[] add metering mode to CLI

1 files changed, 484 insertions, 0 deletions

diff --git a/contrib/libs/clapack/ctgsna.c b/contrib/libs/clapack/ctgsna.c
new file mode 100644
index 0000000000..d235cdb719
--- /dev/null
+++ b/contrib/libs/clapack/ctgsna.c
@@ -0,0 +1,484 @@
+/* ctgsna.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 complex c_b19 = {1.f,0.f};
+static complex c_b20 = {0.f,0.f};
+static logical c_false = FALSE_;
+static integer c__3 = 3;
+
+/* Subroutine */ int ctgsna_(char *job, char *howmny, logical *select, 
+	integer *n, complex *a, integer *lda, complex *b, integer *ldb, 
+	complex *vl, integer *ldvl, complex *vr, integer *ldvr, real *s, real 
+	*dif, integer *mm, integer *m, complex *work, integer *lwork, integer 
+	*iwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, 
+	    vr_offset, i__1;
+    real r__1, r__2;
+    complex q__1;
+
+    /* Builtin functions */
+    double c_abs(complex *);
+
+    /* Local variables */
+    integer i__, k, n1, n2, ks;
+    real eps, cond;
+    integer ierr, ifst;
+    real lnrm;
+    complex yhax, yhbx;
+    integer ilst;
+    real rnrm, scale;
+    extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
+	    *, complex *, integer *);
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
+, complex *, integer *, complex *, integer *, complex *, complex *
+, integer *);
+    integer lwmin;
+    logical wants;
+    complex dummy[1];
+    extern doublereal scnrm2_(integer *, complex *, integer *), slapy2_(real *
+, real *);
+    complex dummy1[1];
+    extern /* Subroutine */ int slabad_(real *, real *);
+    extern doublereal slamch_(char *);
+    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
+	    *, integer *, complex *, integer *), ctgexc_(logical *, 
+	    logical *, integer *, complex *, integer *, complex *, integer *, 
+	    complex *, integer *, complex *, integer *, integer *, integer *, 
+	    integer *), xerbla_(char *, integer *);
+    real bignum;
+    logical wantbh, wantdf, somcon;
+    extern /* Subroutine */ int ctgsyl_(char *, integer *, integer *, integer 
+	    *, complex *, integer *, complex *, integer *, complex *, integer 
+	    *, complex *, integer *, complex *, integer *, complex *, integer 
+	    *, real *, real *, complex *, integer *, integer *, integer *);
+    real smlnum;
+    logical lquery;
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  CTGSNA estimates reciprocal condition numbers for specified */
+/*  eigenvalues and/or eigenvectors of a matrix pair (A, B). */
+
+/*  (A, B) must be in generalized Schur canonical form, that is, A and */
+/*  B are both upper triangular. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  JOB     (input) CHARACTER*1 */
+/*          Specifies whether condition numbers are required for */
+/*          eigenvalues (S) or eigenvectors (DIF): */
+/*          = 'E': for eigenvalues only (S); */
+/*          = 'V': for eigenvectors only (DIF); */
+/*          = 'B': for both eigenvalues and eigenvectors (S and DIF). */
+
+/*  HOWMNY  (input) CHARACTER*1 */
+/*          = 'A': compute condition numbers for all eigenpairs; */
+/*          = 'S': compute condition numbers for selected eigenpairs */
+/*                 specified by the array SELECT. */
+
+/*  SELECT  (input) LOGICAL array, dimension (N) */
+/*          If HOWMNY = 'S', SELECT specifies the eigenpairs for which */
+/*          condition numbers are required. To select condition numbers */
+/*          for the corresponding j-th eigenvalue and/or eigenvector, */
+/*          SELECT(j) must be set to .TRUE.. */
+/*          If HOWMNY = 'A', SELECT is not referenced. */
+
+/*  N       (input) INTEGER */
+/*          The order of the square matrix pair (A, B). N >= 0. */
+
+/*  A       (input) COMPLEX array, dimension (LDA,N) */
+/*          The upper triangular matrix A in the pair (A,B). */
+
+/*  LDA     (input) INTEGER */
+/*          The leading dimension of the array A. LDA >= max(1,N). */
+
+/*  B       (input) COMPLEX array, dimension (LDB,N) */
+/*          The upper triangular matrix B in the pair (A, B). */
+
+/*  LDB     (input) INTEGER */
+/*          The leading dimension of the array B. LDB >= max(1,N). */
+
+/*  VL      (input) COMPLEX array, dimension (LDVL,M) */
+/*          IF JOB = 'E' or 'B', VL must contain left eigenvectors of */
+/*          (A, B), corresponding to the eigenpairs specified by HOWMNY */
+/*          and SELECT.  The eigenvectors must be stored in consecutive */
+/*          columns of VL, as returned by CTGEVC. */
+/*          If JOB = 'V', VL is not referenced. */
+
+/*  LDVL    (input) INTEGER */
+/*          The leading dimension of the array VL. LDVL >= 1; and */
+/*          If JOB = 'E' or 'B', LDVL >= N. */
+
+/*  VR      (input) COMPLEX array, dimension (LDVR,M) */
+/*          IF JOB = 'E' or 'B', VR must contain right eigenvectors of */
+/*          (A, B), corresponding to the eigenpairs specified by HOWMNY */
+/*          and SELECT.  The eigenvectors must be stored in consecutive */
+/*          columns of VR, as returned by CTGEVC. */
+/*          If JOB = 'V', VR is not referenced. */
+
+/*  LDVR    (input) INTEGER */
+/*          The leading dimension of the array VR. LDVR >= 1; */
+/*          If JOB = 'E' or 'B', LDVR >= N. */
+
+/*  S       (output) REAL array, dimension (MM) */
+/*          If JOB = 'E' or 'B', the reciprocal condition numbers of the */
+/*          selected eigenvalues, stored in consecutive elements of the */
+/*          array. */
+/*          If JOB = 'V', S is not referenced. */
+
+/*  DIF     (output) REAL array, dimension (MM) */
+/*          If JOB = 'V' or 'B', the estimated reciprocal condition */
+/*          numbers of the selected eigenvectors, stored in consecutive */
+/*          elements of the array. */
+/*          If the eigenvalues cannot be reordered to compute DIF(j), */
+/*          DIF(j) is set to 0; this can only occur when the true value */
+/*          would be very small anyway. */
+/*          For each eigenvalue/vector specified by SELECT, DIF stores */
+/*          a Frobenius norm-based estimate of Difl. */
+/*          If JOB = 'E', DIF is not referenced. */
+
+/*  MM      (input) INTEGER */
+/*          The number of elements in the arrays S and DIF. MM >= M. */
+
+/*  M       (output) INTEGER */
+/*          The number of elements of the arrays S and DIF used to store */
+/*          the specified condition numbers; for each selected eigenvalue */
+/*          one element is used. If HOWMNY = 'A', M is set to N. */
+
+/*  WORK    (workspace/output) COMPLEX 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. LWORK >= max(1,N). */
+/*          If JOB = 'V' or 'B', LWORK >= max(1,2*N*N). */
+
+/*  IWORK   (workspace) INTEGER array, dimension (N+2) */
+/*          If JOB = 'E', IWORK is not referenced. */
+
+/*  INFO    (output) INTEGER */
+/*          = 0: Successful exit */
+/*          < 0: If INFO = -i, the i-th argument had an illegal value */
+
+/*  Further Details */
+/*  =============== */
+
+/*  The reciprocal of the condition number of the i-th generalized */
+/*  eigenvalue w = (a, b) is defined as */
+
+/*          S(I) = (|v'Au|**2 + |v'Bu|**2)**(1/2) / (norm(u)*norm(v)) */
+
+/*  where u and v are the right and left eigenvectors of (A, B) */
+/*  corresponding to w; |z| denotes the absolute value of the complex */
+/*  number, and norm(u) denotes the 2-norm of the vector u. The pair */
+/*  (a, b) corresponds to an eigenvalue w = a/b (= v'Au/v'Bu) of the */
+/*  matrix pair (A, B). If both a and b equal zero, then (A,B) is */
+/*  singular and S(I) = -1 is returned. */
+
+/*  An approximate error bound on the chordal distance between the i-th */
+/*  computed generalized eigenvalue w and the corresponding exact */
+/*  eigenvalue lambda is */
+
+/*          chord(w, lambda) <=   EPS * norm(A, B) / S(I), */
+
+/*  where EPS is the machine precision. */
+
+/*  The reciprocal of the condition number of the right eigenvector u */
+/*  and left eigenvector v corresponding to the generalized eigenvalue w */
+/*  is defined as follows. Suppose */
+
+/*                   (A, B) = ( a   *  ) ( b  *  )  1 */
+/*                            ( 0  A22 ),( 0 B22 )  n-1 */
+/*                              1  n-1     1 n-1 */
+
+/*  Then the reciprocal condition number DIF(I) is */
+
+/*          Difl[(a, b), (A22, B22)]  = sigma-min( Zl ) */
+
+/*  where sigma-min(Zl) denotes the smallest singular value of */
+
+/*         Zl = [ kron(a, In-1) -kron(1, A22) ] */
+/*              [ kron(b, In-1) -kron(1, B22) ]. */
+
+/*  Here In-1 is the identity matrix of size n-1 and X' is the conjugate */
+/*  transpose of X. kron(X, Y) is the Kronecker product between the */
+/*  matrices X and Y. */
+
+/*  We approximate the smallest singular value of Zl with an upper */
+/*  bound. This is done by CLATDF. */
+
+/*  An approximate error bound for a computed eigenvector VL(i) or */
+/*  VR(i) is given by */
+
+/*                      EPS * norm(A, B) / DIF(i). */
+
+/*  See ref. [2-3] for more details and further references. */
+
+/*  Based on contributions by */
+/*     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
+/*     Umea University, S-901 87 Umea, Sweden. */
+
+/*  References */
+/*  ========== */
+
+/*  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
+/*      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
+/*      M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
+/*      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
+
+/*  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
+/*      Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
+/*      Estimation: Theory, Algorithms and Software, Report */
+/*      UMINF - 94.04, Department of Computing Science, Umea University, */
+/*      S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. */
+/*      To appear in Numerical Algorithms, 1996. */
+
+/*  [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
+/*      for Solving the Generalized Sylvester Equation and Estimating the */
+/*      Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
+/*      Department of Computing Science, Umea University, S-901 87 Umea, */
+/*      Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
+/*      Note 75. */
+/*      To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996. */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Decode and test the input parameters */
+
+    /* Parameter adjustments */
+    --select;
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    vl_dim1 = *ldvl;
+    vl_offset = 1 + vl_dim1;
+    vl -= vl_offset;
+    vr_dim1 = *ldvr;
+    vr_offset = 1 + vr_dim1;
+    vr -= vr_offset;
+    --s;
+    --dif;
+    --work;
+    --iwork;
+
+    /* Function Body */
+    wantbh = lsame_(job, "B");
+    wants = lsame_(job, "E") || wantbh;
+    wantdf = lsame_(job, "V") || wantbh;
+
+    somcon = lsame_(howmny, "S");
+
+    *info = 0;
+    lquery = *lwork == -1;
+
+    if (! wants && ! wantdf) {
+	*info = -1;
+    } else if (! lsame_(howmny, "A") && ! somcon) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*lda < max(1,*n)) {
+	*info = -6;
+    } else if (*ldb < max(1,*n)) {
+	*info = -8;
+    } else if (wants && *ldvl < *n) {
+	*info = -10;
+    } else if (wants && *ldvr < *n) {
+	*info = -12;
+    } else {
+
+/*        Set M to the number of eigenpairs for which condition numbers */
+/*        are required, and test MM. */
+
+	if (somcon) {
+	    *m = 0;
+	    i__1 = *n;
+	    for (k = 1; k <= i__1; ++k) {
+		if (select[k]) {
+		    ++(*m);
+		}
+/* L10: */
+	    }
+	} else {
+	    *m = *n;
+	}
+
+	if (*n == 0) {
+	    lwmin = 1;
+	} else if (lsame_(job, "V") || lsame_(job, 
+		"B")) {
+	    lwmin = (*n << 1) * *n;
+	} else {
+	    lwmin = *n;
+	}
+	work[1].r = (real) lwmin, work[1].i = 0.f;
+
+	if (*mm < *m) {
+	    *info = -15;
+	} else if (*lwork < lwmin && ! lquery) {
+	    *info = -18;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CTGSNA", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+/*     Get machine constants */
+
+    eps = slamch_("P");
+    smlnum = slamch_("S") / eps;
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+    ks = 0;
+    i__1 = *n;
+    for (k = 1; k <= i__1; ++k) {
+
+/*        Determine whether condition numbers are required for the k-th */
+/*        eigenpair. */
+
+	if (somcon) {
+	    if (! select[k]) {
+		goto L20;
+	    }
+	}
+
+	++ks;
+
+	if (wants) {
+
+/*           Compute the reciprocal condition number of the k-th */
+/*           eigenvalue. */
+
+	    rnrm = scnrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
+	    lnrm = scnrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
+	    cgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1 + 1]
+, &c__1, &c_b20, &work[1], &c__1);
+	    cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1);
+	    yhax.r = q__1.r, yhax.i = q__1.i;
+	    cgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1 + 1]
+, &c__1, &c_b20, &work[1], &c__1);
+	    cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1);
+	    yhbx.r = q__1.r, yhbx.i = q__1.i;
+	    r__1 = c_abs(&yhax);
+	    r__2 = c_abs(&yhbx);
+	    cond = slapy2_(&r__1, &r__2);
+	    if (cond == 0.f) {
+		s[ks] = -1.f;
+	    } else {
+		s[ks] = cond / (rnrm * lnrm);
+	    }
+	}
+
+	if (wantdf) {
+	    if (*n == 1) {
+		r__1 = c_abs(&a[a_dim1 + 1]);
+		r__2 = c_abs(&b[b_dim1 + 1]);
+		dif[ks] = slapy2_(&r__1, &r__2);
+	    } else {
+
+/*              Estimate the reciprocal condition number of the k-th */
+/*              eigenvectors. */
+
+/*              Copy the matrix (A, B) to the array WORK and move the */
+/*              (k,k)th pair to the (1,1) position. */
+
+		clacpy_("Full", n, n, &a[a_offset], lda, &work[1], n);
+		clacpy_("Full", n, n, &b[b_offset], ldb, &work[*n * *n + 1], 
+			n);
+		ifst = k;
+		ilst = 1;
+
+		ctgexc_(&c_false, &c_false, n, &work[1], n, &work[*n * *n + 1]
+, n, dummy, &c__1, dummy1, &c__1, &ifst, &ilst, &ierr)
+			;
+
+		if (ierr > 0) {
+
+/*                 Ill-conditioned problem - swap rejected. */
+
+		    dif[ks] = 0.f;
+		} else {
+
+/*                 Reordering successful, solve generalized Sylvester */
+/*                 equation for R and L, */
+/*                            A22 * R - L * A11 = A12 */
+/*                            B22 * R - L * B11 = B12, */
+/*                 and compute estimate of Difl[(A11,B11), (A22, B22)]. */
+
+		    n1 = 1;
+		    n2 = *n - n1;
+		    i__ = *n * *n + 1;
+		    ctgsyl_("N", &c__3, &n2, &n1, &work[*n * n1 + n1 + 1], n, 
+			    &work[1], n, &work[n1 + 1], n, &work[*n * n1 + n1 
+			    + i__], n, &work[i__], n, &work[n1 + i__], n, &
+			    scale, &dif[ks], dummy, &c__1, &iwork[1], &ierr);
+		}
+	    }
+	}
+
+L20:
+	;
+    }
+    work[1].r = (real) lwmin, work[1].i = 0.f;
+    return 0;
+
+/*     End of CTGSNA */
+
+} /* ctgsna_ */