[] add metering mode to CLI

1 files changed, 488 insertions, 0 deletions

diff --git a/contrib/libs/clapack/sgelsy.c b/contrib/libs/clapack/sgelsy.c
new file mode 100644
index 0000000000..c910c23969
--- /dev/null
+++ b/contrib/libs/clapack/sgelsy.c
@@ -0,0 +1,488 @@
+/* sgelsy.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 integer c_n1 = -1;
+static integer c__0 = 0;
+static real c_b31 = 0.f;
+static integer c__2 = 2;
+static real c_b54 = 1.f;
+
+/* Subroutine */ int sgelsy_(integer *m, integer *n, integer *nrhs, real *a, 
+	integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond, 
+	integer *rank, real *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
+    real r__1, r__2;
+
+    /* Local variables */
+    integer i__, j;
+    real c1, c2, s1, s2;
+    integer nb, mn, nb1, nb2, nb3, nb4;
+    real anrm, bnrm, smin, smax;
+    integer iascl, ibscl, ismin, ismax;
+    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
+	    integer *);
+    real wsize;
+    extern /* Subroutine */ int strsm_(char *, char *, char *, char *, 
+	    integer *, integer *, real *, real *, integer *, real *, integer *
+), slaic1_(integer *, integer *, 
+	    real *, real *, real *, real *, real *, real *, real *), sgeqp3_(
+	    integer *, integer *, real *, integer *, integer *, real *, real *
+, integer *, integer *), slabad_(real *, real *);
+    extern doublereal slamch_(char *), slange_(char *, integer *, 
+	    integer *, real *, integer *, real *);
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *);
+    real bignum;
+    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
+	    real *, integer *, integer *, real *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
+	    real *, integer *);
+    integer lwkmin;
+    real sminpr, smaxpr, smlnum;
+    integer lwkopt;
+    logical lquery;
+    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
+	    integer *, real *, integer *, real *, real *, integer *, real *, 
+	    integer *, integer *), sormrz_(char *, char *, 
+	    integer *, integer *, integer *, integer *, real *, integer *, 
+	    real *, real *, integer *, real *, integer *, integer *), stzrzf_(integer *, integer *, real *, integer *, real *, 
+	    real *, integer *, integer *);
+
+
+/*  -- LAPACK driver routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  SGELSY computes the minimum-norm solution to a real linear least */
+/*  squares problem: */
+/*      minimize || A * X - B || */
+/*  using a complete orthogonal factorization of A.  A is an M-by-N */
+/*  matrix which may be rank-deficient. */
+
+/*  Several right hand side vectors b and solution vectors x can be */
+/*  handled in a single call; they are stored as the columns of the */
+/*  M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
+/*  matrix X. */
+
+/*  The routine first computes a QR factorization with column pivoting: */
+/*      A * P = Q * [ R11 R12 ] */
+/*                  [  0  R22 ] */
+/*  with R11 defined as the largest leading submatrix whose estimated */
+/*  condition number is less than 1/RCOND.  The order of R11, RANK, */
+/*  is the effective rank of A. */
+
+/*  Then, R22 is considered to be negligible, and R12 is annihilated */
+/*  by orthogonal transformations from the right, arriving at the */
+/*  complete orthogonal factorization: */
+/*     A * P = Q * [ T11 0 ] * Z */
+/*                 [  0  0 ] */
+/*  The minimum-norm solution is then */
+/*     X = P * Z' [ inv(T11)*Q1'*B ] */
+/*                [        0       ] */
+/*  where Q1 consists of the first RANK columns of Q. */
+
+/*  This routine is basically identical to the original xGELSX except */
+/*  three differences: */
+/*    o The call to the subroutine xGEQPF has been substituted by the */
+/*      the call to the subroutine xGEQP3. This subroutine is a Blas-3 */
+/*      version of the QR factorization with column pivoting. */
+/*    o Matrix B (the right hand side) is updated with Blas-3. */
+/*    o The permutation of matrix B (the right hand side) is faster and */
+/*      more simple. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  M       (input) INTEGER */
+/*          The number of rows of the matrix A.  M >= 0. */
+
+/*  N       (input) INTEGER */
+/*          The number of columns of the matrix A.  N >= 0. */
+
+/*  NRHS    (input) INTEGER */
+/*          The number of right hand sides, i.e., the number of */
+/*          columns of matrices B and X. NRHS >= 0. */
+
+/*  A       (input/output) REAL array, dimension (LDA,N) */
+/*          On entry, the M-by-N matrix A. */
+/*          On exit, A has been overwritten by details of its */
+/*          complete orthogonal factorization. */
+
+/*  LDA     (input) INTEGER */
+/*          The leading dimension of the array A.  LDA >= max(1,M). */
+
+/*  B       (input/output) REAL array, dimension (LDB,NRHS) */
+/*          On entry, the M-by-NRHS right hand side matrix B. */
+/*          On exit, the N-by-NRHS solution matrix X. */
+
+/*  LDB     (input) INTEGER */
+/*          The leading dimension of the array B. LDB >= max(1,M,N). */
+
+/*  JPVT    (input/output) INTEGER array, dimension (N) */
+/*          On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
+/*          to the front of AP, otherwise column i is a free column. */
+/*          On exit, if JPVT(i) = k, then the i-th column of AP */
+/*          was the k-th column of A. */
+
+/*  RCOND   (input) REAL */
+/*          RCOND is used to determine the effective rank of A, which */
+/*          is defined as the order of the largest leading triangular */
+/*          submatrix R11 in the QR factorization with pivoting of A, */
+/*          whose estimated condition number < 1/RCOND. */
+
+/*  RANK    (output) INTEGER */
+/*          The effective rank of A, i.e., the order of the submatrix */
+/*          R11.  This is the same as the order of the submatrix T11 */
+/*          in the complete orthogonal factorization of A. */
+
+/*  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. */
+/*          The unblocked strategy requires that: */
+/*             LWORK >= MAX( MN+3*N+1, 2*MN+NRHS ), */
+/*          where MN = min( M, N ). */
+/*          The block algorithm requires that: */
+/*             LWORK >= MAX( MN+2*N+NB*(N+1), 2*MN+NB*NRHS ), */
+/*          where NB is an upper bound on the blocksize returned */
+/*          by ILAENV for the routines SGEQP3, STZRZF, STZRQF, SORMQR, */
+/*          and SORMRZ. */
+
+/*          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. */
+
+/*  INFO    (output) INTEGER */
+/*          = 0: successful exit */
+/*          < 0: If INFO = -i, the i-th argument had an illegal value. */
+
+/*  Further Details */
+/*  =============== */
+
+/*  Based on contributions by */
+/*    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */
+/*    E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
+/*    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    --jpvt;
+    --work;
+
+    /* Function Body */
+    mn = min(*m,*n);
+    ismin = mn + 1;
+    ismax = (mn << 1) + 1;
+
+/*     Test the input arguments. */
+
+    *info = 0;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*nrhs < 0) {
+	*info = -3;
+    } else if (*lda < max(1,*m)) {
+	*info = -5;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = max(1,*m);
+	if (*ldb < max(i__1,*n)) {
+	    *info = -7;
+	}
+    }
+
+/*     Figure out optimal block size */
+
+    if (*info == 0) {
+	if (mn == 0 || *nrhs == 0) {
+	    lwkmin = 1;
+	    lwkopt = 1;
+	} else {
+	    nb1 = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1);
+	    nb2 = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1);
+	    nb3 = ilaenv_(&c__1, "SORMQR", " ", m, n, nrhs, &c_n1);
+	    nb4 = ilaenv_(&c__1, "SORMRQ", " ", m, n, nrhs, &c_n1);
+/* Computing MAX */
+	    i__1 = max(nb1,nb2), i__1 = max(i__1,nb3);
+	    nb = max(i__1,nb4);
+/* Computing MAX */
+	    i__1 = mn << 1, i__2 = *n + 1, i__1 = max(i__1,i__2), i__2 = mn + 
+		    *nrhs;
+	    lwkmin = mn + max(i__1,i__2);
+/* Computing MAX */
+	    i__1 = lwkmin, i__2 = mn + (*n << 1) + nb * (*n + 1), i__1 = max(
+		    i__1,i__2), i__2 = (mn << 1) + nb * *nrhs;
+	    lwkopt = max(i__1,i__2);
+	}
+	work[1] = (real) lwkopt;
+
+	if (*lwork < lwkmin && ! lquery) {
+	    *info = -12;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("SGELSY", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (mn == 0 || *nrhs == 0) {
+	*rank = 0;
+	return 0;
+    }
+
+/*     Get machine parameters */
+
+    smlnum = slamch_("S") / slamch_("P");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+
+/*     Scale A, B if max entries outside range [SMLNUM,BIGNUM] */
+
+    anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]);
+    iascl = 0;
+    if (anrm > 0.f && anrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 1;
+    } else if (anrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 2;
+    } else if (anrm == 0.f) {
+
+/*        Matrix all zero. Return zero solution. */
+
+	i__1 = max(*m,*n);
+	slaset_("F", &i__1, nrhs, &c_b31, &c_b31, &b[b_offset], ldb);
+	*rank = 0;
+	goto L70;
+    }
+
+    bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
+    ibscl = 0;
+    if (bnrm > 0.f && bnrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	slascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, 
+		 info);
+	ibscl = 1;
+    } else if (bnrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, 
+		 info);
+	ibscl = 2;
+    }
+
+/*     Compute QR factorization with column pivoting of A: */
+/*        A * P = Q * R */
+
+    i__1 = *lwork - mn;
+    sgeqp3_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &i__1, 
+	     info);
+    wsize = mn + work[mn + 1];
+
+/*     workspace: MN+2*N+NB*(N+1). */
+/*     Details of Householder rotations stored in WORK(1:MN). */
+
+/*     Determine RANK using incremental condition estimation */
+
+    work[ismin] = 1.f;
+    work[ismax] = 1.f;
+    smax = (r__1 = a[a_dim1 + 1], dabs(r__1));
+    smin = smax;
+    if ((r__1 = a[a_dim1 + 1], dabs(r__1)) == 0.f) {
+	*rank = 0;
+	i__1 = max(*m,*n);
+	slaset_("F", &i__1, nrhs, &c_b31, &c_b31, &b[b_offset], ldb);
+	goto L70;
+    } else {
+	*rank = 1;
+    }
+
+L10:
+    if (*rank < mn) {
+	i__ = *rank + 1;
+	slaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
+		i__ + i__ * a_dim1], &sminpr, &s1, &c1);
+	slaic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
+		i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
+
+	if (smaxpr * *rcond <= sminpr) {
+	    i__1 = *rank;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		work[ismin + i__ - 1] = s1 * work[ismin + i__ - 1];
+		work[ismax + i__ - 1] = s2 * work[ismax + i__ - 1];
+/* L20: */
+	    }
+	    work[ismin + *rank] = c1;
+	    work[ismax + *rank] = c2;
+	    smin = sminpr;
+	    smax = smaxpr;
+	    ++(*rank);
+	    goto L10;
+	}
+    }
+
+/*     workspace: 3*MN. */
+
+/*     Logically partition R = [ R11 R12 ] */
+/*                             [  0  R22 ] */
+/*     where R11 = R(1:RANK,1:RANK) */
+
+/*     [R11,R12] = [ T11, 0 ] * Y */
+
+    if (*rank < *n) {
+	i__1 = *lwork - (mn << 1);
+	stzrzf_(rank, n, &a[a_offset], lda, &work[mn + 1], &work[(mn << 1) + 
+		1], &i__1, info);
+    }
+
+/*     workspace: 2*MN. */
+/*     Details of Householder rotations stored in WORK(MN+1:2*MN) */
+
+/*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
+
+    i__1 = *lwork - (mn << 1);
+    sormqr_("Left", "Transpose", m, nrhs, &mn, &a[a_offset], lda, &work[1], &
+	    b[b_offset], ldb, &work[(mn << 1) + 1], &i__1, info);
+/* Computing MAX */
+    r__1 = wsize, r__2 = (mn << 1) + work[(mn << 1) + 1];
+    wsize = dmax(r__1,r__2);
+
+/*     workspace: 2*MN+NB*NRHS. */
+
+/*     B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
+
+    strsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b54, &
+	    a[a_offset], lda, &b[b_offset], ldb);
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *n;
+	for (i__ = *rank + 1; i__ <= i__2; ++i__) {
+	    b[i__ + j * b_dim1] = 0.f;
+/* L30: */
+	}
+/* L40: */
+    }
+
+/*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) */
+
+    if (*rank < *n) {
+	i__1 = *n - *rank;
+	i__2 = *lwork - (mn << 1);
+	sormrz_("Left", "Transpose", n, nrhs, rank, &i__1, &a[a_offset], lda, 
+		&work[mn + 1], &b[b_offset], ldb, &work[(mn << 1) + 1], &i__2, 
+		 info);
+    }
+
+/*     workspace: 2*MN+NRHS. */
+
+/*     B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    work[jpvt[i__]] = b[i__ + j * b_dim1];
+/* L50: */
+	}
+	scopy_(n, &work[1], &c__1, &b[j * b_dim1 + 1], &c__1);
+/* L60: */
+    }
+
+/*     workspace: N. */
+
+/*     Undo scaling */
+
+    if (iascl == 1) {
+	slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, 
+		 info);
+	slascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset], 
+		lda, info);
+    } else if (iascl == 2) {
+	slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, 
+		 info);
+	slascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset], 
+		lda, info);
+    }
+    if (ibscl == 1) {
+	slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, 
+		 info);
+    } else if (ibscl == 2) {
+	slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, 
+		 info);
+    }
+
+L70:
+    work[1] = (real) lwkopt;
+
+    return 0;
+
+/*     End of SGELSY */
+
+} /* sgelsy_ */