[] add metering mode to CLI

1 files changed, 515 insertions, 0 deletions

diff --git a/contrib/libs/clapack/dpbsvx.c b/contrib/libs/clapack/dpbsvx.c
new file mode 100644
index 0000000000..5ba6e225a3
--- /dev/null
+++ b/contrib/libs/clapack/dpbsvx.c
@@ -0,0 +1,515 @@
+/* dpbsvx.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;
+
+/* Subroutine */ int dpbsvx_(char *fact, char *uplo, integer *n, integer *kd, 
+	integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, 
+	integer *ldafb, char *equed, doublereal *s, doublereal *b, integer *
+	ldb, doublereal *x, integer *ldx, doublereal *rcond, doublereal *ferr, 
+	 doublereal *berr, doublereal *work, integer *iwork, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 
+	    x_dim1, x_offset, i__1, i__2;
+    doublereal d__1, d__2;
+
+    /* Local variables */
+    integer i__, j, j1, j2;
+    doublereal amax, smin, smax;
+    extern logical lsame_(char *, char *);
+    doublereal scond, anorm;
+    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *);
+    logical equil, rcequ, upper;
+    extern doublereal dlamch_(char *), dlansb_(char *, char *, 
+	    integer *, integer *, doublereal *, integer *, doublereal *);
+    extern /* Subroutine */ int dpbcon_(char *, integer *, integer *, 
+	    doublereal *, integer *, doublereal *, doublereal *, doublereal *, 
+	     integer *, integer *), dlaqsb_(char *, integer *, 
+	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
+	    doublereal *, char *);
+    logical nofact;
+    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
+	    doublereal *, integer *, doublereal *, integer *), 
+	    xerbla_(char *, integer *), dpbequ_(char *, integer *, 
+	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
+	    doublereal *, integer *);
+    doublereal bignum;
+    extern /* Subroutine */ int dpbrfs_(char *, integer *, integer *, integer 
+	    *, doublereal *, integer *, doublereal *, integer *, doublereal *, 
+	     integer *, doublereal *, integer *, doublereal *, doublereal *, 
+	    doublereal *, integer *, integer *), dpbtrf_(char *, 
+	    integer *, integer *, doublereal *, integer *, integer *);
+    integer infequ;
+    extern /* Subroutine */ int dpbtrs_(char *, integer *, integer *, integer 
+	    *, doublereal *, integer *, doublereal *, integer *, integer *);
+    doublereal smlnum;
+
+
+/*  -- LAPACK driver routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  DPBSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to */
+/*  compute the solution to a real system of linear equations */
+/*     A * X = B, */
+/*  where A is an N-by-N symmetric positive definite band matrix and X */
+/*  and B are N-by-NRHS matrices. */
+
+/*  Error bounds on the solution and a condition estimate are also */
+/*  provided. */
+
+/*  Description */
+/*  =========== */
+
+/*  The following steps are performed: */
+
+/*  1. If FACT = 'E', real scaling factors are computed to equilibrate */
+/*     the system: */
+/*        diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B */
+/*     Whether or not the system will be equilibrated depends on the */
+/*     scaling of the matrix A, but if equilibration is used, A is */
+/*     overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */
+
+/*  2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
+/*     factor the matrix A (after equilibration if FACT = 'E') as */
+/*        A = U**T * U,  if UPLO = 'U', or */
+/*        A = L * L**T,  if UPLO = 'L', */
+/*     where U is an upper triangular band matrix, and L is a lower */
+/*     triangular band matrix. */
+
+/*  3. If the leading i-by-i principal minor is not positive definite, */
+/*     then the routine returns with INFO = i. Otherwise, the factored */
+/*     form of A is used to estimate the condition number of the matrix */
+/*     A.  If the reciprocal of the condition number is less than machine */
+/*     precision, INFO = N+1 is returned as a warning, but the routine */
+/*     still goes on to solve for X and compute error bounds as */
+/*     described below. */
+
+/*  4. The system of equations is solved for X using the factored form */
+/*     of A. */
+
+/*  5. Iterative refinement is applied to improve the computed solution */
+/*     matrix and calculate error bounds and backward error estimates */
+/*     for it. */
+
+/*  6. If equilibration was used, the matrix X is premultiplied by */
+/*     diag(S) so that it solves the original system before */
+/*     equilibration. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  FACT    (input) CHARACTER*1 */
+/*          Specifies whether or not the factored form of the matrix A is */
+/*          supplied on entry, and if not, whether the matrix A should be */
+/*          equilibrated before it is factored. */
+/*          = 'F':  On entry, AFB contains the factored form of A. */
+/*                  If EQUED = 'Y', the matrix A has been equilibrated */
+/*                  with scaling factors given by S.  AB and AFB will not */
+/*                  be modified. */
+/*          = 'N':  The matrix A will be copied to AFB and factored. */
+/*          = 'E':  The matrix A will be equilibrated if necessary, then */
+/*                  copied to AFB and factored. */
+
+/*  UPLO    (input) CHARACTER*1 */
+/*          = 'U':  Upper triangle of A is stored; */
+/*          = 'L':  Lower triangle of A is stored. */
+
+/*  N       (input) INTEGER */
+/*          The number of linear equations, i.e., the order of the */
+/*          matrix A.  N >= 0. */
+
+/*  KD      (input) INTEGER */
+/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
+/*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0. */
+
+/*  NRHS    (input) INTEGER */
+/*          The number of right-hand sides, i.e., the number of columns */
+/*          of the matrices B and X.  NRHS >= 0. */
+
+/*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
+/*          On entry, the upper or lower triangle of the symmetric band */
+/*          matrix A, stored in the first KD+1 rows of the array, except */
+/*          if FACT = 'F' and EQUED = 'Y', then A must contain the */
+/*          equilibrated matrix diag(S)*A*diag(S).  The j-th column of A */
+/*          is stored in the j-th column of the array AB as follows: */
+/*          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; */
+/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD). */
+/*          See below for further details. */
+
+/*          On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
+/*          diag(S)*A*diag(S). */
+
+/*  LDAB    (input) INTEGER */
+/*          The leading dimension of the array A.  LDAB >= KD+1. */
+
+/*  AFB     (input or output) DOUBLE PRECISION array, dimension (LDAFB,N) */
+/*          If FACT = 'F', then AFB is an input argument and on entry */
+/*          contains the triangular factor U or L from the Cholesky */
+/*          factorization A = U**T*U or A = L*L**T of the band matrix */
+/*          A, in the same storage format as A (see AB).  If EQUED = 'Y', */
+/*          then AFB is the factored form of the equilibrated matrix A. */
+
+/*          If FACT = 'N', then AFB is an output argument and on exit */
+/*          returns the triangular factor U or L from the Cholesky */
+/*          factorization A = U**T*U or A = L*L**T. */
+
+/*          If FACT = 'E', then AFB is an output argument and on exit */
+/*          returns the triangular factor U or L from the Cholesky */
+/*          factorization A = U**T*U or A = L*L**T of the equilibrated */
+/*          matrix A (see the description of A for the form of the */
+/*          equilibrated matrix). */
+
+/*  LDAFB   (input) INTEGER */
+/*          The leading dimension of the array AFB.  LDAFB >= KD+1. */
+
+/*  EQUED   (input or output) CHARACTER*1 */
+/*          Specifies the form of equilibration that was done. */
+/*          = 'N':  No equilibration (always true if FACT = 'N'). */
+/*          = 'Y':  Equilibration was done, i.e., A has been replaced by */
+/*                  diag(S) * A * diag(S). */
+/*          EQUED is an input argument if FACT = 'F'; otherwise, it is an */
+/*          output argument. */
+
+/*  S       (input or output) DOUBLE PRECISION array, dimension (N) */
+/*          The scale factors for A; not accessed if EQUED = 'N'.  S is */
+/*          an input argument if FACT = 'F'; otherwise, S is an output */
+/*          argument.  If FACT = 'F' and EQUED = 'Y', each element of S */
+/*          must be positive. */
+
+/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
+/*          On entry, the N-by-NRHS right hand side matrix B. */
+/*          On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */
+/*          B is overwritten by diag(S) * B. */
+
+/*  LDB     (input) INTEGER */
+/*          The leading dimension of the array B.  LDB >= max(1,N). */
+
+/*  X       (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */
+/*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to */
+/*          the original system of equations.  Note that if EQUED = 'Y', */
+/*          A and B are modified on exit, and the solution to the */
+/*          equilibrated system is inv(diag(S))*X. */
+
+/*  LDX     (input) INTEGER */
+/*          The leading dimension of the array X.  LDX >= max(1,N). */
+
+/*  RCOND   (output) DOUBLE PRECISION */
+/*          The estimate of the reciprocal condition number of the matrix */
+/*          A after equilibration (if done).  If RCOND is less than the */
+/*          machine precision (in particular, if RCOND = 0), the matrix */
+/*          is singular to working precision.  This condition is */
+/*          indicated by a return code of INFO > 0. */
+
+/*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
+/*          The estimated forward error bound for each solution vector */
+/*          X(j) (the j-th column of the solution matrix X). */
+/*          If XTRUE is the true solution corresponding to X(j), FERR(j) */
+/*          is an estimated upper bound for the magnitude of the largest */
+/*          element in (X(j) - XTRUE) divided by the magnitude of the */
+/*          largest element in X(j).  The estimate is as reliable as */
+/*          the estimate for RCOND, and is almost always a slight */
+/*          overestimate of the true error. */
+
+/*  BERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
+/*          The componentwise relative backward error of each solution */
+/*          vector X(j) (i.e., the smallest relative change in */
+/*          any element of A or B that makes X(j) an exact solution). */
+
+/*  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N) */
+
+/*  IWORK   (workspace) INTEGER array, dimension (N) */
+
+/*  INFO    (output) INTEGER */
+/*          = 0:  successful exit */
+/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/*          > 0:  if INFO = i, and i is */
+/*                <= N:  the leading minor of order i of A is */
+/*                       not positive definite, so the factorization */
+/*                       could not be completed, and the solution has not */
+/*                       been computed. RCOND = 0 is returned. */
+/*                = N+1: U is nonsingular, but RCOND is less than machine */
+/*                       precision, meaning that the matrix is singular */
+/*                       to working precision.  Nevertheless, the */
+/*                       solution and error bounds are computed because */
+/*                       there are a number of situations where the */
+/*                       computed solution can be more accurate than the */
+/*                       value of RCOND would suggest. */
+
+/*  Further Details */
+/*  =============== */
+
+/*  The band storage scheme is illustrated by the following example, when */
+/*  N = 6, KD = 2, and UPLO = 'U': */
+
+/*  Two-dimensional storage of the symmetric matrix A: */
+
+/*     a11  a12  a13 */
+/*          a22  a23  a24 */
+/*               a33  a34  a35 */
+/*                    a44  a45  a46 */
+/*                         a55  a56 */
+/*     (aij=conjg(aji))         a66 */
+
+/*  Band storage of the upper triangle of A: */
+
+/*      *    *   a13  a24  a35  a46 */
+/*      *   a12  a23  a34  a45  a56 */
+/*     a11  a22  a33  a44  a55  a66 */
+
+/*  Similarly, if UPLO = 'L' the format of A is as follows: */
+
+/*     a11  a22  a33  a44  a55  a66 */
+/*     a21  a32  a43  a54  a65   * */
+/*     a31  a42  a53  a64   *    * */
+
+/*  Array elements marked * are not used by the routine. */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1;
+    ab -= ab_offset;
+    afb_dim1 = *ldafb;
+    afb_offset = 1 + afb_dim1;
+    afb -= afb_offset;
+    --s;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    x_dim1 = *ldx;
+    x_offset = 1 + x_dim1;
+    x -= x_offset;
+    --ferr;
+    --berr;
+    --work;
+    --iwork;
+
+    /* Function Body */
+    *info = 0;
+    nofact = lsame_(fact, "N");
+    equil = lsame_(fact, "E");
+    upper = lsame_(uplo, "U");
+    if (nofact || equil) {
+	*(unsigned char *)equed = 'N';
+	rcequ = FALSE_;
+    } else {
+	rcequ = lsame_(equed, "Y");
+	smlnum = dlamch_("Safe minimum");
+	bignum = 1. / smlnum;
+    }
+
+/*     Test the input parameters. */
+
+    if (! nofact && ! equil && ! lsame_(fact, "F")) {
+	*info = -1;
+    } else if (! upper && ! lsame_(uplo, "L")) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*kd < 0) {
+	*info = -4;
+    } else if (*nrhs < 0) {
+	*info = -5;
+    } else if (*ldab < *kd + 1) {
+	*info = -7;
+    } else if (*ldafb < *kd + 1) {
+	*info = -9;
+    } else if (lsame_(fact, "F") && ! (rcequ || lsame_(
+	    equed, "N"))) {
+	*info = -10;
+    } else {
+	if (rcequ) {
+	    smin = bignum;
+	    smax = 0.;
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+		d__1 = smin, d__2 = s[j];
+		smin = min(d__1,d__2);
+/* Computing MAX */
+		d__1 = smax, d__2 = s[j];
+		smax = max(d__1,d__2);
+/* L10: */
+	    }
+	    if (smin <= 0.) {
+		*info = -11;
+	    } else if (*n > 0) {
+		scond = max(smin,smlnum) / min(smax,bignum);
+	    } else {
+		scond = 1.;
+	    }
+	}
+	if (*info == 0) {
+	    if (*ldb < max(1,*n)) {
+		*info = -13;
+	    } else if (*ldx < max(1,*n)) {
+		*info = -15;
+	    }
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DPBSVX", &i__1);
+	return 0;
+    }
+
+    if (equil) {
+
+/*        Compute row and column scalings to equilibrate the matrix A. */
+
+	dpbequ_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, &
+		infequ);
+	if (infequ == 0) {
+
+/*           Equilibrate the matrix. */
+
+	    dlaqsb_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, 
+		    equed);
+	    rcequ = lsame_(equed, "Y");
+	}
+    }
+
+/*     Scale the right-hand side. */
+
+    if (rcequ) {
+	i__1 = *nrhs;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *n;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		b[i__ + j * b_dim1] = s[i__] * b[i__ + j * b_dim1];
+/* L20: */
+	    }
+/* L30: */
+	}
+    }
+
+    if (nofact || equil) {
+
+/*        Compute the Cholesky factorization A = U'*U or A = L*L'. */
+
+	if (upper) {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+/* Computing MAX */
+		i__2 = j - *kd;
+		j1 = max(i__2,1);
+		i__2 = j - j1 + 1;
+		dcopy_(&i__2, &ab[*kd + 1 - j + j1 + j * ab_dim1], &c__1, &
+			afb[*kd + 1 - j + j1 + j * afb_dim1], &c__1);
+/* L40: */
+	    }
+	} else {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+		i__2 = j + *kd;
+		j2 = min(i__2,*n);
+		i__2 = j2 - j + 1;
+		dcopy_(&i__2, &ab[j * ab_dim1 + 1], &c__1, &afb[j * afb_dim1 
+			+ 1], &c__1);
+/* L50: */
+	    }
+	}
+
+	dpbtrf_(uplo, n, kd, &afb[afb_offset], ldafb, info);
+
+/*        Return if INFO is non-zero. */
+
+	if (*info > 0) {
+	    *rcond = 0.;
+	    return 0;
+	}
+    }
+
+/*     Compute the norm of the matrix A. */
+
+    anorm = dlansb_("1", uplo, n, kd, &ab[ab_offset], ldab, &work[1]);
+
+/*     Compute the reciprocal of the condition number of A. */
+
+    dpbcon_(uplo, n, kd, &afb[afb_offset], ldafb, &anorm, rcond, &work[1], &
+	    iwork[1], info);
+
+/*     Compute the solution matrix X. */
+
+    dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
+    dpbtrs_(uplo, n, kd, nrhs, &afb[afb_offset], ldafb, &x[x_offset], ldx, 
+	    info);
+
+/*     Use iterative refinement to improve the computed solution and */
+/*     compute error bounds and backward error estimates for it. */
+
+    dpbrfs_(uplo, n, kd, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, 
+	    &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1]
+, &iwork[1], info);
+
+/*     Transform the solution matrix X to a solution of the original */
+/*     system. */
+
+    if (rcequ) {
+	i__1 = *nrhs;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *n;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		x[i__ + j * x_dim1] = s[i__] * x[i__ + j * x_dim1];
+/* L60: */
+	    }
+/* L70: */
+	}
+	i__1 = *nrhs;
+	for (j = 1; j <= i__1; ++j) {
+	    ferr[j] /= scond;
+/* L80: */
+	}
+    }
+
+/*     Set INFO = N+1 if the matrix is singular to working precision. */
+
+    if (*rcond < dlamch_("Epsilon")) {
+	*info = *n + 1;
+    }
+
+    return 0;
+
+/*     End of DPBSVX */
+
+} /* dpbsvx_ */