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.
461 lines
9.6 KiB
461 lines
9.6 KiB
/* dsterf.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" |
|
|
|
|
|
/* Table of constant values */ |
|
|
|
static integer c__0 = 0; |
|
static integer c__1 = 1; |
|
static doublereal c_b32 = 1.; |
|
|
|
/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, |
|
integer *info) |
|
{ |
|
/* System generated locals */ |
|
integer i__1; |
|
doublereal d__1, d__2, d__3; |
|
|
|
/* Builtin functions */ |
|
double sqrt(doublereal), d_sign(doublereal *, doublereal *); |
|
|
|
/* Local variables */ |
|
doublereal c__; |
|
integer i__, l, m; |
|
doublereal p, r__, s; |
|
integer l1; |
|
doublereal bb, rt1, rt2, eps, rte; |
|
integer lsv; |
|
doublereal eps2, oldc; |
|
integer lend, jtot; |
|
extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal |
|
*, doublereal *, doublereal *); |
|
doublereal gamma, alpha, sigma, anorm; |
|
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *); |
|
integer iscale; |
|
extern /* Subroutine */ int dlascl_(char *, integer *, integer *, |
|
doublereal *, doublereal *, integer *, integer *, doublereal *, |
|
integer *, integer *); |
|
doublereal oldgam, safmin; |
|
extern /* Subroutine */ int xerbla_(char *, integer *); |
|
doublereal safmax; |
|
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *); |
|
extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, |
|
integer *); |
|
integer lendsv; |
|
doublereal ssfmin; |
|
integer nmaxit; |
|
doublereal ssfmax; |
|
|
|
|
|
/* -- LAPACK routine (version 3.2) -- */ |
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
|
/* November 2006 */ |
|
|
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
/* .. Array Arguments .. */ |
|
/* .. */ |
|
|
|
/* Purpose */ |
|
/* ======= */ |
|
|
|
/* DSTERF computes all eigenvalues of a symmetric tridiagonal matrix */ |
|
/* using the Pal-Walker-Kahan variant of the QL or QR algorithm. */ |
|
|
|
/* Arguments */ |
|
/* ========= */ |
|
|
|
/* N (input) INTEGER */ |
|
/* The order of the matrix. N >= 0. */ |
|
|
|
/* D (input/output) DOUBLE PRECISION array, dimension (N) */ |
|
/* On entry, the n diagonal elements of the tridiagonal matrix. */ |
|
/* On exit, if INFO = 0, the eigenvalues in ascending order. */ |
|
|
|
/* E (input/output) DOUBLE PRECISION array, dimension (N-1) */ |
|
/* On entry, the (n-1) subdiagonal elements of the tridiagonal */ |
|
/* matrix. */ |
|
/* On exit, E has been destroyed. */ |
|
|
|
/* INFO (output) INTEGER */ |
|
/* = 0: successful exit */ |
|
/* < 0: if INFO = -i, the i-th argument had an illegal value */ |
|
/* > 0: the algorithm failed to find all of the eigenvalues in */ |
|
/* a total of 30*N iterations; if INFO = i, then i */ |
|
/* elements of E have not converged to zero. */ |
|
|
|
/* ===================================================================== */ |
|
|
|
/* .. Parameters .. */ |
|
/* .. */ |
|
/* .. Local Scalars .. */ |
|
/* .. */ |
|
/* .. External Functions .. */ |
|
/* .. */ |
|
/* .. External Subroutines .. */ |
|
/* .. */ |
|
/* .. Intrinsic Functions .. */ |
|
/* .. */ |
|
/* .. Executable Statements .. */ |
|
|
|
/* Test the input parameters. */ |
|
|
|
/* Parameter adjustments */ |
|
--e; |
|
--d__; |
|
|
|
/* Function Body */ |
|
*info = 0; |
|
|
|
/* Quick return if possible */ |
|
|
|
if (*n < 0) { |
|
*info = -1; |
|
i__1 = -(*info); |
|
xerbla_("DSTERF", &i__1); |
|
return 0; |
|
} |
|
if (*n <= 1) { |
|
return 0; |
|
} |
|
|
|
/* Determine the unit roundoff for this environment. */ |
|
|
|
eps = dlamch_("E"); |
|
/* Computing 2nd power */ |
|
d__1 = eps; |
|
eps2 = d__1 * d__1; |
|
safmin = dlamch_("S"); |
|
safmax = 1. / safmin; |
|
ssfmax = sqrt(safmax) / 3.; |
|
ssfmin = sqrt(safmin) / eps2; |
|
|
|
/* Compute the eigenvalues of the tridiagonal matrix. */ |
|
|
|
nmaxit = *n * 30; |
|
sigma = 0.; |
|
jtot = 0; |
|
|
|
/* Determine where the matrix splits and choose QL or QR iteration */ |
|
/* for each block, according to whether top or bottom diagonal */ |
|
/* element is smaller. */ |
|
|
|
l1 = 1; |
|
|
|
L10: |
|
if (l1 > *n) { |
|
goto L170; |
|
} |
|
if (l1 > 1) { |
|
e[l1 - 1] = 0.; |
|
} |
|
i__1 = *n - 1; |
|
for (m = l1; m <= i__1; ++m) { |
|
if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) * |
|
sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { |
|
e[m] = 0.; |
|
goto L30; |
|
} |
|
/* L20: */ |
|
} |
|
m = *n; |
|
|
|
L30: |
|
l = l1; |
|
lsv = l; |
|
lend = m; |
|
lendsv = lend; |
|
l1 = m + 1; |
|
if (lend == l) { |
|
goto L10; |
|
} |
|
|
|
/* Scale submatrix in rows and columns L to LEND */ |
|
|
|
i__1 = lend - l + 1; |
|
anorm = dlanst_("I", &i__1, &d__[l], &e[l]); |
|
iscale = 0; |
|
if (anorm > ssfmax) { |
|
iscale = 1; |
|
i__1 = lend - l + 1; |
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, |
|
info); |
|
i__1 = lend - l; |
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, |
|
info); |
|
} else if (anorm < ssfmin) { |
|
iscale = 2; |
|
i__1 = lend - l + 1; |
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, |
|
info); |
|
i__1 = lend - l; |
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, |
|
info); |
|
} |
|
|
|
i__1 = lend - 1; |
|
for (i__ = l; i__ <= i__1; ++i__) { |
|
/* Computing 2nd power */ |
|
d__1 = e[i__]; |
|
e[i__] = d__1 * d__1; |
|
/* L40: */ |
|
} |
|
|
|
/* Choose between QL and QR iteration */ |
|
|
|
if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { |
|
lend = lsv; |
|
l = lendsv; |
|
} |
|
|
|
if (lend >= l) { |
|
|
|
/* QL Iteration */ |
|
|
|
/* Look for small subdiagonal element. */ |
|
|
|
L50: |
|
if (l != lend) { |
|
i__1 = lend - 1; |
|
for (m = l; m <= i__1; ++m) { |
|
if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m |
|
+ 1], abs(d__1))) { |
|
goto L70; |
|
} |
|
/* L60: */ |
|
} |
|
} |
|
m = lend; |
|
|
|
L70: |
|
if (m < lend) { |
|
e[m] = 0.; |
|
} |
|
p = d__[l]; |
|
if (m == l) { |
|
goto L90; |
|
} |
|
|
|
/* If remaining matrix is 2 by 2, use DLAE2 to compute its */ |
|
/* eigenvalues. */ |
|
|
|
if (m == l + 1) { |
|
rte = sqrt(e[l]); |
|
dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); |
|
d__[l] = rt1; |
|
d__[l + 1] = rt2; |
|
e[l] = 0.; |
|
l += 2; |
|
if (l <= lend) { |
|
goto L50; |
|
} |
|
goto L150; |
|
} |
|
|
|
if (jtot == nmaxit) { |
|
goto L150; |
|
} |
|
++jtot; |
|
|
|
/* Form shift. */ |
|
|
|
rte = sqrt(e[l]); |
|
sigma = (d__[l + 1] - p) / (rte * 2.); |
|
r__ = dlapy2_(&sigma, &c_b32); |
|
sigma = p - rte / (sigma + d_sign(&r__, &sigma)); |
|
|
|
c__ = 1.; |
|
s = 0.; |
|
gamma = d__[m] - sigma; |
|
p = gamma * gamma; |
|
|
|
/* Inner loop */ |
|
|
|
i__1 = l; |
|
for (i__ = m - 1; i__ >= i__1; --i__) { |
|
bb = e[i__]; |
|
r__ = p + bb; |
|
if (i__ != m - 1) { |
|
e[i__ + 1] = s * r__; |
|
} |
|
oldc = c__; |
|
c__ = p / r__; |
|
s = bb / r__; |
|
oldgam = gamma; |
|
alpha = d__[i__]; |
|
gamma = c__ * (alpha - sigma) - s * oldgam; |
|
d__[i__ + 1] = oldgam + (alpha - gamma); |
|
if (c__ != 0.) { |
|
p = gamma * gamma / c__; |
|
} else { |
|
p = oldc * bb; |
|
} |
|
/* L80: */ |
|
} |
|
|
|
e[l] = s * p; |
|
d__[l] = sigma + gamma; |
|
goto L50; |
|
|
|
/* Eigenvalue found. */ |
|
|
|
L90: |
|
d__[l] = p; |
|
|
|
++l; |
|
if (l <= lend) { |
|
goto L50; |
|
} |
|
goto L150; |
|
|
|
} else { |
|
|
|
/* QR Iteration */ |
|
|
|
/* Look for small superdiagonal element. */ |
|
|
|
L100: |
|
i__1 = lend + 1; |
|
for (m = l; m >= i__1; --m) { |
|
if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m |
|
- 1], abs(d__1))) { |
|
goto L120; |
|
} |
|
/* L110: */ |
|
} |
|
m = lend; |
|
|
|
L120: |
|
if (m > lend) { |
|
e[m - 1] = 0.; |
|
} |
|
p = d__[l]; |
|
if (m == l) { |
|
goto L140; |
|
} |
|
|
|
/* If remaining matrix is 2 by 2, use DLAE2 to compute its */ |
|
/* eigenvalues. */ |
|
|
|
if (m == l - 1) { |
|
rte = sqrt(e[l - 1]); |
|
dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); |
|
d__[l] = rt1; |
|
d__[l - 1] = rt2; |
|
e[l - 1] = 0.; |
|
l += -2; |
|
if (l >= lend) { |
|
goto L100; |
|
} |
|
goto L150; |
|
} |
|
|
|
if (jtot == nmaxit) { |
|
goto L150; |
|
} |
|
++jtot; |
|
|
|
/* Form shift. */ |
|
|
|
rte = sqrt(e[l - 1]); |
|
sigma = (d__[l - 1] - p) / (rte * 2.); |
|
r__ = dlapy2_(&sigma, &c_b32); |
|
sigma = p - rte / (sigma + d_sign(&r__, &sigma)); |
|
|
|
c__ = 1.; |
|
s = 0.; |
|
gamma = d__[m] - sigma; |
|
p = gamma * gamma; |
|
|
|
/* Inner loop */ |
|
|
|
i__1 = l - 1; |
|
for (i__ = m; i__ <= i__1; ++i__) { |
|
bb = e[i__]; |
|
r__ = p + bb; |
|
if (i__ != m) { |
|
e[i__ - 1] = s * r__; |
|
} |
|
oldc = c__; |
|
c__ = p / r__; |
|
s = bb / r__; |
|
oldgam = gamma; |
|
alpha = d__[i__ + 1]; |
|
gamma = c__ * (alpha - sigma) - s * oldgam; |
|
d__[i__] = oldgam + (alpha - gamma); |
|
if (c__ != 0.) { |
|
p = gamma * gamma / c__; |
|
} else { |
|
p = oldc * bb; |
|
} |
|
/* L130: */ |
|
} |
|
|
|
e[l - 1] = s * p; |
|
d__[l] = sigma + gamma; |
|
goto L100; |
|
|
|
/* Eigenvalue found. */ |
|
|
|
L140: |
|
d__[l] = p; |
|
|
|
--l; |
|
if (l >= lend) { |
|
goto L100; |
|
} |
|
goto L150; |
|
|
|
} |
|
|
|
/* Undo scaling if necessary */ |
|
|
|
L150: |
|
if (iscale == 1) { |
|
i__1 = lendsv - lsv + 1; |
|
dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], |
|
n, info); |
|
} |
|
if (iscale == 2) { |
|
i__1 = lendsv - lsv + 1; |
|
dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], |
|
n, info); |
|
} |
|
|
|
/* Check for no convergence to an eigenvalue after a total */ |
|
/* of N*MAXIT iterations. */ |
|
|
|
if (jtot < nmaxit) { |
|
goto L10; |
|
} |
|
i__1 = *n - 1; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
if (e[i__] != 0.) { |
|
++(*info); |
|
} |
|
/* L160: */ |
|
} |
|
goto L180; |
|
|
|
/* Sort eigenvalues in increasing order. */ |
|
|
|
L170: |
|
dlasrt_("I", n, &d__[1], info); |
|
|
|
L180: |
|
return 0; |
|
|
|
/* End of DSTERF */ |
|
|
|
} /* dsterf_ */
|
|
|