[] add metering mode to CLI

1 files changed, 494 insertions, 0 deletions

diff --git a/contrib/libs/clapack/zgbrfs.c b/contrib/libs/clapack/zgbrfs.c
new file mode 100644
index 0000000000..f3827606ad
--- /dev/null
+++ b/contrib/libs/clapack/zgbrfs.c
@@ -0,0 +1,494 @@
+/* zgbrfs.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 doublecomplex c_b1 = {1.,0.};
+static integer c__1 = 1;
+
+/* Subroutine */ int zgbrfs_(char *trans, integer *n, integer *kl, integer *
+	ku, integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *
+	afb, integer *ldafb, integer *ipiv, doublecomplex *b, integer *ldb, 
+	doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+	doublecomplex *work, doublereal *rwork, 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, i__3, i__4, i__5, i__6, i__7;
+    doublereal d__1, d__2, d__3, d__4;
+    doublecomplex z__1;
+
+    /* Builtin functions */
+    double d_imag(doublecomplex *);
+
+    /* Local variables */
+    integer i__, j, k;
+    doublereal s;
+    integer kk;
+    doublereal xk;
+    integer nz;
+    doublereal eps;
+    integer kase;
+    doublereal safe1, safe2;
+    extern logical lsame_(char *, char *);
+    integer isave[3];
+    extern /* Subroutine */ int zgbmv_(char *, integer *, integer *, integer *
+, integer *, doublecomplex *, doublecomplex *, integer *, 
+	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
+	    integer *);
+    integer count;
+    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
+	    doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, 
+	    doublecomplex *, integer *, doublecomplex *, integer *), zlacn2_(
+	    integer *, doublecomplex *, doublecomplex *, doublereal *, 
+	    integer *, integer *);
+    extern doublereal dlamch_(char *);
+    doublereal safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    logical notran;
+    char transn[1], transt[1];
+    doublereal lstres;
+    extern /* Subroutine */ int zgbtrs_(char *, integer *, integer *, integer 
+	    *, integer *, doublecomplex *, integer *, integer *, 
+	    doublecomplex *, integer *, integer *);
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  ZGBRFS improves the computed solution to a system of linear */
+/*  equations when the coefficient matrix is banded, and provides */
+/*  error bounds and backward error estimates for the solution. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  TRANS   (input) CHARACTER*1 */
+/*          Specifies the form of the system of equations: */
+/*          = 'N':  A * X = B     (No transpose) */
+/*          = 'T':  A**T * X = B  (Transpose) */
+/*          = 'C':  A**H * X = B  (Conjugate transpose) */
+
+/*  N       (input) INTEGER */
+/*          The order of the matrix A.  N >= 0. */
+
+/*  KL      (input) INTEGER */
+/*          The number of subdiagonals within the band of A.  KL >= 0. */
+
+/*  KU      (input) INTEGER */
+/*          The number of superdiagonals within the band of A.  KU >= 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) COMPLEX*16 array, dimension (LDAB,N) */
+/*          The original band matrix A, stored in rows 1 to KL+KU+1. */
+/*          The j-th column of A is stored in the j-th column of the */
+/*          array AB as follows: */
+/*          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). */
+
+/*  LDAB    (input) INTEGER */
+/*          The leading dimension of the array AB.  LDAB >= KL+KU+1. */
+
+/*  AFB     (input) COMPLEX*16 array, dimension (LDAFB,N) */
+/*          Details of the LU factorization of the band matrix A, as */
+/*          computed by ZGBTRF.  U is stored as an upper triangular band */
+/*          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
+/*          the multipliers used during the factorization are stored in */
+/*          rows KL+KU+2 to 2*KL+KU+1. */
+
+/*  LDAFB   (input) INTEGER */
+/*          The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1. */
+
+/*  IPIV    (input) INTEGER array, dimension (N) */
+/*          The pivot indices from ZGBTRF; for 1<=i<=N, row i of the */
+/*          matrix was interchanged with row IPIV(i). */
+
+/*  B       (input) COMPLEX*16 array, dimension (LDB,NRHS) */
+/*          The right hand side matrix B. */
+
+/*  LDB     (input) INTEGER */
+/*          The leading dimension of the array B.  LDB >= max(1,N). */
+
+/*  X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS) */
+/*          On entry, the solution matrix X, as computed by ZGBTRS. */
+/*          On exit, the improved solution matrix X. */
+
+/*  LDX     (input) INTEGER */
+/*          The leading dimension of the array X.  LDX >= max(1,N). */
+
+/*  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) COMPLEX*16 array, dimension (2*N) */
+
+/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */
+
+/*  INFO    (output) INTEGER */
+/*          = 0:  successful exit */
+/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
+
+/*  Internal Parameters */
+/*  =================== */
+
+/*  ITMAX is the maximum number of steps of iterative refinement. */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. Statement Functions .. */
+/*     .. */
+/*     .. Statement Function definitions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1;
+    ab -= ab_offset;
+    afb_dim1 = *ldafb;
+    afb_offset = 1 + afb_dim1;
+    afb -= afb_offset;
+    --ipiv;
+    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;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    notran = lsame_(trans, "N");
+    if (! notran && ! lsame_(trans, "T") && ! lsame_(
+	    trans, "C")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*kl < 0) {
+	*info = -3;
+    } else if (*ku < 0) {
+	*info = -4;
+    } else if (*nrhs < 0) {
+	*info = -5;
+    } else if (*ldab < *kl + *ku + 1) {
+	*info = -7;
+    } else if (*ldafb < (*kl << 1) + *ku + 1) {
+	*info = -9;
+    } else if (*ldb < max(1,*n)) {
+	*info = -12;
+    } else if (*ldx < max(1,*n)) {
+	*info = -14;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("ZGBRFS", &i__1);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0 || *nrhs == 0) {
+	i__1 = *nrhs;
+	for (j = 1; j <= i__1; ++j) {
+	    ferr[j] = 0.;
+	    berr[j] = 0.;
+/* L10: */
+	}
+	return 0;
+    }
+
+    if (notran) {
+	*(unsigned char *)transn = 'N';
+	*(unsigned char *)transt = 'C';
+    } else {
+	*(unsigned char *)transn = 'C';
+	*(unsigned char *)transt = 'N';
+    }
+
+/*     NZ = maximum number of nonzero elements in each row of A, plus 1 */
+
+/* Computing MIN */
+    i__1 = *kl + *ku + 2, i__2 = *n + 1;
+    nz = min(i__1,i__2);
+    eps = dlamch_("Epsilon");
+    safmin = dlamch_("Safe minimum");
+    safe1 = nz * safmin;
+    safe2 = safe1 / eps;
+
+/*     Do for each right hand side */
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+
+	count = 1;
+	lstres = 3.;
+L20:
+
+/*        Loop until stopping criterion is satisfied. */
+
+/*        Compute residual R = B - op(A) * X, */
+/*        where op(A) = A, A**T, or A**H, depending on TRANS. */
+
+	zcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
+	z__1.r = -1., z__1.i = -0.;
+	zgbmv_(trans, n, n, kl, ku, &z__1, &ab[ab_offset], ldab, &x[j * 
+		x_dim1 + 1], &c__1, &c_b1, &work[1], &c__1);
+
+/*        Compute componentwise relative backward error from formula */
+
+/*        max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
+
+/*        where abs(Z) is the componentwise absolute value of the matrix */
+/*        or vector Z.  If the i-th component of the denominator is less */
+/*        than SAFE2, then SAFE1 is added to the i-th components of the */
+/*        numerator and denominator before dividing. */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    i__3 = i__ + j * b_dim1;
+	    rwork[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[
+		    i__ + j * b_dim1]), abs(d__2));
+/* L30: */
+	}
+
+/*        Compute abs(op(A))*abs(X) + abs(B). */
+
+	if (notran) {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		kk = *ku + 1 - k;
+		i__3 = k + j * x_dim1;
+		xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[k + j *
+			 x_dim1]), abs(d__2));
+/* Computing MAX */
+		i__3 = 1, i__4 = k - *ku;
+/* Computing MIN */
+		i__6 = *n, i__7 = k + *kl;
+		i__5 = min(i__6,i__7);
+		for (i__ = max(i__3,i__4); i__ <= i__5; ++i__) {
+		    i__3 = kk + i__ + k * ab_dim1;
+		    rwork[i__] += ((d__1 = ab[i__3].r, abs(d__1)) + (d__2 = 
+			    d_imag(&ab[kk + i__ + k * ab_dim1]), abs(d__2))) *
+			     xk;
+/* L40: */
+		}
+/* L50: */
+	    }
+	} else {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		s = 0.;
+		kk = *ku + 1 - k;
+/* Computing MAX */
+		i__5 = 1, i__3 = k - *ku;
+/* Computing MIN */
+		i__6 = *n, i__7 = k + *kl;
+		i__4 = min(i__6,i__7);
+		for (i__ = max(i__5,i__3); i__ <= i__4; ++i__) {
+		    i__5 = kk + i__ + k * ab_dim1;
+		    i__3 = i__ + j * x_dim1;
+		    s += ((d__1 = ab[i__5].r, abs(d__1)) + (d__2 = d_imag(&ab[
+			    kk + i__ + k * ab_dim1]), abs(d__2))) * ((d__3 = 
+			    x[i__3].r, abs(d__3)) + (d__4 = d_imag(&x[i__ + j 
+			    * x_dim1]), abs(d__4)));
+/* L60: */
+		}
+		rwork[k] += s;
+/* L70: */
+	    }
+	}
+	s = 0.;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+/* Computing MAX */
+		i__4 = i__;
+		d__3 = s, d__4 = ((d__1 = work[i__4].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2))) / rwork[i__];
+		s = max(d__3,d__4);
+	    } else {
+/* Computing MAX */
+		i__4 = i__;
+		d__3 = s, d__4 = ((d__1 = work[i__4].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__] 
+			+ safe1);
+		s = max(d__3,d__4);
+	    }
+/* L80: */
+	}
+	berr[j] = s;
+
+/*        Test stopping criterion. Continue iterating if */
+/*           1) The residual BERR(J) is larger than machine epsilon, and */
+/*           2) BERR(J) decreased by at least a factor of 2 during the */
+/*              last iteration, and */
+/*           3) At most ITMAX iterations tried. */
+
+	if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) {
+
+/*           Update solution and try again. */
+
+	    zgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1]
+, &work[1], n, info);
+	    zaxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
+	    lstres = berr[j];
+	    ++count;
+	    goto L20;
+	}
+
+/*        Bound error from formula */
+
+/*        norm(X - XTRUE) / norm(X) .le. FERR = */
+/*        norm( abs(inv(op(A)))* */
+/*           ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
+
+/*        where */
+/*          norm(Z) is the magnitude of the largest component of Z */
+/*          inv(op(A)) is the inverse of op(A) */
+/*          abs(Z) is the componentwise absolute value of the matrix or */
+/*             vector Z */
+/*          NZ is the maximum number of nonzeros in any row of A, plus 1 */
+/*          EPS is machine epsilon */
+
+/*        The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
+/*        is incremented by SAFE1 if the i-th component of */
+/*        abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
+
+/*        Use ZLACN2 to estimate the infinity-norm of the matrix */
+/*           inv(op(A)) * diag(W), */
+/*        where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+		i__4 = i__;
+		rwork[i__] = (d__1 = work[i__4].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
+			;
+	    } else {
+		i__4 = i__;
+		rwork[i__] = (d__1 = work[i__4].r, abs(d__1)) + (d__2 = 
+			d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
+			 + safe1;
+	    }
+/* L90: */
+	}
+
+	kase = 0;
+L100:
+	zlacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
+	if (kase != 0) {
+	    if (kase == 1) {
+
+/*              Multiply by diag(W)*inv(op(A)**H). */
+
+		zgbtrs_(transt, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
+			ipiv[1], &work[1], n, info);
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__4 = i__;
+		    i__5 = i__;
+		    i__3 = i__;
+		    z__1.r = rwork[i__5] * work[i__3].r, z__1.i = rwork[i__5] 
+			    * work[i__3].i;
+		    work[i__4].r = z__1.r, work[i__4].i = z__1.i;
+/* L110: */
+		}
+	    } else {
+
+/*              Multiply by inv(op(A))*diag(W). */
+
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__4 = i__;
+		    i__5 = i__;
+		    i__3 = i__;
+		    z__1.r = rwork[i__5] * work[i__3].r, z__1.i = rwork[i__5] 
+			    * work[i__3].i;
+		    work[i__4].r = z__1.r, work[i__4].i = z__1.i;
+/* L120: */
+		}
+		zgbtrs_(transn, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
+			ipiv[1], &work[1], n, info);
+	    }
+	    goto L100;
+	}
+
+/*        Normalize error. */
+
+	lstres = 0.;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__4 = i__ + j * x_dim1;
+	    d__3 = lstres, d__4 = (d__1 = x[i__4].r, abs(d__1)) + (d__2 = 
+		    d_imag(&x[i__ + j * x_dim1]), abs(d__2));
+	    lstres = max(d__3,d__4);
+/* L130: */
+	}
+	if (lstres != 0.) {
+	    ferr[j] /= lstres;
+	}
+
+/* L140: */
+    }
+
+    return 0;
+
+/*     End of ZGBRFS */
+
+} /* zgbrfs_ */