mirror of https://github.com/opencv/opencv.git
Open Source Computer Vision Library
https://opencv.org/
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
350 lines
8.9 KiB
350 lines
8.9 KiB
/* dlasq3.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 "clapack.h" |
|
|
|
|
|
/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__, |
|
integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig, |
|
doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, |
|
logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, |
|
doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, |
|
doublereal *tau) |
|
{ |
|
/* System generated locals */ |
|
integer i__1; |
|
doublereal d__1, d__2; |
|
|
|
/* Builtin functions */ |
|
double sqrt(doublereal); |
|
|
|
/* Local variables */ |
|
doublereal s, t; |
|
integer j4, nn; |
|
doublereal eps, tol; |
|
integer n0in, ipn4; |
|
doublereal tol2, temp; |
|
extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *, |
|
integer *, integer *, doublereal *, doublereal *, doublereal *, |
|
doublereal *, doublereal *, doublereal *, doublereal *, integer *, |
|
doublereal *), dlasq5_(integer *, integer *, doublereal *, |
|
integer *, doublereal *, doublereal *, doublereal *, doublereal *, |
|
doublereal *, doublereal *, doublereal *, logical *), dlasq6_( |
|
integer *, integer *, doublereal *, integer *, doublereal *, |
|
doublereal *, doublereal *, doublereal *, doublereal *, |
|
doublereal *); |
|
extern doublereal dlamch_(char *); |
|
extern logical disnan_(doublereal *); |
|
|
|
|
|
/* -- LAPACK routine (version 3.2) -- */ |
|
|
|
/* -- Contributed by Osni Marques of the Lawrence Berkeley National -- */ |
|
/* -- Laboratory and Beresford Parlett of the Univ. of California at -- */ |
|
/* -- Berkeley -- */ |
|
/* -- November 2008 -- */ |
|
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ |
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ |
|
|
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
/* .. Array Arguments .. */ |
|
/* .. */ |
|
|
|
/* Purpose */ |
|
/* ======= */ |
|
|
|
/* DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. */ |
|
/* In case of failure it changes shifts, and tries again until output */ |
|
/* is positive. */ |
|
|
|
/* Arguments */ |
|
/* ========= */ |
|
|
|
/* I0 (input) INTEGER */ |
|
/* First index. */ |
|
|
|
/* N0 (input) INTEGER */ |
|
/* Last index. */ |
|
|
|
/* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) */ |
|
/* Z holds the qd array. */ |
|
|
|
/* PP (input/output) INTEGER */ |
|
/* PP=0 for ping, PP=1 for pong. */ |
|
/* PP=2 indicates that flipping was applied to the Z array */ |
|
/* and that the initial tests for deflation should not be */ |
|
/* performed. */ |
|
|
|
/* DMIN (output) DOUBLE PRECISION */ |
|
/* Minimum value of d. */ |
|
|
|
/* SIGMA (output) DOUBLE PRECISION */ |
|
/* Sum of shifts used in current segment. */ |
|
|
|
/* DESIG (input/output) DOUBLE PRECISION */ |
|
/* Lower order part of SIGMA */ |
|
|
|
/* QMAX (input) DOUBLE PRECISION */ |
|
/* Maximum value of q. */ |
|
|
|
/* NFAIL (output) INTEGER */ |
|
/* Number of times shift was too big. */ |
|
|
|
/* ITER (output) INTEGER */ |
|
/* Number of iterations. */ |
|
|
|
/* NDIV (output) INTEGER */ |
|
/* Number of divisions. */ |
|
|
|
/* IEEE (input) LOGICAL */ |
|
/* Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */ |
|
|
|
/* TTYPE (input/output) INTEGER */ |
|
/* Shift type. */ |
|
|
|
/* DMIN1, DMIN2, DN, DN1, DN2, G, TAU (input/output) DOUBLE PRECISION */ |
|
/* These are passed as arguments in order to save their values */ |
|
/* between calls to DLASQ3. */ |
|
|
|
/* ===================================================================== */ |
|
|
|
/* .. Parameters .. */ |
|
/* .. */ |
|
/* .. Local Scalars .. */ |
|
/* .. */ |
|
/* .. External Subroutines .. */ |
|
/* .. */ |
|
/* .. External Function .. */ |
|
/* .. */ |
|
/* .. Intrinsic Functions .. */ |
|
/* .. */ |
|
/* .. Executable Statements .. */ |
|
|
|
/* Parameter adjustments */ |
|
--z__; |
|
|
|
/* Function Body */ |
|
n0in = *n0; |
|
eps = dlamch_("Precision"); |
|
tol = eps * 100.; |
|
/* Computing 2nd power */ |
|
d__1 = tol; |
|
tol2 = d__1 * d__1; |
|
|
|
/* Check for deflation. */ |
|
|
|
L10: |
|
|
|
if (*n0 < *i0) { |
|
return 0; |
|
} |
|
if (*n0 == *i0) { |
|
goto L20; |
|
} |
|
nn = (*n0 << 2) + *pp; |
|
if (*n0 == *i0 + 1) { |
|
goto L40; |
|
} |
|
|
|
/* Check whether E(N0-1) is negligible, 1 eigenvalue. */ |
|
|
|
if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - |
|
4] > tol2 * z__[nn - 7]) { |
|
goto L30; |
|
} |
|
|
|
L20: |
|
|
|
z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma; |
|
--(*n0); |
|
goto L10; |
|
|
|
/* Check whether E(N0-2) is negligible, 2 eigenvalues. */ |
|
|
|
L30: |
|
|
|
if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[ |
|
nn - 11]) { |
|
goto L50; |
|
} |
|
|
|
L40: |
|
|
|
if (z__[nn - 3] > z__[nn - 7]) { |
|
s = z__[nn - 3]; |
|
z__[nn - 3] = z__[nn - 7]; |
|
z__[nn - 7] = s; |
|
} |
|
if (z__[nn - 5] > z__[nn - 3] * tol2) { |
|
t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5; |
|
s = z__[nn - 3] * (z__[nn - 5] / t); |
|
if (s <= t) { |
|
s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.))); |
|
} else { |
|
s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s))); |
|
} |
|
t = z__[nn - 7] + (s + z__[nn - 5]); |
|
z__[nn - 3] *= z__[nn - 7] / t; |
|
z__[nn - 7] = t; |
|
} |
|
z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma; |
|
z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma; |
|
*n0 += -2; |
|
goto L10; |
|
|
|
L50: |
|
if (*pp == 2) { |
|
*pp = 0; |
|
} |
|
|
|
/* Reverse the qd-array, if warranted. */ |
|
|
|
if (*dmin__ <= 0. || *n0 < n0in) { |
|
if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) { |
|
ipn4 = *i0 + *n0 << 2; |
|
i__1 = *i0 + *n0 - 1 << 1; |
|
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { |
|
temp = z__[j4 - 3]; |
|
z__[j4 - 3] = z__[ipn4 - j4 - 3]; |
|
z__[ipn4 - j4 - 3] = temp; |
|
temp = z__[j4 - 2]; |
|
z__[j4 - 2] = z__[ipn4 - j4 - 2]; |
|
z__[ipn4 - j4 - 2] = temp; |
|
temp = z__[j4 - 1]; |
|
z__[j4 - 1] = z__[ipn4 - j4 - 5]; |
|
z__[ipn4 - j4 - 5] = temp; |
|
temp = z__[j4]; |
|
z__[j4] = z__[ipn4 - j4 - 4]; |
|
z__[ipn4 - j4 - 4] = temp; |
|
/* L60: */ |
|
} |
|
if (*n0 - *i0 <= 4) { |
|
z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1]; |
|
z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp]; |
|
} |
|
/* Computing MIN */ |
|
d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1]; |
|
*dmin2 = min(d__1,d__2); |
|
/* Computing MIN */ |
|
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1] |
|
, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3]; |
|
z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2); |
|
/* Computing MIN */ |
|
d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 = |
|
min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4]; |
|
z__[(*n0 << 2) - *pp] = min(d__1,d__2); |
|
/* Computing MAX */ |
|
d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1, |
|
d__2), d__2 = z__[(*i0 << 2) + *pp + 1]; |
|
*qmax = max(d__1,d__2); |
|
*dmin__ = -0.; |
|
} |
|
} |
|
|
|
/* Choose a shift. */ |
|
|
|
dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2, |
|
tau, ttype, g); |
|
|
|
/* Call dqds until DMIN > 0. */ |
|
|
|
L70: |
|
|
|
dlasq5_(i0, n0, &z__[1], pp, tau, dmin__, dmin1, dmin2, dn, dn1, dn2, |
|
ieee); |
|
|
|
*ndiv += *n0 - *i0 + 2; |
|
++(*iter); |
|
|
|
/* Check status. */ |
|
|
|
if (*dmin__ >= 0. && *dmin1 > 0.) { |
|
|
|
/* Success. */ |
|
|
|
goto L90; |
|
|
|
} else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol |
|
* (*sigma + *dn1) && abs(*dn) < tol * *sigma) { |
|
|
|
/* Convergence hidden by negative DN. */ |
|
|
|
z__[(*n0 - 1 << 2) - *pp + 2] = 0.; |
|
*dmin__ = 0.; |
|
goto L90; |
|
} else if (*dmin__ < 0.) { |
|
|
|
/* TAU too big. Select new TAU and try again. */ |
|
|
|
++(*nfail); |
|
if (*ttype < -22) { |
|
|
|
/* Failed twice. Play it safe. */ |
|
|
|
*tau = 0.; |
|
} else if (*dmin1 > 0.) { |
|
|
|
/* Late failure. Gives excellent shift. */ |
|
|
|
*tau = (*tau + *dmin__) * (1. - eps * 2.); |
|
*ttype += -11; |
|
} else { |
|
|
|
/* Early failure. Divide by 4. */ |
|
|
|
*tau *= .25; |
|
*ttype += -12; |
|
} |
|
goto L70; |
|
} else if (disnan_(dmin__)) { |
|
|
|
/* NaN. */ |
|
|
|
if (*tau == 0.) { |
|
goto L80; |
|
} else { |
|
*tau = 0.; |
|
goto L70; |
|
} |
|
} else { |
|
|
|
/* Possible underflow. Play it safe. */ |
|
|
|
goto L80; |
|
} |
|
|
|
/* Risk of underflow. */ |
|
|
|
L80: |
|
dlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2); |
|
*ndiv += *n0 - *i0 + 2; |
|
++(*iter); |
|
*tau = 0.; |
|
|
|
L90: |
|
if (*tau < *sigma) { |
|
*desig += *tau; |
|
t = *sigma + *desig; |
|
*desig -= t - *sigma; |
|
} else { |
|
t = *sigma + *tau; |
|
*desig = *sigma - (t - *tau) + *desig; |
|
} |
|
*sigma = t; |
|
|
|
return 0; |
|
|
|
/* End of DLASQ3 */ |
|
|
|
} /* dlasq3_ */
|
|
|