ctot[0];
+    for (j = 1; j <= i__1; ++j) {
+	js = indx[i__];
+	scopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1);
+	z__[i__] = d__[js];
+	++i__;
+	iq1 += *n1;
+/* L140: */
+    }
+
+    i__1 = ctot[1];
+    for (j = 1; j <= i__1; ++j) {
+	js = indx[i__];
+	scopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1);
+	scopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1);
+	z__[i__] = d__[js];
+	++i__;
+	iq1 += *n1;
+	iq2 += n2;
+/* L150: */
+    }
+
+    i__1 = ctot[2];
+    for (j = 1; j <= i__1; ++j) {
+	js = indx[i__];
+	scopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1);
+	z__[i__] = d__[js];
+	++i__;
+	iq2 += n2;
+/* L160: */
+    }
+
+    iq1 = iq2;
+    i__1 = ctot[3];
+    for (j = 1; j <= i__1; ++j) {
+	js = indx[i__];
+	scopy_(n, &q[js * q_dim1 + 1], &c__1, &q2[iq2], &c__1);
+	iq2 += *n;
+	z__[i__] = d__[js];
+	++i__;
+/* L170: */
+    }
+
+/*     The deflated eigenvalues and their corresponding vectors go back */
+/*     into the last N - K slots of D and Q respectively. */
+
+    slacpy_("A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq);
+    i__1 = *n - *k;
+    scopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1);
+
+/*     Copy CTOT into COLTYP for referencing in SLAED3. */
+
+    for (j = 1; j <= 4; ++j) {
+	coltyp[j] = ctot[j - 1];
+/* L180: */
+    }
+
+L190:
+    return 0;
+
+/*     End of SLAED2 */
+
+} /* slaed2_ */