[] add metering mode to CLI

1 files changed, 530 insertions, 0 deletions

diff --git a/contrib/libs/clapack/strsen.c b/contrib/libs/clapack/strsen.c
new file mode 100644
index 0000000000..8698273051
--- /dev/null
+++ b/contrib/libs/clapack/strsen.c
@@ -0,0 +1,530 @@
+/* strsen.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_n1 = -1;
+
+/* Subroutine */ int strsen_(char *job, char *compq, logical *select, integer 
+	*n, real *t, integer *ldt, real *q, integer *ldq, real *wr, real *wi, 
+	integer *m, real *s, real *sep, real *work, integer *lwork, integer *
+	iwork, integer *liwork, integer *info)
+{
+    /* System generated locals */
+    integer q_dim1, q_offset, t_dim1, t_offset, i__1, i__2;
+    real r__1, r__2;
+
+    /* Builtin functions */
+    double sqrt(doublereal);
+
+    /* Local variables */
+    integer k, n1, n2, kk, nn, ks;
+    real est;
+    integer kase;
+    logical pair;
+    integer ierr;
+    logical swap;
+    real scale;
+    extern logical lsame_(char *, char *);
+    integer isave[3], lwmin;
+    logical wantq, wants;
+    real rnorm;
+    extern /* Subroutine */ int slacn2_(integer *, real *, real *, integer *, 
+	    real *, integer *, integer *);
+    extern doublereal slange_(char *, integer *, integer *, real *, integer *, 
+	     real *);
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    logical wantbh;
+    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
+	    integer *, real *, integer *);
+    integer liwmin;
+    extern /* Subroutine */ int strexc_(char *, integer *, real *, integer *, 
+	    real *, integer *, integer *, integer *, real *, integer *);
+    logical wantsp, lquery;
+    extern /* Subroutine */ int strsyl_(char *, char *, integer *, integer *, 
+	    integer *, real *, integer *, real *, integer *, real *, integer *
+, real *, integer *);
+
+
+/*  -- 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 */
+/*  ======= */
+
+/*  STRSEN reorders the real Schur factorization of a real matrix */
+/*  A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in */
+/*  the leading diagonal blocks of the upper quasi-triangular matrix T, */
+/*  and the leading columns of Q form an orthonormal basis of the */
+/*  corresponding right invariant subspace. */
+
+/*  Optionally the routine computes the reciprocal condition numbers of */
+/*  the cluster of eigenvalues and/or the invariant subspace. */
+
+/*  T must be in Schur canonical form (as returned by SHSEQR), that is, */
+/*  block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each */
+/*  2-by-2 diagonal block has its diagonal elemnts equal and its */
+/*  off-diagonal elements of opposite sign. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  JOB     (input) CHARACTER*1 */
+/*          Specifies whether condition numbers are required for the */
+/*          cluster of eigenvalues (S) or the invariant subspace (SEP): */
+/*          = 'N': none; */
+/*          = 'E': for eigenvalues only (S); */
+/*          = 'V': for invariant subspace only (SEP); */
+/*          = 'B': for both eigenvalues and invariant subspace (S and */
+/*                 SEP). */
+
+/*  COMPQ   (input) CHARACTER*1 */
+/*          = 'V': update the matrix Q of Schur vectors; */
+/*          = 'N': do not update Q. */
+
+/*  SELECT  (input) LOGICAL array, dimension (N) */
+/*          SELECT specifies the eigenvalues in the selected cluster. To */
+/*          select a real eigenvalue w(j), SELECT(j) must be set to */
+/*          .TRUE.. To select a complex conjugate pair of eigenvalues */
+/*          w(j) and w(j+1), corresponding to a 2-by-2 diagonal block, */
+/*          either SELECT(j) or SELECT(j+1) or both must be set to */
+/*          .TRUE.; a complex conjugate pair of eigenvalues must be */
+/*          either both included in the cluster or both excluded. */
+
+/*  N       (input) INTEGER */
+/*          The order of the matrix T. N >= 0. */
+
+/*  T       (input/output) REAL array, dimension (LDT,N) */
+/*          On entry, the upper quasi-triangular matrix T, in Schur */
+/*          canonical form. */
+/*          On exit, T is overwritten by the reordered matrix T, again in */
+/*          Schur canonical form, with the selected eigenvalues in the */
+/*          leading diagonal blocks. */
+
+/*  LDT     (input) INTEGER */
+/*          The leading dimension of the array T. LDT >= max(1,N). */
+
+/*  Q       (input/output) REAL array, dimension (LDQ,N) */
+/*          On entry, if COMPQ = 'V', the matrix Q of Schur vectors. */
+/*          On exit, if COMPQ = 'V', Q has been postmultiplied by the */
+/*          orthogonal transformation matrix which reorders T; the */
+/*          leading M columns of Q form an orthonormal basis for the */
+/*          specified invariant subspace. */
+/*          If COMPQ = 'N', Q is not referenced. */
+
+/*  LDQ     (input) INTEGER */
+/*          The leading dimension of the array Q. */
+/*          LDQ >= 1; and if COMPQ = 'V', LDQ >= N. */
+
+/*  WR      (output) REAL array, dimension (N) */
+/*  WI      (output) REAL array, dimension (N) */
+/*          The real and imaginary parts, respectively, of the reordered */
+/*          eigenvalues of T. The eigenvalues are stored in the same */
+/*          order as on the diagonal of T, with WR(i) = T(i,i) and, if */
+/*          T(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) > 0 and */
+/*          WI(i+1) = -WI(i). Note that if a complex eigenvalue is */
+/*          sufficiently ill-conditioned, then its value may differ */
+/*          significantly from its value before reordering. */
+
+/*  M       (output) INTEGER */
+/*          The dimension of the specified invariant subspace. */
+/*          0 < = M <= N. */
+
+/*  S       (output) REAL */
+/*          If JOB = 'E' or 'B', S is a lower bound on the reciprocal */
+/*          condition number for the selected cluster of eigenvalues. */
+/*          S cannot underestimate the true reciprocal condition number */
+/*          by more than a factor of sqrt(N). If M = 0 or N, S = 1. */
+/*          If JOB = 'N' or 'V', S is not referenced. */
+
+/*  SEP     (output) REAL */
+/*          If JOB = 'V' or 'B', SEP is the estimated reciprocal */
+/*          condition number of the specified invariant subspace. If */
+/*          M = 0 or N, SEP = norm(T). */
+/*          If JOB = 'N' or 'E', SEP is not referenced. */
+
+/*  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
+/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+
+/*  LWORK   (input) INTEGER */
+/*          The dimension of the array WORK. */
+/*          If JOB = 'N', LWORK >= max(1,N); */
+/*          if JOB = 'E', LWORK >= max(1,M*(N-M)); */
+/*          if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)). */
+
+/*          If LWORK = -1, then a workspace query is assumed; the routine */
+/*          only calculates the optimal size of the WORK array, returns */
+/*          this value as the first entry of the WORK array, and no error */
+/*          message related to LWORK is issued by XERBLA. */
+
+/*  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK)) */
+/*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
+
+/*  LIWORK  (input) INTEGER */
+/*          The dimension of the array IWORK. */
+/*          If JOB = 'N' or 'E', LIWORK >= 1; */
+/*          if JOB = 'V' or 'B', LIWORK >= max(1,M*(N-M)). */
+
+/*          If LIWORK = -1, then a workspace query is assumed; the */
+/*          routine only calculates the optimal size of the IWORK array, */
+/*          returns this value as the first entry of the IWORK array, and */
+/*          no error message related to LIWORK is issued by XERBLA. */
+
+/*  INFO    (output) INTEGER */
+/*          = 0: successful exit */
+/*          < 0: if INFO = -i, the i-th argument had an illegal value */
+/*          = 1: reordering of T failed because some eigenvalues are too */
+/*               close to separate (the problem is very ill-conditioned); */
+/*               T may have been partially reordered, and WR and WI */
+/*               contain the eigenvalues in the same order as in T; S and */
+/*               SEP (if requested) are set to zero. */
+
+/*  Further Details */
+/*  =============== */
+
+/*  STRSEN first collects the selected eigenvalues by computing an */
+/*  orthogonal transformation Z to move them to the top left corner of T. */
+/*  In other words, the selected eigenvalues are the eigenvalues of T11 */
+/*  in: */
+
+/*                Z'*T*Z = ( T11 T12 ) n1 */
+/*                         (  0  T22 ) n2 */
+/*                            n1  n2 */
+
+/*  where N = n1+n2 and Z' means the transpose of Z. The first n1 columns */
+/*  of Z span the specified invariant subspace of T. */
+
+/*  If T has been obtained from the real Schur factorization of a matrix */
+/*  A = Q*T*Q', then the reordered real Schur factorization of A is given */
+/*  by A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span */
+/*  the corresponding invariant subspace of A. */
+
+/*  The reciprocal condition number of the average of the eigenvalues of */
+/*  T11 may be returned in S. S lies between 0 (very badly conditioned) */
+/*  and 1 (very well conditioned). It is computed as follows. First we */
+/*  compute R so that */
+
+/*                         P = ( I  R ) n1 */
+/*                             ( 0  0 ) n2 */
+/*                               n1 n2 */
+
+/*  is the projector on the invariant subspace associated with T11. */
+/*  R is the solution of the Sylvester equation: */
+
+/*                        T11*R - R*T22 = T12. */
+
+/*  Let F-norm(M) denote the Frobenius-norm of M and 2-norm(M) denote */
+/*  the two-norm of M. Then S is computed as the lower bound */
+
+/*                      (1 + F-norm(R)**2)**(-1/2) */
+
+/*  on the reciprocal of 2-norm(P), the true reciprocal condition number. */
+/*  S cannot underestimate 1 / 2-norm(P) by more than a factor of */
+/*  sqrt(N). */
+
+/*  An approximate error bound for the computed average of the */
+/*  eigenvalues of T11 is */
+
+/*                         EPS * norm(T) / S */
+
+/*  where EPS is the machine precision. */
+
+/*  The reciprocal condition number of the right invariant subspace */
+/*  spanned by the first n1 columns of Z (or of Q*Z) is returned in SEP. */
+/*  SEP is defined as the separation of T11 and T22: */
+
+/*                     sep( T11, T22 ) = sigma-min( C ) */
+
+/*  where sigma-min(C) is the smallest singular value of the */
+/*  n1*n2-by-n1*n2 matrix */
+
+/*     C  = kprod( I(n2), T11 ) - kprod( transpose(T22), I(n1) ) */
+
+/*  I(m) is an m by m identity matrix, and kprod denotes the Kronecker */
+/*  product. We estimate sigma-min(C) by the reciprocal of an estimate of */
+/*  the 1-norm of inverse(C). The true reciprocal 1-norm of inverse(C) */
+/*  cannot differ from sigma-min(C) by more than a factor of sqrt(n1*n2). */
+
+/*  When SEP is small, small changes in T can cause large changes in */
+/*  the invariant subspace. An approximate bound on the maximum angular */
+/*  error in the computed right invariant subspace is */
+
+/*                      EPS * norm(T) / SEP */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Decode and test the input parameters */
+
+    /* Parameter adjustments */
+    --select;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1;
+    t -= t_offset;
+    q_dim1 = *ldq;
+    q_offset = 1 + q_dim1;
+    q -= q_offset;
+    --wr;
+    --wi;
+    --work;
+    --iwork;
+
+    /* Function Body */
+    wantbh = lsame_(job, "B");
+    wants = lsame_(job, "E") || wantbh;
+    wantsp = lsame_(job, "V") || wantbh;
+    wantq = lsame_(compq, "V");
+
+    *info = 0;
+    lquery = *lwork == -1;
+    if (! lsame_(job, "N") && ! wants && ! wantsp) {
+	*info = -1;
+    } else if (! lsame_(compq, "N") && ! wantq) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*ldt < max(1,*n)) {
+	*info = -6;
+    } else if (*ldq < 1 || wantq && *ldq < *n) {
+	*info = -8;
+    } else {
+
+/*        Set M to the dimension of the specified invariant subspace, */
+/*        and test LWORK and LIWORK. */
+
+	*m = 0;
+	pair = FALSE_;
+	i__1 = *n;
+	for (k = 1; k <= i__1; ++k) {
+	    if (pair) {
+		pair = FALSE_;
+	    } else {
+		if (k < *n) {
+		    if (t[k + 1 + k * t_dim1] == 0.f) {
+			if (select[k]) {
+			    ++(*m);
+			}
+		    } else {
+			pair = TRUE_;
+			if (select[k] || select[k + 1]) {
+			    *m += 2;
+			}
+		    }
+		} else {
+		    if (select[*n]) {
+			++(*m);
+		    }
+		}
+	    }
+/* L10: */
+	}
+
+	n1 = *m;
+	n2 = *n - *m;
+	nn = n1 * n2;
+
+	if (wantsp) {
+/* Computing MAX */
+	    i__1 = 1, i__2 = nn << 1;
+	    lwmin = max(i__1,i__2);
+	    liwmin = max(1,nn);
+	} else if (lsame_(job, "N")) {
+	    lwmin = max(1,*n);
+	    liwmin = 1;
+	} else if (lsame_(job, "E")) {
+	    lwmin = max(1,nn);
+	    liwmin = 1;
+	}
+
+	if (*lwork < lwmin && ! lquery) {
+	    *info = -15;
+	} else if (*liwork < liwmin && ! lquery) {
+	    *info = -17;
+	}
+    }
+
+    if (*info == 0) {
+	work[1] = (real) lwmin;
+	iwork[1] = liwmin;
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("STRSEN", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible. */
+
+    if (*m == *n || *m == 0) {
+	if (wants) {
+	    *s = 1.f;
+	}
+	if (wantsp) {
+	    *sep = slange_("1", n, n, &t[t_offset], ldt, &work[1]);
+	}
+	goto L40;
+    }
+
+/*     Collect the selected blocks at the top-left corner of T. */
+
+    ks = 0;
+    pair = FALSE_;
+    i__1 = *n;
+    for (k = 1; k <= i__1; ++k) {
+	if (pair) {
+	    pair = FALSE_;
+	} else {
+	    swap = select[k];
+	    if (k < *n) {
+		if (t[k + 1 + k * t_dim1] != 0.f) {
+		    pair = TRUE_;
+		    swap = swap || select[k + 1];
+		}
+	    }
+	    if (swap) {
+		++ks;
+
+/*              Swap the K-th block to position KS. */
+
+		ierr = 0;
+		kk = k;
+		if (k != ks) {
+		    strexc_(compq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
+			    kk, &ks, &work[1], &ierr);
+		}
+		if (ierr == 1 || ierr == 2) {
+
+/*                 Blocks too close to swap: exit. */
+
+		    *info = 1;
+		    if (wants) {
+			*s = 0.f;
+		    }
+		    if (wantsp) {
+			*sep = 0.f;
+		    }
+		    goto L40;
+		}
+		if (pair) {
+		    ++ks;
+		}
+	    }
+	}
+/* L20: */
+    }
+
+    if (wants) {
+
+/*        Solve Sylvester equation for R: */
+
+/*           T11*R - R*T22 = scale*T12 */
+
+	slacpy_("F", &n1, &n2, &t[(n1 + 1) * t_dim1 + 1], ldt, &work[1], &n1);
+	strsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 + 1 + (n1 
+		+ 1) * t_dim1], ldt, &work[1], &n1, &scale, &ierr);
+
+/*        Estimate the reciprocal of the condition number of the cluster */
+/*        of eigenvalues. */
+
+	rnorm = slange_("F", &n1, &n2, &work[1], &n1, &work[1]);
+	if (rnorm == 0.f) {
+	    *s = 1.f;
+	} else {
+	    *s = scale / (sqrt(scale * scale / rnorm + rnorm) * sqrt(rnorm));
+	}
+    }
+
+    if (wantsp) {
+
+/*        Estimate sep(T11,T22). */
+
+	est = 0.f;
+	kase = 0;
+L30:
+	slacn2_(&nn, &work[nn + 1], &work[1], &iwork[1], &est, &kase, isave);
+	if (kase != 0) {
+	    if (kase == 1) {
+
+/*              Solve  T11*R - R*T22 = scale*X. */
+
+		strsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 + 
+			1 + (n1 + 1) * t_dim1], ldt, &work[1], &n1, &scale, &
+			ierr);
+	    } else {
+
+/*              Solve  T11'*R - R*T22' = scale*X. */
+
+		strsyl_("T", "T", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 + 
+			1 + (n1 + 1) * t_dim1], ldt, &work[1], &n1, &scale, &
+			ierr);
+	    }
+	    goto L30;
+	}
+
+	*sep = scale / est;
+    }
+
+L40:
+
+/*     Store the output eigenvalues in WR and WI. */
+
+    i__1 = *n;
+    for (k = 1; k <= i__1; ++k) {
+	wr[k] = t[k + k * t_dim1];
+	wi[k] = 0.f;
+/* L50: */
+    }
+    i__1 = *n - 1;
+    for (k = 1; k <= i__1; ++k) {
+	if (t[k + 1 + k * t_dim1] != 0.f) {
+	    wi[k] = sqrt((r__1 = t[k + (k + 1) * t_dim1], dabs(r__1))) * sqrt(
+		    (r__2 = t[k + 1 + k * t_dim1], dabs(r__2)));
+	    wi[k + 1] = -wi[k];
+	}
+/* L60: */
+    }
+
+    work[1] = (real) lwmin;
+    iwork[1] = liwmin;
+
+    return 0;
+
+/*     End of STRSEN */
+
+} /* strsen_ */