[] add metering mode to CLI

1 files changed, 484 insertions, 0 deletions

diff --git a/contrib/libs/clapack/shseqr.c b/contrib/libs/clapack/shseqr.c
new file mode 100644
index 0000000000..533949dfd5
--- /dev/null
+++ b/contrib/libs/clapack/shseqr.c
@@ -0,0 +1,484 @@
+/* shseqr.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_b11 = 0.f;
+static real c_b12 = 1.f;
+static integer c__12 = 12;
+static integer c__2 = 2;
+static integer c__49 = 49;
+
+/* Subroutine */ int shseqr_(char *job, char *compz, integer *n, integer *ilo, 
+	 integer *ihi, real *h__, integer *ldh, real *wr, real *wi, real *z__, 
+	 integer *ldz, real *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    address a__1[2];
+    integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2[2], i__3;
+    real r__1;
+    char ch__1[2];
+
+    /* Builtin functions */
+    /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
+
+    /* Local variables */
+    integer i__;
+    real hl[2401]	/* was [49][49] */;
+    integer kbot, nmin;
+    extern logical lsame_(char *, char *);
+    logical initz;
+    real workl[49];
+    logical wantt, wantz;
+    extern /* Subroutine */ int slaqr0_(logical *, logical *, integer *, 
+	    integer *, integer *, real *, integer *, real *, real *, integer *
+, integer *, real *, integer *, real *, integer *, integer *), 
+	    xerbla_(char *, integer *);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *);
+    extern /* Subroutine */ int slahqr_(logical *, logical *, integer *, 
+	    integer *, integer *, real *, integer *, real *, real *, integer *
+, integer *, real *, integer *, integer *), slacpy_(char *, 
+	    integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
+	    real *, integer *);
+    logical lquery;
+
+
+/*  -- LAPACK driver routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+/*     Purpose */
+/*     ======= */
+
+/*     SHSEQR computes the eigenvalues of a Hessenberg matrix H */
+/*     and, optionally, the matrices T and Z from the Schur decomposition */
+/*     H = Z T Z**T, where T is an upper quasi-triangular matrix (the */
+/*     Schur form), and Z is the orthogonal matrix of Schur vectors. */
+
+/*     Optionally Z may be postmultiplied into an input orthogonal */
+/*     matrix Q so that this routine can give the Schur factorization */
+/*     of a matrix A which has been reduced to the Hessenberg form H */
+/*     by the orthogonal matrix Q:  A = Q*H*Q**T = (QZ)*T*(QZ)**T. */
+
+/*     Arguments */
+/*     ========= */
+
+/*     JOB   (input) CHARACTER*1 */
+/*           = 'E':  compute eigenvalues only; */
+/*           = 'S':  compute eigenvalues and the Schur form T. */
+
+/*     COMPZ (input) CHARACTER*1 */
+/*           = 'N':  no Schur vectors are computed; */
+/*           = 'I':  Z is initialized to the unit matrix and the matrix Z */
+/*                   of Schur vectors of H is returned; */
+/*           = 'V':  Z must contain an orthogonal matrix Q on entry, and */
+/*                   the product Q*Z is returned. */
+
+/*     N     (input) INTEGER */
+/*           The order of the matrix H.  N .GE. 0. */
+
+/*     ILO   (input) INTEGER */
+/*     IHI   (input) INTEGER */
+/*           It is assumed that H is already upper triangular in rows */
+/*           and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
+/*           set by a previous call to SGEBAL, and then passed to SGEHRD */
+/*           when the matrix output by SGEBAL is reduced to Hessenberg */
+/*           form. Otherwise ILO and IHI should be set to 1 and N */
+/*           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. */
+/*           If N = 0, then ILO = 1 and IHI = 0. */
+
+/*     H     (input/output) REAL array, dimension (LDH,N) */
+/*           On entry, the upper Hessenberg matrix H. */
+/*           On exit, if INFO = 0 and JOB = 'S', then H contains the */
+/*           upper quasi-triangular matrix T from the Schur decomposition */
+/*           (the Schur form); 2-by-2 diagonal blocks (corresponding to */
+/*           complex conjugate pairs of eigenvalues) are returned in */
+/*           standard form, with H(i,i) = H(i+1,i+1) and */
+/*           H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and JOB = 'E', the */
+/*           contents of H are unspecified on exit.  (The output value of */
+/*           H when INFO.GT.0 is given under the description of INFO */
+/*           below.) */
+
+/*           Unlike earlier versions of SHSEQR, this subroutine may */
+/*           explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 */
+/*           or j = IHI+1, IHI+2, ... N. */
+
+/*     LDH   (input) INTEGER */
+/*           The leading dimension of the array H. LDH .GE. max(1,N). */
+
+/*     WR    (output) REAL array, dimension (N) */
+/*     WI    (output) REAL array, dimension (N) */
+/*           The real and imaginary parts, respectively, of the computed */
+/*           eigenvalues. If two eigenvalues are computed as a complex */
+/*           conjugate pair, they are stored in consecutive elements of */
+/*           WR and WI, say the i-th and (i+1)th, with WI(i) .GT. 0 and */
+/*           WI(i+1) .LT. 0. If JOB = 'S', the eigenvalues are stored in */
+/*           the same order as on the diagonal of the Schur form returned */
+/*           in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 */
+/*           diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and */
+/*           WI(i+1) = -WI(i). */
+
+/*     Z     (input/output) REAL array, dimension (LDZ,N) */
+/*           If COMPZ = 'N', Z is not referenced. */
+/*           If COMPZ = 'I', on entry Z need not be set and on exit, */
+/*           if INFO = 0, Z contains the orthogonal matrix Z of the Schur */
+/*           vectors of H.  If COMPZ = 'V', on entry Z must contain an */
+/*           N-by-N matrix Q, which is assumed to be equal to the unit */
+/*           matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, */
+/*           if INFO = 0, Z contains Q*Z. */
+/*           Normally Q is the orthogonal matrix generated by SORGHR */
+/*           after the call to SGEHRD which formed the Hessenberg matrix */
+/*           H. (The output value of Z when INFO.GT.0 is given under */
+/*           the description of INFO below.) */
+
+/*     LDZ   (input) INTEGER */
+/*           The leading dimension of the array Z.  if COMPZ = 'I' or */
+/*           COMPZ = 'V', then LDZ.GE.MAX(1,N).  Otherwize, LDZ.GE.1. */
+
+/*     WORK  (workspace/output) REAL array, dimension (LWORK) */
+/*           On exit, if INFO = 0, WORK(1) returns an estimate of */
+/*           the optimal value for LWORK. */
+
+/*     LWORK (input) INTEGER */
+/*           The dimension of the array WORK.  LWORK .GE. max(1,N) */
+/*           is sufficient and delivers very good and sometimes */
+/*           optimal performance.  However, LWORK as large as 11*N */
+/*           may be required for optimal performance.  A workspace */
+/*           query is recommended to determine the optimal workspace */
+/*           size. */
+
+/*           If LWORK = -1, then SHSEQR does a workspace query. */
+/*           In this case, SHSEQR checks the input parameters and */
+/*           estimates the optimal workspace size for the given */
+/*           values of N, ILO and IHI.  The estimate is returned */
+/*           in WORK(1).  No error message related to LWORK is */
+/*           issued by XERBLA.  Neither H nor Z are accessed. */
+
+
+/*     INFO  (output) INTEGER */
+/*             =  0:  successful exit */
+/*           .LT. 0:  if INFO = -i, the i-th argument had an illegal */
+/*                    value */
+/*           .GT. 0:  if INFO = i, SHSEQR failed to compute all of */
+/*                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR */
+/*                and WI contain those eigenvalues which have been */
+/*                successfully computed.  (Failures are rare.) */
+
+/*                If INFO .GT. 0 and JOB = 'E', then on exit, the */
+/*                remaining unconverged eigenvalues are the eigen- */
+/*                values of the upper Hessenberg matrix rows and */
+/*                columns ILO through INFO of the final, output */
+/*                value of H. */
+
+/*                If INFO .GT. 0 and JOB   = 'S', then on exit */
+
+/*           (*)  (initial value of H)*U  = U*(final value of H) */
+
+/*                where U is an orthogonal matrix.  The final */
+/*                value of H is upper Hessenberg and quasi-triangular */
+/*                in rows and columns INFO+1 through IHI. */
+
+/*                If INFO .GT. 0 and COMPZ = 'V', then on exit */
+
+/*                  (final value of Z)  =  (initial value of Z)*U */
+
+/*                where U is the orthogonal matrix in (*) (regard- */
+/*                less of the value of JOB.) */
+
+/*                If INFO .GT. 0 and COMPZ = 'I', then on exit */
+/*                      (final value of Z)  = U */
+/*                where U is the orthogonal matrix in (*) (regard- */
+/*                less of the value of JOB.) */
+
+/*                If INFO .GT. 0 and COMPZ = 'N', then Z is not */
+/*                accessed. */
+
+/*     ================================================================ */
+/*             Default values supplied by */
+/*             ILAENV(ISPEC,'SHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). */
+/*             It is suggested that these defaults be adjusted in order */
+/*             to attain best performance in each particular */
+/*             computational environment. */
+
+/*            ISPEC=12: The SLAHQR vs SLAQR0 crossover point. */
+/*                      Default: 75. (Must be at least 11.) */
+
+/*            ISPEC=13: Recommended deflation window size. */
+/*                      This depends on ILO, IHI and NS.  NS is the */
+/*                      number of simultaneous shifts returned */
+/*                      by ILAENV(ISPEC=15).  (See ISPEC=15 below.) */
+/*                      The default for (IHI-ILO+1).LE.500 is NS. */
+/*                      The default for (IHI-ILO+1).GT.500 is 3*NS/2. */
+
+/*            ISPEC=14: Nibble crossover point. (See IPARMQ for */
+/*                      details.)  Default: 14% of deflation window */
+/*                      size. */
+
+/*            ISPEC=15: Number of simultaneous shifts in a multishift */
+/*                      QR iteration. */
+
+/*                      If IHI-ILO+1 is ... */
+
+/*                      greater than      ...but less    ... the */
+/*                      or equal to ...      than        default is */
+
+/*                           1               30          NS =   2(+) */
+/*                          30               60          NS =   4(+) */
+/*                          60              150          NS =  10(+) */
+/*                         150              590          NS =  ** */
+/*                         590             3000          NS =  64 */
+/*                        3000             6000          NS = 128 */
+/*                        6000             infinity      NS = 256 */
+
+/*                  (+)  By default some or all matrices of this order */
+/*                       are passed to the implicit double shift routine */
+/*                       SLAHQR and this parameter is ignored.  See */
+/*                       ISPEC=12 above and comments in IPARMQ for */
+/*                       details. */
+
+/*                 (**)  The asterisks (**) indicate an ad-hoc */
+/*                       function of N increasing from 10 to 64. */
+
+/*            ISPEC=16: Select structured matrix multiply. */
+/*                      If the number of simultaneous shifts (specified */
+/*                      by ISPEC=15) is less than 14, then the default */
+/*                      for ISPEC=16 is 0.  Otherwise the default for */
+/*                      ISPEC=16 is 2. */
+
+/*     ================================================================ */
+/*     Based on contributions by */
+/*        Karen Braman and Ralph Byers, Department of Mathematics, */
+/*        University of Kansas, USA */
+
+/*     ================================================================ */
+/*     References: */
+/*       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
+/*       Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */
+/*       Performance, SIAM Journal of Matrix Analysis, volume 23, pages */
+/*       929--947, 2002. */
+
+/*       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
+/*       Algorithm Part II: Aggressive Early Deflation, SIAM Journal */
+/*       of Matrix Analysis, volume 23, pages 948--973, 2002. */
+
+/*     ================================================================ */
+/*     .. Parameters .. */
+
+/*     ==== Matrices of order NTINY or smaller must be processed by */
+/*     .    SLAHQR because of insufficient subdiagonal scratch space. */
+/*     .    (This is a hard limit.) ==== */
+
+/*     ==== NL allocates some local workspace to help small matrices */
+/*     .    through a rare SLAHQR failure.  NL .GT. NTINY = 11 is */
+/*     .    required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom- */
+/*     .    mended.  (The default value of NMIN is 75.)  Using NL = 49 */
+/*     .    allows up to six simultaneous shifts and a 16-by-16 */
+/*     .    deflation window.  ==== */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     ==== Decode and check the input parameters. ==== */
+
+    /* Parameter adjustments */
+    h_dim1 = *ldh;
+    h_offset = 1 + h_dim1;
+    h__ -= h_offset;
+    --wr;
+    --wi;
+    z_dim1 = *ldz;
+    z_offset = 1 + z_dim1;
+    z__ -= z_offset;
+    --work;
+
+    /* Function Body */
+    wantt = lsame_(job, "S");
+    initz = lsame_(compz, "I");
+    wantz = initz || lsame_(compz, "V");
+    work[1] = (real) max(1,*n);
+    lquery = *lwork == -1;
+
+    *info = 0;
+    if (! lsame_(job, "E") && ! wantt) {
+	*info = -1;
+    } else if (! lsame_(compz, "N") && ! wantz) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*ilo < 1 || *ilo > max(1,*n)) {
+	*info = -4;
+    } else if (*ihi < min(*ilo,*n) || *ihi > *n) {
+	*info = -5;
+    } else if (*ldh < max(1,*n)) {
+	*info = -7;
+    } else if (*ldz < 1 || wantz && *ldz < max(1,*n)) {
+	*info = -11;
+    } else if (*lwork < max(1,*n) && ! lquery) {
+	*info = -13;
+    }
+
+    if (*info != 0) {
+
+/*        ==== Quick return in case of invalid argument. ==== */
+
+	i__1 = -(*info);
+	xerbla_("SHSEQR", &i__1);
+	return 0;
+
+    } else if (*n == 0) {
+
+/*        ==== Quick return in case N = 0; nothing to do. ==== */
+
+	return 0;
+
+    } else if (lquery) {
+
+/*        ==== Quick return in case of a workspace query ==== */
+
+	slaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[
+		1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
+/*        ==== Ensure reported workspace size is backward-compatible with */
+/*        .    previous LAPACK versions. ==== */
+/* Computing MAX */
+	r__1 = (real) max(1,*n);
+	work[1] = dmax(r__1,work[1]);
+	return 0;
+
+    } else {
+
+/*        ==== copy eigenvalues isolated by SGEBAL ==== */
+
+	i__1 = *ilo - 1;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    wr[i__] = h__[i__ + i__ * h_dim1];
+	    wi[i__] = 0.f;
+/* L10: */
+	}
+	i__1 = *n;
+	for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
+	    wr[i__] = h__[i__ + i__ * h_dim1];
+	    wi[i__] = 0.f;
+/* L20: */
+	}
+
+/*        ==== Initialize Z, if requested ==== */
+
+	if (initz) {
+	    slaset_("A", n, n, &c_b11, &c_b12, &z__[z_offset], ldz)
+		    ;
+	}
+
+/*        ==== Quick return if possible ==== */
+
+	if (*ilo == *ihi) {
+	    wr[*ilo] = h__[*ilo + *ilo * h_dim1];
+	    wi[*ilo] = 0.f;
+	    return 0;
+	}
+
+/*        ==== SLAHQR/SLAQR0 crossover point ==== */
+
+/* Writing concatenation */
+	i__2[0] = 1, a__1[0] = job;
+	i__2[1] = 1, a__1[1] = compz;
+	s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
+	nmin = ilaenv_(&c__12, "SHSEQR", ch__1, n, ilo, ihi, lwork);
+	nmin = max(11,nmin);
+
+/*        ==== SLAQR0 for big matrices; SLAHQR for small ones ==== */
+
+	if (*n > nmin) {
+	    slaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], 
+		    &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, 
+		    info);
+	} else {
+
+/*           ==== Small matrix ==== */
+
+	    slahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], 
+		    &wi[1], ilo, ihi, &z__[z_offset], ldz, info);
+
+	    if (*info > 0) {
+
+/*              ==== A rare SLAHQR failure!  SLAQR0 sometimes succeeds */
+/*              .    when SLAHQR fails. ==== */
+
+		kbot = *info;
+
+		if (*n >= 49) {
+
+/*                 ==== Larger matrices have enough subdiagonal scratch */
+/*                 .    space to call SLAQR0 directly. ==== */
+
+		    slaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset], 
+			    ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], 
+			    ldz, &work[1], lwork, info);
+
+		} else {
+
+/*                 ==== Tiny matrices don't have enough subdiagonal */
+/*                 .    scratch space to benefit from SLAQR0.  Hence, */
+/*                 .    tiny matrices must be copied into a larger */
+/*                 .    array before calling SLAQR0. ==== */
+
+		    slacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
+		    hl[*n + 1 + *n * 49 - 50] = 0.f;
+		    i__1 = 49 - *n;
+		    slaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) *
+			     49 - 49], &c__49);
+		    slaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, &
+			    wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, 
+			    workl, &c__49, info);
+		    if (wantt || *info != 0) {
+			slacpy_("A", n, n, hl, &c__49, &h__[h_offset], ldh);
+		    }
+		}
+	    }
+	}
+
+/*        ==== Clear out the trash, if necessary. ==== */
+
+	if ((wantt || *info != 0) && *n > 2) {
+	    i__1 = *n - 2;
+	    i__3 = *n - 2;
+	    slaset_("L", &i__1, &i__3, &c_b11, &c_b11, &h__[h_dim1 + 3], ldh);
+	}
+
+/*        ==== Ensure reported workspace size is backward-compatible with */
+/*        .    previous LAPACK versions. ==== */
+
+/* Computing MAX */
+	r__1 = (real) max(1,*n);
+	work[1] = dmax(r__1,work[1]);
+    }
+
+/*     ==== End of SHSEQR ==== */
+
+    return 0;
+} /* shseqr_ */