X-Git-Url: https://vcs.maemo.org/git/?a=blobdiff_plain;f=3rdparty%2Flapack%2Fdlasq2.c;fp=3rdparty%2Flapack%2Fdlasq2.c;h=c898a152589defcb6388e6fa497eca9cafd684d6;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hp=0000000000000000000000000000000000000000;hpb=454138ff8a20f6edb9b65a910101403d8b520643;p=opencv

diff --git a/3rdparty/lapack/dlasq2.c b/3rdparty/lapack/dlasq2.c
new file mode 100644
index 0000000..c898a15
--- /dev/null
+++ b/3rdparty/lapack/dlasq2.c
@@ -0,0 +1,548 @@
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c__2 = 2;
+static integer c__10 = 10;
+static integer c__3 = 3;
+static integer c__4 = 4;
+static integer c__11 = 11;
+
+/* Subroutine */ int dlasq2_(integer *n, doublereal *z__, integer *info)
+{
+    /* System generated locals */
+    integer i__1, i__2, i__3;
+    doublereal d__1, d__2;
+
+    /* Builtin functions */
+    double sqrt(doublereal);
+
+    /* Local variables */
+    doublereal d__, e;
+    integer k;
+    doublereal s, t;
+    integer i0, i4, n0;
+    doublereal dn;
+    integer pp;
+    doublereal dn1, dn2, eps, tau, tol;
+    integer ipn4;
+    doublereal tol2;
+    logical ieee;
+    integer nbig;
+    doublereal dmin__, emin, emax;
+    integer ndiv, iter;
+    doublereal qmin, temp, qmax, zmax;
+    integer splt;
+    doublereal dmin1, dmin2;
+    integer nfail;
+    doublereal desig, trace, sigma;
+    integer iinfo, ttype;
+    extern /* Subroutine */ int dlazq3_(integer *, integer *, doublereal *, 
+	    integer *, doublereal *, doublereal *, doublereal *, doublereal *, 
+	     integer *, integer *, integer *, logical *, integer *, 
+	    doublereal *, doublereal *, doublereal *, doublereal *, 
+	    doublereal *, doublereal *);
+    extern doublereal dlamch_(char *);
+    integer iwhila, iwhilb;
+    doublereal oldemn, safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *);
+    extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, 
+	    integer *);
+
+
+/*  -- LAPACK routine (version 3.1) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     Modified to call DLAZQ3 in place of DLASQ3, 13 Feb 03, SJH. */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  DLASQ2 computes all the eigenvalues of the symmetric positive */
+/*  definite tridiagonal matrix associated with the qd array Z to high */
+/*  relative accuracy are computed to high relative accuracy, in the */
+/*  absence of denormalization, underflow and overflow. */
+
+/*  To see the relation of Z to the tridiagonal matrix, let L be a */
+/*  unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */
+/*  let U be an upper bidiagonal matrix with 1's above and diagonal */
+/*  Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */
+/*  symmetric tridiagonal to which it is similar. */
+
+/*  Note : DLASQ2 defines a logical variable, IEEE, which is true */
+/*  on machines which follow ieee-754 floating-point standard in their */
+/*  handling of infinities and NaNs, and false otherwise. This variable */
+/*  is passed to DLAZQ3. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  N     (input) INTEGER */
+/*        The number of rows and columns in the matrix. N >= 0. */
+
+/*  Z     (workspace) DOUBLE PRECISION array, dimension ( 4*N ) */
+/*        On entry Z holds the qd array. On exit, entries 1 to N hold */
+/*        the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */
+/*        trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */
+/*        N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */
+/*        holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */
+/*        shifts that failed. */
+
+/*  INFO  (output) INTEGER */
+/*        = 0: successful exit */
+/*        < 0: if the i-th argument is a scalar and had an illegal */
+/*             value, then INFO = -i, if the i-th argument is an */
+/*             array and the j-entry had an illegal value, then */
+/*             INFO = -(i*100+j) */
+/*        > 0: the algorithm failed */
+/*              = 1, a split was marked by a positive value in E */
+/*              = 2, current block of Z not diagonalized after 30*N */
+/*                   iterations (in inner while loop) */
+/*              = 3, termination criterion of outer while loop not met */
+/*                   (program created more than N unreduced blocks) */
+
+/*  Further Details */
+/*  =============== */
+/*  Local Variables: I0:N0 defines a current unreduced segment of Z. */
+/*  The shifts are accumulated in SIGMA. Iteration count is in ITER. */
+/*  Ping-pong is controlled by PP (alternates between 0 and 1). */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Test the input arguments. */
+/*     (in case DLASQ2 is not called by DLASQ1) */
+
+    /* Parameter adjustments */
+    --z__;
+
+    /* Function Body */
+    *info = 0;
+    eps = dlamch_("Precision");
+    safmin = dlamch_("Safe minimum");
+    tol = eps * 100.;
+/* Computing 2nd power */
+    d__1 = tol;
+    tol2 = d__1 * d__1;
+
+    if (*n < 0) {
+	*info = -1;
+	xerbla_("DLASQ2", &c__1);
+	return 0;
+    } else if (*n == 0) {
+	return 0;
+    } else if (*n == 1) {
+
+/*        1-by-1 case. */
+
+	if (z__[1] < 0.) {
+	    *info = -201;
+	    xerbla_("DLASQ2", &c__2);
+	}
+	return 0;
+    } else if (*n == 2) {
+
+/*        2-by-2 case. */
+
+	if (z__[2] < 0. || z__[3] < 0.) {
+	    *info = -2;
+	    xerbla_("DLASQ2", &c__2);
+	    return 0;
+	} else if (z__[3] > z__[1]) {
+	    d__ = z__[3];
+	    z__[3] = z__[1];
+	    z__[1] = d__;
+	}
+	z__[5] = z__[1] + z__[2] + z__[3];
+	if (z__[2] > z__[3] * tol2) {
+	    t = (z__[1] - z__[3] + z__[2]) * .5;
+	    s = z__[3] * (z__[2] / t);
+	    if (s <= t) {
+		s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.) + 1.)));
+	    } else {
+		s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s)));
+	    }
+	    t = z__[1] + (s + z__[2]);
+	    z__[3] *= z__[1] / t;
+	    z__[1] = t;
+	}
+	z__[2] = z__[3];
+	z__[6] = z__[2] + z__[1];
+	return 0;
+    }
+
+/*     Check for negative data and compute sums of q's and e's. */
+
+    z__[*n * 2] = 0.;
+    emin = z__[2];
+    qmax = 0.;
+    zmax = 0.;
+    d__ = 0.;
+    e = 0.;
+
+    i__1 = *n - 1 << 1;
+    for (k = 1; k <= i__1; k += 2) {
+	if (z__[k] < 0.) {
+	    *info = -(k + 200);
+	    xerbla_("DLASQ2", &c__2);
+	    return 0;
+	} else if (z__[k + 1] < 0.) {
+	    *info = -(k + 201);
+	    xerbla_("DLASQ2", &c__2);
+	    return 0;
+	}
+	d__ += z__[k];
+	e += z__[k + 1];
+/* Computing MAX */
+	d__1 = qmax, d__2 = z__[k];
+	qmax = max(d__1,d__2);
+/* Computing MIN */
+	d__1 = emin, d__2 = z__[k + 1];
+	emin = min(d__1,d__2);
+/* Computing MAX */
+	d__1 = max(qmax,zmax), d__2 = z__[k + 1];
+	zmax = max(d__1,d__2);
+/* L10: */
+    }
+    if (z__[(*n << 1) - 1] < 0.) {
+	*info = -((*n << 1) + 199);
+	xerbla_("DLASQ2", &c__2);
+	return 0;
+    }
+    d__ += z__[(*n << 1) - 1];
+/* Computing MAX */
+    d__1 = qmax, d__2 = z__[(*n << 1) - 1];
+    qmax = max(d__1,d__2);
+    zmax = max(qmax,zmax);
+
+/*     Check for diagonality. */
+
+    if (e == 0.) {
+	i__1 = *n;
+	for (k = 2; k <= i__1; ++k) {
+	    z__[k] = z__[(k << 1) - 1];
+/* L20: */
+	}
+	dlasrt_("D", n, &z__[1], &iinfo);
+	z__[(*n << 1) - 1] = d__;
+	return 0;
+    }
+
+    trace = d__ + e;
+
+/*     Check for zero data. */
+
+    if (trace == 0.) {
+	z__[(*n << 1) - 1] = 0.;
+	return 0;
+    }
+
+/*     Check whether the machine is IEEE conformable. */
+
+    ieee = ilaenv_(&c__10, "DLASQ2", "N", &c__1, &c__2, &c__3, &c__4) == 1 && ilaenv_(&c__11, "DLASQ2", "N", &c__1, &c__2, 
+	     &c__3, &c__4) == 1;
+
+/*     Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */
+
+    for (k = *n << 1; k >= 2; k += -2) {
+	z__[k * 2] = 0.;
+	z__[(k << 1) - 1] = z__[k];
+	z__[(k << 1) - 2] = 0.;
+	z__[(k << 1) - 3] = z__[k - 1];
+/* L30: */
+    }
+
+    i0 = 1;
+    n0 = *n;
+
+/*     Reverse the qd-array, if warranted. */
+
+    if (z__[(i0 << 2) - 3] * 1.5 < z__[(n0 << 2) - 3]) {
+	ipn4 = i0 + n0 << 2;
+	i__1 = i0 + n0 - 1 << 1;
+	for (i4 = i0 << 2; i4 <= i__1; i4 += 4) {
+	    temp = z__[i4 - 3];
+	    z__[i4 - 3] = z__[ipn4 - i4 - 3];
+	    z__[ipn4 - i4 - 3] = temp;
+	    temp = z__[i4 - 1];
+	    z__[i4 - 1] = z__[ipn4 - i4 - 5];
+	    z__[ipn4 - i4 - 5] = temp;
+/* L40: */
+	}
+    }
+
+/*     Initial split checking via dqd and Li's test. */
+
+    pp = 0;
+
+    for (k = 1; k <= 2; ++k) {
+
+	d__ = z__[(n0 << 2) + pp - 3];
+	i__1 = (i0 << 2) + pp;
+	for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) {
+	    if (z__[i4 - 1] <= tol2 * d__) {
+		z__[i4 - 1] = -0.;
+		d__ = z__[i4 - 3];
+	    } else {
+		d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1]));
+	    }
+/* L50: */
+	}
+
+/*        dqd maps Z to ZZ plus Li's test. */
+
+	emin = z__[(i0 << 2) + pp + 1];
+	d__ = z__[(i0 << 2) + pp - 3];
+	i__1 = (n0 - 1 << 2) + pp;
+	for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) {
+	    z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1];
+	    if (z__[i4 - 1] <= tol2 * d__) {
+		z__[i4 - 1] = -0.;
+		z__[i4 - (pp << 1) - 2] = d__;
+		z__[i4 - (pp << 1)] = 0.;
+		d__ = z__[i4 + 1];
+	    } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && 
+		    safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) {
+		temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2];
+		z__[i4 - (pp << 1)] = z__[i4 - 1] * temp;
+		d__ *= temp;
+	    } else {
+		z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - (
+			pp << 1) - 2]);
+		d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]);
+	    }
+/* Computing MIN */
+	    d__1 = emin, d__2 = z__[i4 - (pp << 1)];
+	    emin = min(d__1,d__2);
+/* L60: */
+	}
+	z__[(n0 << 2) - pp - 2] = d__;
+
+/*        Now find qmax. */
+
+	qmax = z__[(i0 << 2) - pp - 2];
+	i__1 = (n0 << 2) - pp - 2;
+	for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) {
+/* Computing MAX */
+	    d__1 = qmax, d__2 = z__[i4];
+	    qmax = max(d__1,d__2);
+/* L70: */
+	}
+
+/*        Prepare for the next iteration on K. */
+
+	pp = 1 - pp;
+/* L80: */
+    }
+
+/*     Initialise variables to pass to DLAZQ3 */
+
+    ttype = 0;
+    dmin1 = 0.;
+    dmin2 = 0.;
+    dn = 0.;
+    dn1 = 0.;
+    dn2 = 0.;
+    tau = 0.;
+
+    iter = 2;
+    nfail = 0;
+    ndiv = n0 - i0 << 1;
+
+    i__1 = *n + 1;
+    for (iwhila = 1; iwhila <= i__1; ++iwhila) {
+	if (n0 < 1) {
+	    goto L150;
+	}
+
+/*        While array unfinished do */
+
+/*        E(N0) holds the value of SIGMA when submatrix in I0:N0 */
+/*        splits from the rest of the array, but is negated. */
+
+	desig = 0.;
+	if (n0 == *n) {
+	    sigma = 0.;
+	} else {
+	    sigma = -z__[(n0 << 2) - 1];
+	}
+	if (sigma < 0.) {
+	    *info = 1;
+	    return 0;
+	}
+
+/*        Find last unreduced submatrix's top index I0, find QMAX and */
+/*        EMIN. Find Gershgorin-type bound if Q's much greater than E's. */
+
+	emax = 0.;
+	if (n0 > i0) {
+	    emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1));
+	} else {
+	    emin = 0.;
+	}
+	qmin = z__[(n0 << 2) - 3];
+	qmax = qmin;
+	for (i4 = n0 << 2; i4 >= 8; i4 += -4) {
+	    if (z__[i4 - 5] <= 0.) {
+		goto L100;
+	    }
+	    if (qmin >= emax * 4.) {
+/* Computing MIN */
+		d__1 = qmin, d__2 = z__[i4 - 3];
+		qmin = min(d__1,d__2);
+/* Computing MAX */
+		d__1 = emax, d__2 = z__[i4 - 5];
+		emax = max(d__1,d__2);
+	    }
+/* Computing MAX */
+	    d__1 = qmax, d__2 = z__[i4 - 7] + z__[i4 - 5];
+	    qmax = max(d__1,d__2);
+/* Computing MIN */
+	    d__1 = emin, d__2 = z__[i4 - 5];
+	    emin = min(d__1,d__2);
+/* L90: */
+	}
+	i4 = 4;
+
+L100:
+	i0 = i4 / 4;
+
+/*        Store EMIN for passing to DLAZQ3. */
+
+	z__[(n0 << 2) - 1] = emin;
+
+/*        Put -(initial shift) into DMIN. */
+
+/* Computing MAX */
+	d__1 = 0., d__2 = qmin - sqrt(qmin) * 2. * sqrt(emax);
+	dmin__ = -max(d__1,d__2);
+
+/*        Now I0:N0 is unreduced. PP = 0 for ping, PP = 1 for pong. */
+
+	pp = 0;
+
+	nbig = (n0 - i0 + 1) * 30;
+	i__2 = nbig;
+	for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) {
+	    if (i0 > n0) {
+		goto L130;
+	    }
+
+/*           While submatrix unfinished take a good dqds step. */
+
+	    dlazq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, &
+		    nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, &
+		    dn1, &dn2, &tau);
+
+	    pp = 1 - pp;
+
+/*           When EMIN is very small check for splits. */
+
+	    if (pp == 0 && n0 - i0 >= 3) {
+		if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 *
+			 sigma) {
+		    splt = i0 - 1;
+		    qmax = z__[(i0 << 2) - 3];
+		    emin = z__[(i0 << 2) - 1];
+		    oldemn = z__[i0 * 4];
+		    i__3 = n0 - 3 << 2;
+		    for (i4 = i0 << 2; i4 <= i__3; i4 += 4) {
+			if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= 
+				tol2 * sigma) {
+			    z__[i4 - 1] = -sigma;
+			    splt = i4 / 4;
+			    qmax = 0.;
+			    emin = z__[i4 + 3];
+			    oldemn = z__[i4 + 4];
+			} else {
+/* Computing MAX */
+			    d__1 = qmax, d__2 = z__[i4 + 1];
+			    qmax = max(d__1,d__2);
+/* Computing MIN */
+			    d__1 = emin, d__2 = z__[i4 - 1];
+			    emin = min(d__1,d__2);
+/* Computing MIN */
+			    d__1 = oldemn, d__2 = z__[i4];
+			    oldemn = min(d__1,d__2);
+			}
+/* L110: */
+		    }
+		    z__[(n0 << 2) - 1] = emin;
+		    z__[n0 * 4] = oldemn;
+		    i0 = splt + 1;
+		}
+	    }
+
+/* L120: */
+	}
+
+	*info = 2;
+	return 0;
+
+/*        end IWHILB */
+
+L130:
+
+/* L140: */
+	;
+    }
+
+    *info = 3;
+    return 0;
+
+/*     end IWHILA */
+
+L150:
+
+/*     Move q's to the front. */
+
+    i__1 = *n;
+    for (k = 2; k <= i__1; ++k) {
+	z__[k] = z__[(k << 2) - 3];
+/* L160: */
+    }
+
+/*     Sort and compute sum of eigenvalues. */
+
+    dlasrt_("D", n, &z__[1], &iinfo);
+
+    e = 0.;
+    for (k = *n; k >= 1; --k) {
+	e += z__[k];
+/* L170: */
+    }
+
+/*     Store trace, sum(eigenvalues) and information on performance. */
+
+    z__[(*n << 1) + 1] = trace;
+    z__[(*n << 1) + 2] = e;
+    z__[(*n << 1) + 3] = (doublereal) iter;
+/* Computing 2nd power */
+    i__1 = *n;
+    z__[(*n << 1) + 4] = (doublereal) ndiv / (doublereal) (i__1 * i__1);
+    z__[(*n << 1) + 5] = nfail * 100. / (doublereal) iter;
+    return 0;
+
+/*     End of DLASQ2 */
+
+} /* dlasq2_ */