Known to work with: | Known not to work with:
-----------------------+----------------------------
- Cint 5.14.25 | Cint 5.14.24
- Cint 5.14.26 | Cint 5.14.29
+ Cint 5.14.31 | Cint before 5.14.29
+
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
This file records noteworthy changes.
+0.5.4 (?? 2000)
+* Algorithms in class matrix (determinant and solve) were replaced by
+ less brain-dead ones and should now have much better performance.
+* Checks were reorganized and split up into three parts:
+ a) exams (small tests with predefined input)
+ b) checks (lenghty consistency checks)
+ c) timings (for crude benchmarking)
+
0.5.3 (23 February 2000)
* A more flexible scheme for registering functions was implemented,
allowing for remembering, too.
## Process this file with automake to produce Makefile.in
-TESTS = run_checks
-check_PROGRAMS = check_ginac
-check_ginac_SOURCES = paranoia_check.cpp numeric_output.cpp \
- numeric_consist.cpp powerlaws.cpp expand_subs.cpp inifcns_consist.cpp \
- differentiation.cpp poly_gcd.cpp normalization.cpp matrix_checks.cpp \
- linear_solve.cpp series_expansion.cpp lortensor_check.cpp \
- fcntimer.cpp main.cpp check.h
-check_ginac_LDADD = ../ginac/libginac.la
+TESTS = run_exams run_checks run_times
+check_PROGRAMS = exams checks times
+exams_SOURCES = exam_paranoia.cpp exam_numeric.cpp exam_powerlaws.cpp \
+ exam_differentiation.cpp exam_polygcd.cpp exam_normalization.cpp \
+ exam_pseries.cpp exam_matrices.cpp exam_lsolve.cpp exam_noncommut.cpp \
+ exam_misc.cpp exams.cpp exams.h
+exams_LDADD = ../ginac/libginac.la
+checks_SOURCES = check_numeric.cpp check_inifcns.cpp check_matrices.cpp \
+ check_lsolve.cpp genex.cpp checks.cpp checks.h
+checks_LDADD = ../ginac/libginac.la
+times_SOURCES = time_dennyfliegner.cpp time_gammaseries.cpp timer.cpp \
+ times.cpp times.h
+times_LDADD = ../ginac/libginac.la
INCLUDES = -I$(srcdir)/../ginac
-CLEANFILES = result.out
-EXTRA_DIST = result.ref run_checks
+CLEANFILES = exams.out checks.out times.out
+EXTRA_DIST = exams.ref checks.ref times.ref run_exams run_checks run_times
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
VERSION = @VERSION@
YACC = @YACC@
-TESTS = run_checks
-check_PROGRAMS = check_ginac
-check_ginac_SOURCES = paranoia_check.cpp numeric_output.cpp numeric_consist.cpp powerlaws.cpp expand_subs.cpp inifcns_consist.cpp differentiation.cpp poly_gcd.cpp normalization.cpp matrix_checks.cpp linear_solve.cpp series_expansion.cpp lortensor_check.cpp fcntimer.cpp main.cpp check.h
+TESTS = run_exams run_checks run_times
+check_PROGRAMS = exams checks times
+exams_SOURCES = exam_paranoia.cpp exam_numeric.cpp exam_powerlaws.cpp exam_differentiation.cpp exam_polygcd.cpp exam_normalization.cpp exam_pseries.cpp exam_matrices.cpp exam_lsolve.cpp exam_noncommut.cpp exam_misc.cpp exams.cpp exams.h
-check_ginac_LDADD = ../ginac/libginac.la
+exams_LDADD = ../ginac/libginac.la
+checks_SOURCES = check_numeric.cpp check_inifcns.cpp check_matrices.cpp check_lsolve.cpp genex.cpp checks.cpp checks.h
+
+checks_LDADD = ../ginac/libginac.la
+times_SOURCES = time_dennyfliegner.cpp time_gammaseries.cpp timer.cpp times.cpp times.h
+
+times_LDADD = ../ginac/libginac.la
INCLUDES = -I$(srcdir)/../ginac
-CLEANFILES = result.out
-EXTRA_DIST = result.ref run_checks
+CLEANFILES = exams.out checks.out times.out
+EXTRA_DIST = exams.ref checks.ref times.ref run_exams run_checks run_times
mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
CONFIG_HEADER = ../config.h
CONFIG_CLEAN_FILES =
CPPFLAGS = @CPPFLAGS@
LDFLAGS = @LDFLAGS@
LIBS = @LIBS@
-check_ginac_OBJECTS = paranoia_check.o numeric_output.o \
-numeric_consist.o powerlaws.o expand_subs.o inifcns_consist.o \
-differentiation.o poly_gcd.o normalization.o matrix_checks.o \
-linear_solve.o series_expansion.o lortensor_check.o fcntimer.o main.o
-check_ginac_DEPENDENCIES = ../ginac/libginac.la
-check_ginac_LDFLAGS =
+exams_OBJECTS = exam_paranoia.o exam_numeric.o exam_powerlaws.o \
+exam_differentiation.o exam_polygcd.o exam_normalization.o \
+exam_pseries.o exam_matrices.o exam_lsolve.o exam_noncommut.o \
+exam_misc.o exams.o
+exams_DEPENDENCIES = ../ginac/libginac.la
+exams_LDFLAGS =
+checks_OBJECTS = check_numeric.o check_inifcns.o check_matrices.o \
+check_lsolve.o genex.o checks.o
+checks_DEPENDENCIES = ../ginac/libginac.la
+checks_LDFLAGS =
+times_OBJECTS = time_dennyfliegner.o time_gammaseries.o timer.o times.o
+times_DEPENDENCIES = ../ginac/libginac.la
+times_LDFLAGS =
CXXFLAGS = @CXXFLAGS@
CXXCOMPILE = $(CXX) $(DEFS) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(AM_CXXFLAGS) $(CXXFLAGS)
LTCXXCOMPILE = $(LIBTOOL) --mode=compile $(CXX) $(DEFS) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(AM_CXXFLAGS) $(CXXFLAGS)
TAR = tar
GZIP_ENV = --best
-DEP_FILES = .deps/differentiation.P .deps/expand_subs.P \
-.deps/fcntimer.P .deps/inifcns_consist.P .deps/linear_solve.P \
-.deps/lortensor_check.P .deps/main.P .deps/matrix_checks.P \
-.deps/normalization.P .deps/numeric_consist.P .deps/numeric_output.P \
-.deps/paranoia_check.P .deps/poly_gcd.P .deps/powerlaws.P \
-.deps/series_expansion.P
-SOURCES = $(check_ginac_SOURCES)
-OBJECTS = $(check_ginac_OBJECTS)
+DEP_FILES = .deps/check_inifcns.P .deps/check_lsolve.P \
+.deps/check_matrices.P .deps/check_numeric.P .deps/checks.P \
+.deps/exam_differentiation.P .deps/exam_lsolve.P .deps/exam_matrices.P \
+.deps/exam_misc.P .deps/exam_noncommut.P .deps/exam_normalization.P \
+.deps/exam_numeric.P .deps/exam_paranoia.P .deps/exam_polygcd.P \
+.deps/exam_powerlaws.P .deps/exam_pseries.P .deps/exams.P .deps/genex.P \
+.deps/time_dennyfliegner.P .deps/time_gammaseries.P .deps/timer.P \
+.deps/times.P
+SOURCES = $(exams_SOURCES) $(checks_SOURCES) $(times_SOURCES)
+OBJECTS = $(exams_OBJECTS) $(checks_OBJECTS) $(times_OBJECTS)
all: all-redirect
.SUFFIXES:
maintainer-clean-libtool:
-check_ginac: $(check_ginac_OBJECTS) $(check_ginac_DEPENDENCIES)
- @rm -f check_ginac
- $(CXXLINK) $(check_ginac_LDFLAGS) $(check_ginac_OBJECTS) $(check_ginac_LDADD) $(LIBS)
+exams: $(exams_OBJECTS) $(exams_DEPENDENCIES)
+ @rm -f exams
+ $(CXXLINK) $(exams_LDFLAGS) $(exams_OBJECTS) $(exams_LDADD) $(LIBS)
+
+checks: $(checks_OBJECTS) $(checks_DEPENDENCIES)
+ @rm -f checks
+ $(CXXLINK) $(checks_LDFLAGS) $(checks_OBJECTS) $(checks_LDADD) $(LIBS)
+
+times: $(times_OBJECTS) $(times_DEPENDENCIES)
+ @rm -f times
+ $(CXXLINK) $(times_LDFLAGS) $(times_OBJECTS) $(times_LDADD) $(LIBS)
.cpp.o:
$(CXXCOMPILE) -c $<
.cpp.lo:
-/** @file inifcns_consist.cpp
+/** @file check_inifcns.cpp
*
* This test routine applies assorted tests on initially known higher level
* functions. */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "checks.h"
/* Some tests on the sine trigonometric function. */
static unsigned inifcns_consist_sin(void)
{
unsigned result = 0;
- bool errorflag;
+ bool errorflag = false;
// sin(n*Pi) == 0?
errorflag = false;
errorflag = false;
ex argument;
numeric epsilon(double(1e-8));
- for (int n=-240; n<=240; ++n) {
+ for (int n=-340; n<=340; ++n) {
argument = n*Pi/60;
if (abs(sin(evalf(argument))-evalf(sin(argument)))>epsilon) {
clog << "sin(" << argument << ") returns "
errorflag = false;
ex argument;
numeric epsilon(double(1e-8));
- for (int n=-240; n<=240; ++n) {
+ for (int n=-340; n<=340; ++n) {
argument = n*Pi/60;
if (abs(cos(evalf(argument))-evalf(cos(argument)))>epsilon) {
clog << "cos(" << argument << ") returns "
errorflag = false;
ex argument;
numeric epsilon(double(1e-8));
- for (int n=-240; n<=240; ++n) {
+ for (int n=-340; n<=340; ++n) {
if (!(n%30) && (n%60)) // skip poles
++n;
argument = n*Pi/60;
return result;
}
-unsigned inifcns_consist(void)
+unsigned check_inifcns(void)
{
unsigned result = 0;
- cout << "checking consistency of symbolic functions..." << flush;
+ cout << "checking consistency of symbolic functions" << flush;
clog << "---------consistency of symbolic functions:" << endl;
- result += inifcns_consist_sin();
- result += inifcns_consist_cos();
- result += inifcns_consist_tan();
- result += inifcns_consist_trans();
- result += inifcns_consist_gamma();
- result += inifcns_consist_psi();
- result += inifcns_consist_zeta();
+ result += inifcns_consist_sin(); cout << '.' << flush;
+ result += inifcns_consist_cos(); cout << '.' << flush;
+ result += inifcns_consist_tan(); cout << '.' << flush;
+ result += inifcns_consist_trans(); cout << '.' << flush;
+ result += inifcns_consist_gamma(); cout << '.' << flush;
+ result += inifcns_consist_psi(); cout << '.' << flush;
+ result += inifcns_consist_zeta(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
return result;
--- /dev/null
+/** @file check_lsolve.cpp
+ *
+ * These test routines do some simple checks on solving linear systems of
+ * symbolic equations. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#include "checks.h"
+
+static unsigned lsolve1(int size)
+{
+ // A dense size x size matrix in dense univariate random polynomials
+ // of order 4.
+ unsigned result = 0;
+ symbol a("a");
+ ex sol;
+
+ // Create two dense linear matrices A and B where all entries are random
+ // univariate polynomials
+ matrix A(size,size), B(size,2), X(size,2);
+ for (int ro=0; ro<size; ++ro) {
+ for (int co=0; co<size; ++co)
+ A.set(ro,co,dense_univariate_poly(a, 5));
+ for (int co=0; co<2; ++co)
+ B.set(ro,co,dense_univariate_poly(a, 5));
+ }
+ if (A.determinant().is_zero())
+ clog << "lsolve1: singular system!" << endl;
+
+ // Solve the system A*X==B:
+ X = A.old_solve(B);
+
+ // check the result:
+ bool errorflag = false;
+ matrix Aux(size,2);
+ Aux = A.mul(X).sub(B);
+ for (int ro=0; ro<size && !errorflag; ++ro)
+ for (int co=0; co<2; ++co)
+ if (!(Aux(ro,co)).normal().is_zero())
+ errorflag = true;
+ if (errorflag) {
+ clog << "Our solve method claims that A*X==B, with matrices" << endl
+ << "A == " << A << endl
+ << "X == " << X << endl
+ << "B == " << B << endl;
+ ++result;
+ }
+ return result;
+}
+
+static unsigned lsolve2(int size)
+{
+ // A dense size x size matrix in dense bivariate random polynomials
+ // of order 2.
+ unsigned result = 0;
+ symbol a("a"), b("b");
+ ex sol;
+
+ // Create two dense linear matrices A and B where all entries are dense random
+ // bivariate polynomials:
+ matrix A(size,size), B(size,2), X(size,2);
+ for (int ro=0; ro<size; ++ro) {
+ for (int co=0; co<size; ++co)
+ A.set(ro,co,dense_bivariate_poly(a,b,2));
+ for (int co=0; co<2; ++co)
+ B.set(ro,co,dense_bivariate_poly(a,b,2));
+ }
+ if (A.determinant().is_zero())
+ clog << "lsolve2: singular system!" << endl;
+
+ // Solve the system A*X==B:
+ X = A.old_solve(B);
+
+ // check the result:
+ bool errorflag = false;
+ matrix Aux(size,2);
+ Aux = A.mul(X).sub(B);
+ for (int ro=0; ro<size && !errorflag; ++ro)
+ for (int co=0; co<2; ++co)
+ if (!(Aux(ro,co)).normal().is_zero())
+ errorflag = true;
+ if (errorflag) {
+ clog << "Our solve method claims that A*X==B, with matrices" << endl
+ << "A == " << A << endl
+ << "X == " << X << endl
+ << "B == " << B << endl;
+ ++result;
+ }
+ return result;
+}
+
+unsigned check_lsolve(void)
+{
+ unsigned result = 0;
+
+ cout << "checking linear solve" << flush;
+ clog << "---------linear solve:" << endl;
+
+ //result += lsolve1(2); cout << '.' << flush;
+ //result += lsolve1(3); cout << '.' << flush;
+ //result += lsolve2(2); cout << '.' << flush;
+ //result += lsolve2(3); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
+}
--- /dev/null
+/** @file check_matrices.cpp
+ *
+ * Here we test manipulations on GiNaC's symbolic matrices. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#include "checks.h"
+
+// determinants of some sparse symbolic size x size matrices
+static unsigned matrix_determinants(void)
+{
+ unsigned result = 0;
+ symbol a("a");
+
+ for (int size=3; size<16; ++size) {
+ matrix A(size,size);
+ for (int c=0; c<size; ++c) {
+ for (int r=0;r<size-1; ++r)
+ // populate 10 percent of the entries, the rest remains 0:
+ if (!(int)(10.0*rand()/(RAND_MAX+1.0)))
+ A.set(r,c,dense_univariate_poly(a,5));
+ // set the last line to a linear combination of two other lines
+ // to guarantee that the determinant vanishes:
+ A.set(size-1,c,A(0,c)-A(size-2,c));
+ }
+ if (!A.determinant().is_zero()) {
+ clog << "Determinant of " << size << "x" << size << " matrix "
+ << endl << A << endl
+ << "was not found to vanish!" << endl;
+ ++result;
+ }
+ }
+
+ return result;
+}
+
+unsigned check_matrices(void)
+{
+ unsigned result = 0;
+
+ cout << "checking symbolic matrix manipulations" << flush;
+ clog << "---------symbolic matrix manipulations:" << endl;
+
+ result += matrix_determinants(); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
+}
--- /dev/null
+/** @file check_numeric.cpp
+ *
+ * These exams creates some numbers and check the result of several boolean
+ * tests on these numbers like is_integer() etc... */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#include "checks.h"
+
+#ifndef NO_NAMESPACE_GINAC
+using namespace GiNaC;
+#endif // ndef NO_NAMESPACE_GINAC
+
+/* Simple and maybe somewhat pointless consistency tests of assorted tests and
+ * conversions. */
+static unsigned check_numeric1(void)
+{
+ unsigned result = 0;
+ bool errorflag = false;
+ int re_q, im_q;
+
+ // Check some numerator and denominator calculations:
+ for (int i=0; i<200; ++i) {
+ do { re_q = rand(); } while (re_q == 0);
+ do { im_q = rand(); } while (im_q == 0);
+ numeric r(rand()-RAND_MAX/2, re_q);
+ numeric i(rand()-RAND_MAX/2, im_q);
+ numeric z = r + I*i;
+ numeric p = numer(z);
+ numeric q = denom(z);
+ numeric res = p/q;
+ if (res != z) {
+ clog << z << " erroneously transformed into "
+ << p << "/" << q << " by numer() and denom()" << endl;
+ errorflag = true;
+ }
+ }
+ if (errorflag)
+ ++result;
+
+ return result;
+}
+
+static unsigned check_numeric2(void)
+{
+ unsigned result = 0;
+ bool errorflag = false;
+ int i_num, i_den;
+
+ // Check non-nested radicals (n/d)^(m/n) in ex wrapper class:
+ for (int i=0; i<200; ++i) { // FIXME: run to ~200
+ for (int j=2; j<13; ++j) {
+ // construct an exponent 1/j...
+ numeric nm(1,j);
+ nm += numeric(int(20.0*rand()/(RAND_MAX+1.0))-10);
+ // ...a numerator...
+ do { i_num = rand(); } while (i_num == 0);
+ numeric num(i_num);
+ // ...and a denominator.
+ do { i_den = (rand())/100; } while (i_den == 0);
+ numeric den(i_den);
+ // construct the radicals:
+ ex radical = pow(ex(num)/ex(den),ex(nm));
+ numeric floating = pow(num/den,nm);
+ // test the result:
+ if (is_ex_of_type(radical,numeric)) {
+ clog << "(" << num << "/" << den << ")^(" << nm
+ << ") should have been a product, instead it's "
+ << radical << endl;
+ errorflag = true;
+ }
+ numeric ratio = ex_to_numeric(evalf(radical))/floating;
+ if (ratio>1.0001 && ratio<0.9999) {
+ clog << "(" << num << "/" << den << ")^(" << nm
+ << ") erroneously evaluated to " << radical;
+ errorflag = true;
+ }
+ }
+ }
+ if (errorflag)
+ ++result;
+
+ return result;
+}
+
+unsigned check_numeric(void)
+{
+ unsigned result = 0;
+
+ cout << "checking consistency of numeric types" << flush;
+ clog << "---------consistency of numeric types:" << endl;
+
+ result += check_numeric1(); cout << '.' << flush;
+ result += check_numeric2(); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
+}
--- /dev/null
+/** @file checks.cpp
+ *
+ * Main program that calls the individual tests. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#include <stdexcept>
+#include <iostream>
+#include <time.h>
+
+#include "checks.h"
+
+int main()
+{
+ unsigned result = 0;
+
+ srand((unsigned)time(NULL));
+
+ try {
+ for (int i=0; i<1; ++i)
+ result += check_numeric();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ for (int i=0; i<1; ++i)
+ result += check_inifcns();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ for (int i=0; i<1; ++i)
+ result += check_matrices();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ for (int i=0; i<1; ++i)
+ result += check_lsolve();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ if (result) {
+ cout << "Error: something went wrong. ";
+ if (result == 1) {
+ cout << "(one failure)" << endl;
+ } else {
+ cout << "(" << result << " individual failures)" << endl;
+ }
+ cout << "please check check.out against check.ref for more details."
+ << endl << "happy debugging!" << endl;
+ }
+
+ return result;
+}
-/** @file check.h
+/** @file checks.h
*
* Prototypes for all individual checks. */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#ifndef CHECK_H
-#define CHECK_H
-
-// fcntimer is defined in timer.cpp and used for timing check functions only:
-unsigned fcntimer(unsigned fcn());
-
-// prototypes for all individual checks must be unsigned fcn() in order to be
-// able to use fcntimer() as a wrapper:
-unsigned paranoia_check();
-unsigned numeric_output();
-unsigned numeric_consist();
-unsigned powerlaws();
-unsigned expand_subs();
-unsigned inifcns_consist();
-unsigned differentiation();
-unsigned poly_gcd();
-unsigned normalization();
-unsigned matrix_checks();
-unsigned linear_solve();
-unsigned series_expansion();
-unsigned lortensor_check();
-
-#endif // ndef CHECK_H
+#ifndef CHECKS_H
+#define CHECKS_H
+
+// For rand() and friends:
+#include <stdlib.h>
+
+#include "ginac.h"
+
+#ifndef NO_NAMESPACE_GINAC
+using namespace GiNaC;
+#endif // ndef NO_NAMESPACE_GINAC
+
+// prototypes for the expression generating functions in:
+const ex dense_univariate_poly(const symbol & x, unsigned degree);
+const ex dense_bivariate_poly(const symbol & x1, const symbol & x2, unsigned degree);
+
+// prototypes for all individual checks should be unsigned fcn():
+unsigned check_numeric();
+unsigned check_inifcns();
+unsigned check_matrices();
+unsigned check_lsolve();
+
+#endif // ndef CHECKS_H
--- /dev/null
+---------consistency of numeric types:
+(no output)
+---------consistency of symbolic functions:
+(no output)
+---------symbolic matrix manipulations:
+(no output)
+---------linear solve:
+(no output)
-/** @file differentiation.cpp
+/** @file exam_differentiation.cpp
*
* Tests for symbolic differentiation, including various functions. */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "exams.h"
static unsigned check_diff(const ex &e, const symbol &x,
const ex &d, unsigned nth=1)
}
// Simple (expanded) polynomials
-static unsigned differentiation1(void)
+static unsigned exam_differentiation1(void)
{
unsigned result = 0;
symbol x("x"), y("y");
}
// Trigonometric functions
-static unsigned differentiation2(void)
+static unsigned exam_differentiation2(void)
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
}
// exp function
-static unsigned differentiation3(void)
+static unsigned exam_differentiation3(void)
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
}
// log functions
-static unsigned differentiation4(void)
+static unsigned exam_differentiation4(void)
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
}
// Functions with two variables
-static unsigned differentiation5(void)
+static unsigned exam_differentiation5(void)
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
}
// Series
-static unsigned differentiation6(void)
+static unsigned exam_differentiation6(void)
{
symbol x("x");
ex e, d, ed;
return 0;
}
-unsigned differentiation(void)
+unsigned exam_differentiation(void)
{
unsigned result = 0;
- cout << "checking symbolic differentiation..." << flush;
- clog << "---------symbolic differentiation:" << endl;
+ cout << "examining symbolic differentiation" << flush;
+ clog << "----------symbolic differentiation:" << endl;
- result += differentiation1();
- result += differentiation2();
- result += differentiation3();
- result += differentiation4();
- result += differentiation5();
- result += differentiation6();
+ result += exam_differentiation1(); cout << '.' << flush;
+ result += exam_differentiation2(); cout << '.' << flush;
+ result += exam_differentiation3(); cout << '.' << flush;
+ result += exam_differentiation4(); cout << '.' << flush;
+ result += exam_differentiation5(); cout << '.' << flush;
+ result += exam_differentiation6(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
return result;
}
-/** @file linear_solve.cpp
+/** @file exam_lsolve.cpp
*
- * These test routines do some simple checks on solving linear systems of
- * symbolic equations. */
+ * These exams test solving small linear systems of symbolic equations. */
/*
* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
+#include "exams.h"
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
-
-static unsigned lsolve1(void)
+static unsigned exam_lsolve1(void)
{
// A trivial example.
unsigned result = 0;
return result;
}
-static unsigned lsolve2a(void)
+static unsigned exam_lsolve2a(void)
{
- // An example from the Maple online-help.
+ // An example from the Maple online help.
unsigned result = 0;
symbol a("a"), b("b"), x("x"), y("y");
lst eqns, vars;
return result;
}
-static unsigned lsolve2b(void)
+static unsigned exam_lsolve2b(void)
{
- // A boring example from Mathematica's online-help.
+ // A boring example from Mathematica's online help.
unsigned result = 0;
symbol x("x"), y("y");
lst eqns, vars;
return result;
}
-static unsigned lsolve2c(void)
+static unsigned exam_lsolve2c(void)
{
- // An example from the Maple online-help.
+ // An example from the Maple online help.
unsigned result = 0;
symbol x("x"), y("y");
lst eqns, vars;
return result;
}
-unsigned linear_solve(void)
+unsigned exam_lsolve(void)
{
unsigned result = 0;
- cout << "checking linear solve..." << flush;
- clog << "---------linear solve:" << endl;
+ cout << "examining linear solve" << flush;
+ clog << "----------linear solve:" << endl;
- result += lsolve1();
- result += lsolve2a();
- result += lsolve2b();
- result += lsolve2c();
+ result += exam_lsolve1(); cout << '.' << flush;
+ result += exam_lsolve2a(); cout << '.' << flush;
+ result += exam_lsolve2b(); cout << '.' << flush;
+ result += exam_lsolve2c(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
return result;
-/** @file matrix_checks.cpp
+/** @file exam_matrices.cpp
*
- * Here we test manipulations on GiNaC's symbolic matrices. */
+ * Here we examine manipulations on GiNaC's symbolic matrices. */
/*
* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
*/
#include <stdexcept>
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "exams.h"
static unsigned matrix_determinants(void)
{
unsigned result = 0;
ex det;
- matrix m1(1,1), m2(2,2), m3(3,3);
+ matrix m1(1,1), m2(2,2), m3(3,3), m4(4,4);
symbol a("a"), b("b"), c("c");
symbol d("d"), e("e"), f("f");
symbol g("g"), h("h"), i("i");
++result;
}
+ // check sparse symbolic 4x4 matrix determinant
+ m4.set(0,1,a).set(1,0,b).set(3,2,c).set(2,3,d);
+ det = m4.determinant();
+ if (det != a*b*c*d) {
+ clog << "determinant of 4x4 matrix " << m4
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
// check characteristic polynomial
m3.set(0,0,a).set(0,1,-2).set(0,2,2);
m3.set(1,0,3).set(1,1,a-1).set(1,2,2);
bool caught=false;
try {
m5 = inverse(m4);
- }
- catch (std::runtime_error err) {
+ } catch (std::runtime_error err) {
caught=true;
}
if (!caught) {
return result;
}
-unsigned matrix_checks(void)
+unsigned exam_matrices(void)
{
unsigned result = 0;
- cout << "checking symbolic matrix manipulations..." << flush;
- clog << "---------symbolic matrix manipulations:" << endl;
-
- result += matrix_determinants();
- result += matrix_invert1();
- result += matrix_invert2();
- result += matrix_invert3();
- result += matrix_misc();
+ cout << "examining symbolic matrix manipulations" << flush;
+ clog << "----------symbolic matrix manipulations:" << endl;
+
+ result += matrix_determinants(); cout << '.' << flush;
+ result += matrix_invert1(); cout << '.' << flush;
+ result += matrix_invert2(); cout << '.' << flush;
+ result += matrix_invert3(); cout << '.' << flush;
+ result += matrix_misc(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
return result;
-/** @file expand_subs.cpp
+/** @file exam_misc.cpp
*
- * The first test routine implements Denny Fliegner's quick consistency check:
- * e = (a0 + a1 + a2 + a3 + ...)^2
- * expand e
- * substitute a0 by (-a2 - a3 - ...) in e
- * expand e
- * after which e should be just a1^2.
- * In addition, a simpler modification is tested in the second test:
- * e = (a0 + a1)^200
- * expand e
- * substitute a0 by -a1 in e
- * after which e should return 0 (without expanding). */
-
+ */
/*
* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
*
*/
-#include "ginac.h"
+#include "exams.h"
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
-
-#define VECSIZE 100
-
-static unsigned expand_subs1(void)
+#define VECSIZE 30
+static unsigned exam_expand_subs(void)
{
+ unsigned result = 0;
symbol a1("a1");
symbol a[VECSIZE];
ex e, aux;
-
+
a[1] = a1;
for (unsigned i=0; i<VECSIZE; ++i) {
e = e + a[i];
}
-
+
// prepare aux so it will swallow anything but a1^2:
aux = -e + a[0] + a[1];
e = expand(subs(expand(pow(e, 2)), a[0] == aux));
-
+
if (e != pow(a1,2)) {
clog << "Denny Fliegner's quick consistency check erroneously returned "
<< e << "." << endl;
- return 1;
+ ++result;
}
- return 0;
+
+ return result;
}
-static unsigned expand_subs2(void)
+/* A simple modification of Denny Fliegner's three step consistency test:
+ * 1) e = (a0 + a1)^200
+ * 2) expand e
+ * 3) substitute a0 by -a1 in e
+ * after which e should return 0 (without expanding). */
+static unsigned exam_expand_subs2(void)
{
+ unsigned result = 0;
symbol a("a"), b("b");
ex e, f;
-
- // Here the final expand() should be superflous. For no particular reason
- // at all, we don't use the wrapper-functions but the methods instead:
+
e = pow(a+b,200).expand();
f = e.subs(a == -b);
if (f != 0) {
clog << "e = pow(a+b,200).expand(); f = e.subs(a == -b); erroneously returned "
<< f << " instead of simplifying to 0." << endl;
- return 1;
+ ++result;
}
- return 0;
+
+ return result;
}
-unsigned expand_subs(void)
+unsigned exam_misc(void)
{
unsigned result = 0;
-
- cout << "checking commutative expansion and substitution..." << flush;
- clog << "---------commutative expansion and substitution:" << endl;
- result += expand_subs1();
- result += expand_subs2();
+ cout << "examining miscellaneous other things" << flush;
+ clog << "----------miscellaneous other things:" << endl;
+
+ result += exam_expand_subs(); cout << '.' << flush;
+ result += exam_expand_subs2(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
-
+
return result;
}
-/** @file lortensor_check.cpp
+/** @file exam_noncommut.cpp
*
* Here we test manipulations on GiNaC's lortensors. */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include <stdexcept>
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "exams.h"
static unsigned lortensor_check1(void)
{
return result;
}
-unsigned lortensor_check(void)
+unsigned exam_noncommut(void)
{
unsigned result = 0;
- cout << "checking manipulations of lortensor objects..." << flush;
- clog << "---------manipulations of lortensor objects:" << endl;
+ cout << "examining behaviour of noncommutative objects" << flush;
+ clog << "----------behaviour of noncommutative objects:" << endl;
- result += lortensor_check1();
- result += lortensor_check2();
+ result += lortensor_check1(); cout << '.' << flush;
+ result += lortensor_check2(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
return result;
-/** @file normalization.cpp
+/** @file exam_normalization.cpp
*
* Rational function normalization test suite. */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "exams.h"
static symbol w("w"), x("x"), y("y"), z("z");
return 0;
}
-static unsigned normal1(void)
+static unsigned exam_normal1(void)
{
unsigned result = 0;
ex e, d;
e = pow(x, -1) + x/(x+1);
d = (pow(x, 2)+x+1)/(x*(x+1));
result += check_normal(e, d);
-
- // Fraction cancellation
- e = numeric(1)/2 * z * (2*x + 2*y);
- d = z * (x + y);
- result += check_normal(e, d);
- e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w);
- d = z * (x + y) * (x + w);
- result += check_normal(e, d);
-
- e = (3*x + 3*y) * (w/3 + z/3);
- d = (x + y) * (w + z);
- result += check_normal(e, d);
+ return result;
+}
+static unsigned exam_normal2(void)
+{
+ unsigned result = 0;
+ ex e, d;
+
+ // Fraction cancellation
+ e = numeric(1)/2 * z * (2*x + 2*y);
+ d = z * (x + y);
+ result += check_normal(e, d);
+
+ e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w);
+ d = z * (x + y) * (x + w);
+ result += check_normal(e, d);
+
+ e = (3*x + 3*y) * (w/3 + z/3);
+ d = (x + y) * (w + z);
+ result += check_normal(e, d);
+
e = (pow(x, 2) - pow(y, 2)) / pow(x-y, 3);
d = (x + y) / (pow(x, 2) + pow(y, 2) - x * y * 2);
result += check_normal(e, d);
e = (pow(x, -1) + x) / (pow(x , 2) * 2 + 2);
d = pow(x * 2, -1);
result += check_normal(e, d);
+
+ // Fraction cancellation with rational coefficients
+ e = (pow(x, 2) - pow(y, 2)) / pow(x/2 - y/2, 3);
+ d = (8 * x + 8 * y) / (pow(x, 2) + pow(y, 2) - x * y * 2);
+ result += check_normal(e, d);
+
+ // Fraction cancellation with rational coefficients
+ e = z/5 * (x/7 + y/10) / (x/14 + y/20);
+ d = 2*z/5;
+ result += check_normal(e, d);
+
+ return result;
+}
- // Fraction cancellation with rational coefficients
- e = (pow(x, 2) - pow(y, 2)) / pow(x/2 - y/2, 3);
- d = (8 * x + 8 * y) / (pow(x, 2) + pow(y, 2) - x * y * 2);
- result += check_normal(e, d);
-
- // Fraction cancellation with rational coefficients
- e = z/5 * (x/7 + y/10) / (x/14 + y/20);
- d = 2*z/5;
- result += check_normal(e, d);
+static unsigned exam_normal3(void)
+{
+ unsigned result = 0;
+ ex e, d;
// Distribution of powers
e = pow(x/y, 2);
d = pow((pow(x, 2) + 1) / x, numeric(1)/2);
result += check_normal(e, d);
+ return result;
+}
+
+static unsigned exam_normal4(void)
+{
+ unsigned result = 0;
+ ex e, d;
+
// Replacement of functions with temporary symbols and fraction cancellation
e = pow(sin(x), 2) - pow(cos(x), 2);
e /= sin(x) + cos(x);
return result;
}
-unsigned normalization(void)
+unsigned exam_normalization(void)
{
unsigned result = 0;
- cout << "checking rational function normalization..." << flush;
- clog << "---------rational function normalization:" << endl;
+ cout << "examining rational function normalization" << flush;
+ clog << "----------rational function normalization:" << endl;
- result += normal1();
+ result += exam_normal1(); cout << '.' << flush;
+ result += exam_normal2(); cout << '.' << flush;
+ result += exam_normal3(); cout << '.' << flush;
+ result += exam_normal4(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
+
return result;
}
-/** @file numeric_consist.cpp
+/** @file exam_numeric.cpp
*
- * This test routine creates some numbers and check the result of several
- * boolean tests on these numbers like is_integer() etc... */
+ * These exams creates some numbers and check the result of several boolean
+ * tests on these numbers like is_integer() etc... */
/*
* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include <stdlib.h>
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "exams.h"
/* Simple and maybe somewhat pointless consistency tests of assorted tests and
* conversions. */
-static unsigned numeric_consist1(void)
+static unsigned exam_numeric1(void)
{
unsigned result = 0;
numeric test_int1(42);
++result;
}
- // Check some numerator and denominator calculations:
- for (int i=0; i<10; ++i) {
- int re_q, im_q;
- do { re_q = rand(); } while (re_q == 0);
- do { im_q = rand(); } while (im_q == 0);
- numeric r(rand()-RAND_MAX/2, re_q);
- numeric i(rand()-RAND_MAX/2, im_q);
- numeric z = r + I*i;
- numeric p = numer(z);
- numeric q = denom(z);
- numeric res = p/q;
- if (res != z) {
- clog << z << " erroneously transformed into "
- << p << "/" << q << " by numer() and denom()" << endl;
- ++result;
- }
- }
return result;
}
* Implementing a workaround sadly introduced another bug on May 28th 1999
* that was fixed on May 31st. The workaround turned out to be stupid and
* the original bug in CLN was finally killed on September 2nd. */
-static unsigned numeric_consist2(void)
+static unsigned exam_numeric2(void)
{
unsigned result = 0;
/* Assorted tests to ensure some crucial functions behave exactly as specified
* in the documentation. */
-static unsigned numeric_consist3(void)
+static unsigned exam_numeric3(void)
{
unsigned result = 0;
numeric calc_rem, calc_quo;
/* Now we perform some less trivial checks about several functions which should
* return exact numbers if possible. */
-static unsigned numeric_consist4(void)
+static unsigned exam_numeric4(void)
{
unsigned result = 0;
bool passed;
return result;
}
-unsigned numeric_consist(void)
+unsigned exam_numeric(void)
{
unsigned result = 0;
-
- cout << "checking consistency of numeric types..." << flush;
- clog << "---------consistency of numeric types:" << endl;
- result += numeric_consist1();
- result += numeric_consist2();
- result += numeric_consist3();
- result += numeric_consist4();
-
+ cout << "examining consistency of numeric types" << flush;
+ clog << "----------consistency of numeric types:" << endl;
+
+ result += exam_numeric1(); cout << '.' << flush;
+ result += exam_numeric2(); cout << '.' << flush;
+ result += exam_numeric3(); cout << '.' << flush;
+ result += exam_numeric4(); cout << '.' << flush;
+
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
return result;
-/** @file paranoia_check.cpp
+/** @file exam_paranoia.cpp
*
* This set of tests checks for some of GiNaC's oopses which showed up during
* development. Things were evaluated wrongly and so. Such a sick behaviour
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "exams.h"
// The very first pair of historic problems had its roots in power.cpp and was
// finally resolved on April 27th 1999. (Fixing the first on April 23rd
// actually introduced the second.)
-static unsigned paranoia_check1(void)
+static unsigned exam_paranoia1(void)
{
unsigned result = 0;
symbol x("x"), y("y"), z("z");
// And here the second oops which showed up until May 17th 1999. It had to do
// with lexicographic canonicalization and thus showed up only if the variables
// had the names as given here:
-static unsigned paranoia_check2(void)
+static unsigned exam_paranoia2(void)
{
unsigned result = 0;
symbol x("x"), y("y"), z("z");
// The third bug was introduced on May 18th 1999, discovered on May 19 and
// fixed that same day. It worked when x was substituted by 1 but not with
// other numbers:
-static unsigned paranoia_check3(void)
+static unsigned exam_paranoia3(void)
{
unsigned result = 0;
symbol x("x"), y("y");
}
// The fourth bug was also discovered on May 19th 1999 and fixed immediately:
-static unsigned paranoia_check4(void)
+static unsigned exam_paranoia4(void)
{
unsigned result = 0;
symbol x("x");
}
// The fifth oops was discovered on May 20th 1999 and fixed a day later:
-static unsigned paranoia_check5(void)
+static unsigned exam_paranoia5(void)
{
unsigned result = 0;
symbol x("x"), y("y");
}
// This one was discovered on Jun 1st 1999 and fixed the same day:
-static unsigned paranoia_check6(void)
+static unsigned exam_paranoia6(void)
{
unsigned result = 0;
symbol x("x");
// This one was introduced on June 1st 1999 by some aggressive manual
// optimization. Discovered and fixed on June 2nd.
-static unsigned paranoia_check7(void)
+static unsigned exam_paranoia7(void)
{
unsigned result = 0;
symbol x("x"), y("y");
// This one was a result of the rewrite of mul::max_coefficient when we
// introduced the overall_coefficient field in expairseq objects on Oct 1st
// 1999. Fixed on Oct 4th.
-static unsigned paranoia_check8(void)
+static unsigned exam_paranoia8(void)
{
unsigned result = 0;
symbol x("x");
// Z[X]. multiply_lcm() forgot to multiply the x-linear term with the LCM of
// the coefficient's denominators (2 in this case). Introduced on Jan 25th
// 2000 and fixed on Jan 31th.
-static unsigned paranoia_check9(void)
+static unsigned exam_paranoia9(void)
{
unsigned result = 0;
symbol x("x");
// and on Feb 13th 2000 I found out that things like 2^(3/2) throw an exception
// "power::eval(): pow(0,0) is undefined" instead of simplifying to 2*2^(1/2).
// It was fixed that same day.
-static unsigned paranoia_check10(void)
+static unsigned exam_paranoia10(void)
{
unsigned result = 0;
// add::normal() forgot to multiply the denominator of the overall_coeff of
// its expanded and normalized children with the denominator of the expanded
// child (did you get this? Well, never mind...). Fixed on Feb 21th 2000.
-static unsigned paranoia_check11(void)
+static unsigned exam_paranoia11(void)
{
unsigned result = 0;
symbol x("x");
return result;
}
-unsigned paranoia_check(void)
+unsigned exam_paranoia(void)
{
unsigned result = 0;
-
- cout << "checking several ex-bugs just out of pure paranoia..." << flush;
- clog << "---------several ex-bugs just out of pure paranoia:" << endl;
-
- result += paranoia_check1();
- result += paranoia_check2();
- result += paranoia_check3();
- result += paranoia_check4();
- result += paranoia_check5();
- result += paranoia_check6();
- result += paranoia_check7();
- result += paranoia_check8();
- result += paranoia_check9();
- result += paranoia_check10();
- result += paranoia_check11();
-
+
+ cout << "examining several historic failures just out of paranoia" << flush;
+ clog << "----------several historic failures:" << endl;
+
+ result += exam_paranoia1(); cout << '.' << flush;
+ result += exam_paranoia2(); cout << '.' << flush;
+ result += exam_paranoia3(); cout << '.' << flush;
+ result += exam_paranoia4(); cout << '.' << flush;
+ result += exam_paranoia5(); cout << '.' << flush;
+ result += exam_paranoia6(); cout << '.' << flush;
+ result += exam_paranoia7(); cout << '.' << flush;
+ result += exam_paranoia8(); cout << '.' << flush;
+ result += exam_paranoia9(); cout << '.' << flush;
+ result += exam_paranoia10(); cout << '.' << flush;
+ result += exam_paranoia11(); cout << '.' << flush;
+
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
-
+
return result;
}
-/** @file poly_gcd.cpp
+/** @file exam_polygcd.cpp
*
* Some test with polynomial GCD calculations. See also the checks for
* rational function normalization in normalization.cpp. */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
+#include "exams.h"
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
-
-const int MAX_VARIABLES = 5;
+const int MAX_VARIABLES = 3;
static symbol x("x"), z("z");
static symbol y[MAX_VARIABLES];
ex p = x - y * z + 1;
ex q = x - y + z * 3;
- for (int j=1; j<=3; j++) {
+ for (int j=1; j<=MAX_VARIABLES; j++) {
for (int k=j+1; k<=4; k++) {
ex d = pow(p, j) * pow(q, j);
ex f = pow(p, j) * pow(q, k);
return 0;
}
-unsigned poly_gcd(void)
+unsigned exam_polygcd(void)
{
unsigned result = 0;
-
- cout << "checking polynomial GCD computation..." << flush;
- clog << "---------polynomial GCD computation:" << endl;
-
- result += poly_gcd1();
- result += poly_gcd2();
- result += poly_gcd3();
-// result += poly_gcd3p(); // takes extremely long (PRS "worst" case)
- result += poly_gcd4();
- result += poly_gcd5();
- result += poly_gcd5p();
- result += poly_gcd6();
- result += poly_gcd7();
-
+
+ cout << "examining polynomial GCD computation" << flush;
+ clog << "----------polynomial GCD computation:" << endl;
+
+ result += poly_gcd1(); cout << '.' << flush;
+ result += poly_gcd2(); cout << '.' << flush;
+ result += poly_gcd3(); cout << '.' << flush;
+ result += poly_gcd3p(); cout << '.' << flush; // takes extremely long (PRS "worst" case)
+ result += poly_gcd4(); cout << '.' << flush;
+ result += poly_gcd5(); cout << '.' << flush;
+ result += poly_gcd5p(); cout << '.' << flush;
+ result += poly_gcd6(); cout << '.' << flush;
+ result += poly_gcd7(); cout << '.' << flush;
+
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
+
return result;
}
-/** @file powerlaws.cpp
+/** @file exam_powerlaws.cpp
*
* Tests for power laws. You shouldn't try to draw much inspiration from
* this code, it is a sanity check rather deeply rooted in GiNaC's classes. */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
+#include "exams.h"
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
-
-static unsigned powerlaws1(void)
+static unsigned exam_powerlaws1(void)
{
// (x^a)^b = x^(a*b)
return 0;
}
-static unsigned powerlaws2(void)
+static unsigned exam_powerlaws2(void)
{
// (a*x)^b = a^b * x^b
return 0;
}
-static unsigned powerlaws3(void)
+static unsigned exam_powerlaws3(void)
{
// numeric evaluation
return 0;
}
-static unsigned powerlaws4(void)
+static unsigned exam_powerlaws4(void)
{
// test for mul::eval()
return 0;
}
-unsigned powerlaws(void)
+unsigned exam_powerlaws(void)
{
unsigned result = 0;
- cout << "checking power laws..." << flush;
- clog << "---------power laws:" << endl;
+ cout << "examining power laws" << flush;
+ clog << "----------power laws:" << endl;
- result += powerlaws1();
- result += powerlaws2();
- result += powerlaws3();
- result += powerlaws4();
+ result += exam_powerlaws1(); cout << '.' << flush;
+ result += exam_powerlaws2(); cout << '.' << flush;
+ result += exam_powerlaws3(); cout << '.' << flush;
+ result += exam_powerlaws4(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
+
return result;
}
-/** @file series_expansion.cpp
+/** @file exam_pseries.cpp
*
* Series expansion test (Laurent and Taylor series). */
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
+#include "exams.h"
static symbol x("x");
}
// Series expansion
-static unsigned series1(void)
+static unsigned exam_series1(void)
{
unsigned result = 0;
ex e, d;
}
// Series addition
-static unsigned series2(void)
+static unsigned exam_series2(void)
{
unsigned result = 0;
ex e, d;
}
// Series multiplication
-static unsigned series3(void)
+static unsigned exam_series3(void)
{
unsigned result = 0;
ex e, d;
}
// Order term handling
-static unsigned series4(void)
+static unsigned exam_series4(void)
{
unsigned result = 0;
ex e, d;
}
// Series of special functions
-static unsigned series5(void)
+static unsigned exam_series5(void)
{
unsigned result = 0;
ex e, d;
return result;
}
-unsigned series_expansion(void)
+unsigned exam_pseries(void)
{
unsigned result = 0;
- cout << "checking series expansion..." << flush;
- clog << "---------series expansion:" << endl;
+ cout << "examining series expansion" << flush;
+ clog << "----------series expansion:" << endl;
- result += series1();
- result += series2();
- result += series3();
- result += series4();
- result += series5();
+ result += exam_series1(); cout << '.' << flush;
+ result += exam_series2(); cout << '.' << flush;
+ result += exam_series3(); cout << '.' << flush;
+ result += exam_series4(); cout << '.' << flush;
+ result += exam_series5(); cout << '.' << flush;
if (!result) {
- cout << " passed ";
+ cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
- cout << " failed ";
+ cout << " failed " << endl;
}
return result;
}
--- /dev/null
+/** @file exams.cpp
+ *
+ * Main program that calls all individual exams. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#include <stdexcept>
+#include <iostream>
+
+#include "exams.h"
+
+int main()
+{
+ unsigned result = 0;
+
+ try {
+ result += exam_paranoia();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_numeric();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_powerlaws();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_differentiation();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_polygcd();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_normalization();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_pseries();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_matrices();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_lsolve();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_noncommut();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ result += exam_misc();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ if (result) {
+ cout << "Error: something went wrong. ";
+ if (result == 1) {
+ cout << "(one failure)" << endl;
+ } else {
+ cout << "(" << result << " individual failures)" << endl;
+ }
+ cout << "please check exam.out against exam.ref for more details."
+ << endl << "happy debugging!" << endl;
+ }
+
+ return result;
+}
--- /dev/null
+/** @file exams.h
+ *
+ * Prototypes for all individual exams. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#ifndef EXAMS_H
+#define EXAMS_H
+
+#include "ginac.h"
+
+#ifndef NO_NAMESPACE_GINAC
+using namespace GiNaC;
+#endif // ndef NO_NAMESPACE_GINAC
+
+// prototypes for all individual checks should be unsigned fcn():
+unsigned exam_paranoia();
+unsigned exam_numeric();
+unsigned exam_powerlaws();
+unsigned exam_differentiation();
+unsigned exam_polygcd();
+unsigned exam_normalization();
+unsigned exam_pseries();
+unsigned exam_matrices();
+unsigned exam_lsolve();
+unsigned exam_noncommut();
+unsigned exam_misc();
+
+#endif // ndef EXAMS_H
--- /dev/null
+----------several historic failures:
+(no output)
+----------consistency of numeric types:
+(no output)
+----------power laws:
+(no output)
+----------symbolic differentiation:
+(no output)
+----------polynomial GCD computation:
+(no output)
+----------rational function normalization:
+(no output)
+----------series expansion:
+(no output)
+----------symbolic matrix manipulations:
+(no output)
+----------linear solve:
+(no output)
+----------behaviour of noncommutative objects:
+(no output)
+----------miscellaneous other things:
+(no output)
--- /dev/null
+/** @file genex.cpp
+ *
+ * Provides some routines for generating expressions that are later used as input
+ * in the consistency checks. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+// For rand() and friends:
+#include <stdlib.h>
+
+#include "ginac.h"
+
+#ifndef NO_NAMESPACE_GINAC
+using namespace GiNaC;
+#endif // ndef NO_NAMESPACE_GINAC
+
+/* Create a dense univariate random polynomial in x.
+ * (of the form 9 - 22*a - 17*a^2 + 14*a^3 + 7*a^4 + 7a^5 if degree==5) */
+const ex
+dense_univariate_poly(const symbol & x, unsigned degree)
+{
+ ex unipoly;
+
+ for (unsigned i=0; i<=degree; ++i)
+ unipoly += numeric((rand()-RAND_MAX/2))*pow(x,i);
+
+ return unipoly;
+}
+
+/* Create a dense bivariate random polynomial in x1 and x2.
+ * (of the form 9 + 52*x1 - 27*x1^2 + 84*x2 + 7*x2^2 - 12*x1*x2 if degree ==2) */
+const ex
+dense_bivariate_poly(const symbol & x1, const symbol & x2, unsigned degree)
+{
+ ex bipoly;
+
+ for (unsigned i1=0; i1<=degree; ++i1)
+ for (unsigned i2=0; i2<=degree-i1; ++i2)
+ bipoly += numeric((rand()-RAND_MAX/2))*pow(x1,i1)*pow(x2,i2);
+
+ return bipoly;
+}
+++ /dev/null
-/** @file numeric_output.cpp
- *
- * Test output of numeric types. */
-
-/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 2 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
- */
-
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
-
-unsigned numeric_output(void)
-{
- unsigned result = 0;
-
- cout << "checking output of numeric types..." << flush;
- clog << "---------output of numeric types:" << endl;
-
- unsigned long Digits_before = Digits;
- Digits = 222;
- clog << "Using " << Digits << " digits" << endl;
- clog << Pi << " evalfs to: " << Pi.evalf() << endl;
- clog << Catalan << " evalfs to: " << Catalan.evalf() << endl;
- clog << EulerGamma << " evalfs to: " << EulerGamma.evalf() << endl;
- clog << "Complex integers: ";
- clog << "{(0,0)=" << ex(0 + 0*I) << "} ";
- clog << "{(1,0)=" << ex(1 + 0*I) << "} ";
- clog << "{(1,1)=" << ex(1 + 1*I) << "} ";
- clog << "{(0,1)=" << ex(0 + 1*I) << "} ";
- clog << "{(-1,1)=" << ex(-1 + 1*I) << "} ";
- clog << "{(-1,0)=" << ex(-1 + 0*I) << "} ";
- clog << "{(-1,-1)=" << ex(-1 - 1*I) << "} ";
- clog << "{(0,-1)=" << ex(0 - 1*I) << "} ";
- clog << "{(1,-1)=" << ex(1 - 1*I) << "} " << endl;
- Digits = Digits_before;
-
- if (! result) {
- cout << " passed ";
- } else {
- cout << " failed ";
- }
-
- return result;
-}
+++ /dev/null
----------several ex-bugs just out of pure paranoia:
-(no output)
----------output of numeric types:
-Using 222 digits
-Pi evalfs to: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648235L0
-Catalan evalfs to: 0.915965594177219015054603514932384110774149374281672134266498119621763019776254769479356512926115106248574422619196199579035898803325859059431594737481158406995332028773319460519038727478164087865909024706484152163000228727640942388L0
-EulerGamma evalfs to: 0.577215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151777L0
-Complex integers: {(0,0)=0} {(1,0)=1} {(1,1)=1+I} {(0,1)=I} {(-1,1)=-1+I} {(-1,0)=-1} {(-1,-1)=-1-I} {(0,-1)=-I} {(1,-1)=1-I}
----------consistency of numeric types:
-(no output)
----------power laws:
-(no output)
----------commutative expansion and substitution:
-(no output)
----------consistency of symbolic functions:
-(no output)
----------symbolic differentiation:
-(no output)
----------polynomial GCD computation:
-(no output)
----------rational function normalization:
-(no output)
----------symbolic matrix manipulations:
-(no output)
----------linear solve:
-(no output)
----------series expansion:
-(no output)
----------manipulations of lortensor objects:
-(no output)
#! /bin/sh
-echo "Running checks..."
-./check_ginac 2>result.out
-echo "Comparing output..."
-cmp ${srcdir}/result.ref result.out
+echo "GiNaC will now run through some rather costly consistency checks:"
+./checks 2>checks.out
+cmp ${srcdir}/checks.ref checks.out
--- /dev/null
+#! /bin/sh
+echo "GiNaC will now take an exam with specific input (like a pupils' exam):"
+./exams 2>exams.out
+cmp ${srcdir}/exams.ref exams.out
--- /dev/null
+#! /bin/sh
+echo "GiNaC will now run through some basic timings:"
+./times 2>times.out
+cmp ${srcdir}/times.ref times.out
--- /dev/null
+/** @file time_dennyfliegner.cpp
+ *
+ * The first test routine implements Denny Fliegner's quick consistency check:
+ * 1) e = (a0 + a1 + a2 + a3 + ...)^2, in expanded form
+ * 2) substitute a0 by (-a2 - a3 - ...) in e
+ * 3) expand e
+ * after which e should be just a1^2. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#include "times.h"
+
+#define VECSIZE 200
+
+static unsigned expand_subs(unsigned size)
+{
+ unsigned result = 0;
+ symbol a1("a1");
+ symbol a[VECSIZE];
+ ex e, aux;
+
+ a[1] = a1;
+ for (unsigned i=0; i<size; ++i) {
+ e = e + a[i];
+ }
+
+ // prepare aux so it will swallow anything but a1^2:
+ aux = -e + a[0] + a[1];
+ e = expand(subs(expand(pow(e, 2)), a[0] == aux));
+
+ if (e != pow(a1,2)) {
+ clog << "Denny Fliegner's quick consistency check erroneously returned "
+ << e << "." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned time_dennyfliegner(void)
+{
+ unsigned result = 0;
+
+ cout << "timing commutative expansion and substitution" << flush;
+ clog << "-------commutative expansion and substitution:" << endl;
+
+ vector<unsigned> sizes;
+ vector<double> times;
+ timer rolex;
+
+ sizes.push_back(40);
+ sizes.push_back(60);
+ sizes.push_back(100);
+ sizes.push_back(150);
+
+ for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
+ rolex.start();
+ result += expand_subs(*i); cout << '.' << flush;
+ times.push_back(rolex.read());
+ }
+
+ if (!result) {
+ cout << " passed ";
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed ";
+ }
+ // print the report:
+ cout << endl << " size: ";
+ for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
+ cout << '\t' << (*i);
+ }
+ cout << endl << " time/s:";
+ for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i) {
+ cout << '\t' << (*i);
+ }
+ cout << endl;
+
+ return result;
+}
--- /dev/null
+/** @file time_gammaseries.cpp
+ *
+ * Some timings on series expansion of the gamma function around a pole. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#include "times.h"
+
+unsigned gammaseries(unsigned order)
+{
+ unsigned result = 0;
+ symbol x;
+
+ ex myseries = series(gamma(x),x,0,order);
+ // compute the last coefficient numerically:
+ ex last_coeff = myseries.coeff(x,order-1).evalf();
+ // compute a bound for that coefficient using a variation of the leading
+ // term in Stirling's formula:
+ ex bound = evalf(exp(ex(-.57721566490153286*(order-1)))/(order-1));
+ if (evalf(abs((last_coeff-pow(-1,order))/bound)) > numeric(1)) {
+ clog << "The " << order-1
+ << "th order coefficient in the power series expansion of gamma(0) was erroneously found to be "
+ << last_coeff << ", violating a simple estimate." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned time_gammaseries(void)
+{
+ unsigned result = 0;
+
+ cout << "timing Laurent series expansion of gamma function" << flush;
+ clog << "-------Laurent series expansion of gamma function:" << endl;
+
+ vector<unsigned> sizes;
+ vector<double> times;
+ timer omega;
+
+ sizes.push_back(10);
+ sizes.push_back(15);
+ sizes.push_back(20);
+ sizes.push_back(25);
+
+ for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
+ omega.start();
+ result += gammaseries(*i); cout << '.' << flush;
+ times.push_back(omega.read());
+ }
+
+ if (!result) {
+ cout << " passed ";
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed ";
+ }
+ // print the report:
+ cout << endl << " order: ";
+ for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
+ cout << '\t' << (*i);
+ }
+ cout << endl << " time/s:";
+ for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i) {
+ cout << '\t' << (*i);
+ }
+ cout << endl;
+
+ return result;
+}
-/** @file fcntimer.cpp
+/** @file timer.cpp
*
- * Function execution timer. */
+ * A simple stop watch class. */
/*
* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include "times.h"
-#include <stdio.h>
-#include <sys/resource.h>
+timer::timer(void) : on(false)
+{
+ getrusage(RUSAGE_SELF, &used1);
+ getrusage(RUSAGE_SELF, &used2);
+}
+void timer::start(void)
+{
+ on = true;
+ getrusage(RUSAGE_SELF, &used1);
+ getrusage(RUSAGE_SELF, &used2);
+}
-// fcntimer() is a little wrapper around GiNaC's automated checks. All those
-// functions are passed void and return unsigned. fcntimer() accepts one such
-// function fcn(), returns its result and as a side-effect prints to stdout how
-// much CPU time was consumed by fcn's execution in the fashion "(0.07s)\n".
-unsigned fcntimer(unsigned fcn())
+void timer::stop(void)
{
- unsigned fcnresult;
- struct rusage used1, used2;
- double elapsed;
+ on = false;
+ getrusage(RUSAGE_SELF, &used2);
+}
- // time the execution of the function:
+void timer::reset(void)
+{
getrusage(RUSAGE_SELF, &used1);
- fcnresult = fcn();
getrusage(RUSAGE_SELF, &used2);
+}
- // add elapsed user and system time in microseconds:
+double timer::read(void)
+{
+ double elapsed;
+ if (this->running())
+ getrusage(RUSAGE_SELF, &used2);
elapsed = ((used2.ru_utime.tv_sec - used1.ru_utime.tv_sec) +
(used2.ru_stime.tv_sec - used1.ru_stime.tv_sec) +
(used2.ru_utime.tv_usec - used1.ru_utime.tv_usec) / 1e6 +
(used2.ru_stime.tv_usec - used1.ru_stime.tv_usec) / 1e6);
+ // round to 10ms for safety:
+ return 0.01*int(elapsed*100+0.5);
+}
- printf("(%.2fs)\n", elapsed);
-
- return fcnresult;
+bool timer::running(void)
+{
+ return on;
}
-/** @file main.cpp
+/** @file times.cpp
*
- * Main program that calls all individual tests. */
+ * Main program that calls the individual timings. */
/*
* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
#include <stdexcept>
#include <iostream>
-#include "check.h"
+#include "times.h"
int main()
{
unsigned result = 0;
try {
- for (int i=0; i<1; ++i) {
- result += fcntimer(paranoia_check);
- result += fcntimer(numeric_output);
- result += fcntimer(numeric_consist);
- result += fcntimer(powerlaws);
- result += fcntimer(expand_subs);
- result += fcntimer(inifcns_consist);
- result += fcntimer(differentiation);
- result += fcntimer(poly_gcd);
- result += fcntimer(normalization);
- result += fcntimer(matrix_checks);
- result += fcntimer(linear_solve);
- result += fcntimer(series_expansion);
- result += fcntimer(lortensor_check);
- }
+ for (int i=0; i<1; ++i)
+ result += time_dennyfliegner();
} catch (const exception &e) {
- cout << "error: caught an exception: " << e.what() << endl;
- result++;
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
+ }
+
+ try {
+ for (int i=0; i<1; ++i)
+ result += time_gammaseries();
+ } catch (const exception &e) {
+ cout << "Error: caught exception " << e.what() << endl;
+ ++result;
}
if (result) {
- cout << "error: something went wrong. ";
+ cout << "Error: something went wrong. ";
if (result == 1) {
cout << "(one failure)" << endl;
} else {
cout << "(" << result << " individual failures)" << endl;
}
- cout << "please check result.out against result.ref for more details."
+ cout << "please check times.out against times.ref for more details."
<< endl << "happy debugging!" << endl;
}
-
+
return result;
}
--- /dev/null
+/** @file times.h
+ *
+ * Prototypes for all individual timings. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
+
+#ifndef CHECKS_H
+#define CHECKS_H
+
+#include <sys/resource.h>
+#include <stdlib.h>
+#include <vector>
+
+#include "ginac.h"
+
+#ifndef NO_NAMESPACE_GINAC
+using namespace GiNaC;
+#endif // ndef NO_NAMESPACE_GINAC
+
+class timer {
+public:
+ timer();
+ void start(void);
+ void stop(void);
+ void reset(void);
+ double read(void);
+ bool running(void);
+private:
+ bool on;
+ struct rusage used1, used2;
+};
+
+// prototypes for all individual timings should be unsigned fcn():
+unsigned time_dennyfliegner();
+unsigned time_gammaseries();
+
+#endif // ndef CHECKS_H
--- /dev/null
+-------commutative expansion and substitution:
+(no output)
+-------Laurent series expansion of gamma function:
+(no output)
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
/* The number of bytes in a long long. */
#undef SIZEOF_LONG_LONG
+/* Define if you have the tgetent function. */
+#undef HAVE_TGETENT
+
/* Define if you have the <algorithm> header file. */
#undef HAVE_ALGORITHM
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
matrix vars(symbols.nops(),1);
for (unsigned r=0; r<eqns.nops(); r++) {
- ex eq=eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
- ex linpart=eq;
+ ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
+ ex linpart = eq;
for (unsigned c=0; c<symbols.nops(); c++) {
- ex co=eq.coeff(ex_to_symbol(symbols.op(c)),1);
+ ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
linpart -= co*symbols.op(c);
sys.set(r,c,co);
}
// test if system is linear and fill vars matrix
for (unsigned i=0; i<symbols.nops(); i++) {
vars.set(i,0,symbols.op(i));
- if (sys.has(symbols.op(i))) {
+ if (sys.has(symbols.op(i)))
throw(std::logic_error("lsolve: system is not linear"));
- }
- if (rhs.has(symbols.op(i))) {
+ if (rhs.has(symbols.op(i)))
throw(std::logic_error("lsolve: system is not linear"));
- }
}
//matrix solution=sys.solve(rhs);
matrix solution;
try {
- solution=sys.fraction_free_elim(vars,rhs);
+ solution = sys.fraction_free_elim(vars,rhs);
} catch (const runtime_error & e) {
// probably singular matrix (or other error)
// return empty solution list
*/
#include <algorithm>
+#include <map>
#include <stdexcept>
#include "matrix.h"
#include "archive.h"
#include "utils.h"
#include "debugmsg.h"
+#include "numeric.h"
#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
int matrix::compare_same_type(const basic & other) const
{
GINAC_ASSERT(is_exactly_of_type(other, matrix));
- const matrix & o=static_cast<matrix &>(const_cast<basic &>(other));
+ const matrix & o = static_cast<matrix &>(const_cast<basic &>(other));
// compare number of rows
- if (row != o.rows()) {
+ if (row != o.rows())
return row < o.rows() ? -1 : 1;
- }
// compare number of columns
- if (col != o.cols()) {
+ if (col != o.cols())
return col < o.cols() ? -1 : 1;
- }
// equal number of rows and columns, compare individual elements
int cmpval;
for (unsigned r=0; r<row; ++r) {
for (unsigned c=0; c<col; ++c) {
- cmpval=((*this)(r,c)).compare(o(r,c));
+ cmpval = ((*this)(r,c)).compare(o(r,c));
if (cmpval!=0) return cmpval;
}
}
}
ensure_if_modifiable();
- m[ro*col+co]=value;
+ m[ro*col+co] = value;
return *this;
}
{
exvector trans(col*row);
- for (unsigned r=0; r<col; ++r) {
- for (unsigned c=0; c<row; ++c) {
+ for (unsigned r=0; r<col; ++r)
+ for (unsigned c=0; c<row; ++c)
trans[r*row+c] = m[c*col+r];
- }
- }
- return matrix(col,row,trans);
-}
-
-/* Determiant of purely numeric matrix, using pivoting. This routine is only
- * called internally by matrix::determinant(). */
-ex determinant_numeric(const matrix & M)
-{
- GINAC_ASSERT(M.rows()==M.cols()); // cannot happen, just in case...
- matrix tmp(M);
- ex det=_ex1();
- ex piv;
-
- for (unsigned r1=0; r1<M.rows(); ++r1) {
- int indx = tmp.pivot(r1);
- if (indx == -1) {
- return _ex0();
- }
- if (indx != 0) {
- det *= _ex_1();
- }
- det = det * tmp.m[r1*M.cols()+r1];
- for (unsigned r2=r1+1; r2<M.rows(); ++r2) {
- piv = tmp.m[r2*M.cols()+r1] / tmp.m[r1*M.cols()+r1];
- for (unsigned c=r1+1; c<M.cols(); c++) {
- tmp.m[r2*M.cols()+c] -= piv * tmp.m[r1*M.cols()+c];
- }
- }
- }
- return det;
-}
-
-// Compute the sign of a permutation of a vector of things, used internally
-// by determinant_symbolic_perm() where it is instantiated for int.
-template <typename T>
-int permutation_sign(vector<T> s)
-{
- if (s.size() < 2)
- return 0;
- int sigma=1;
- for (typename vector<T>::iterator i=s.begin(); i!=s.end()-1; ++i) {
- for (typename vector<T>::iterator j=i+1; j!=s.end(); ++j) {
- if (*i == *j)
- return 0;
- if (*i > *j) {
- iter_swap(i,j);
- sigma = -sigma;
- }
- }
- }
- return sigma;
-}
-
-/** Determinant built by application of the full permutation group. This
- * routine is only called internally by matrix::determinant(). */
-ex determinant_symbolic_perm(const matrix & M)
-{
- GINAC_ASSERT(M.rows()==M.cols()); // cannot happen, just in case...
-
- if (M.rows()==1) { // speed things up
- return M(0,0);
- }
-
- ex det;
- ex term;
- vector<unsigned> sigma(M.cols());
- for (unsigned i=0; i<M.cols(); ++i) sigma[i]=i;
-
- do {
- term = M(sigma[0],0);
- for (unsigned i=1; i<M.cols(); ++i) term *= M(sigma[i],i);
- det += permutation_sign(sigma)*term;
- } while (next_permutation(sigma.begin(), sigma.end()));
-
- return det;
-}
-
-/** Recursive determiant for small matrices having at least one symbolic entry.
- * This algorithm is also known as Laplace-expansion. This routine is only
- * called internally by matrix::determinant(). */
-ex determinant_symbolic_minor(const matrix & M)
-{
- GINAC_ASSERT(M.rows()==M.cols()); // cannot happen, just in case...
-
- if (M.rows()==1) { // end of recursion
- return M(0,0);
- }
- if (M.rows()==2) { // speed things up
- return (M(0,0)*M(1,1)-
- M(1,0)*M(0,1));
- }
- if (M.rows()==3) { // speed things up even a little more
- return ((M(2,1)*M(0,2)-M(2,2)*M(0,1))*M(1,0)+
- (M(1,2)*M(0,1)-M(1,1)*M(0,2))*M(2,0)+
- (M(2,2)*M(1,1)-M(2,1)*M(1,2))*M(0,0));
- }
- ex det;
- matrix minorM(M.rows()-1,M.cols()-1);
- for (unsigned r1=0; r1<M.rows(); ++r1) {
- // assemble the minor matrix
- for (unsigned r=0; r<minorM.rows(); ++r) {
- for (unsigned c=0; c<minorM.cols(); ++c) {
- if (r<r1) {
- minorM.set(r,c,M(r,c+1));
- } else {
- minorM.set(r,c,M(r+1,c+1));
- }
- }
- }
- // recurse down
- if (r1%2) {
- det -= M(r1,0) * determinant_symbolic_minor(minorM);
- } else {
- det += M(r1,0) * determinant_symbolic_minor(minorM);
- }
- }
- return det;
+ return matrix(col,row,trans);
}
/* Leverrier algorithm for large matrices having at least one symbolic entry.
* This routine is only called internally by matrix::determinant(). The
- * algorithm is deemed bad for symbolic matrices since it returns expressions
- * that are very hard to canonicalize. */
-/*ex determinant_symbolic_leverrier(const matrix & M)
+ * algorithm is very bad for symbolic matrices since it returns expressions
+ * that are quite hard to expand. */
+/*ex matrix::determinant_symbolic_leverrier(const matrix & M)
*{
* GINAC_ASSERT(M.rows()==M.cols()); // cannot happen, just in case...
*
// check, if there are non-numeric entries in the matrix:
for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r) {
if (!(*r).info(info_flags::numeric)) {
- if (normalized) {
- return determinant_symbolic_minor(*this).normal();
- } else {
- return determinant_symbolic_perm(*this);
- }
+ if (normalized)
+ // return determinant_symbolic_minor().normal();
+ return determinant_symbolic_minor().normal();
+ else
+ return determinant_symbolic_perm();
}
}
// if it turns out that all elements are numeric
- return determinant_numeric(*this);
+ return determinant_numeric();
}
/** Trace of a matrix.
}
ex tr;
- for (unsigned r=0; r<col; ++r) {
+ for (unsigned r=0; r<col; ++r)
tr += m[r*col+r];
- }
+
return tr;
}
}
matrix M(*this);
- for (unsigned r=0; r<col; ++r) {
+ for (unsigned r=0; r<col; ++r)
M.m[r*col+r] -= lambda;
- }
+
return (M.determinant());
}
matrix tmp(row,col);
// set tmp to the unit matrix
- for (unsigned i=0; i<col; ++i) {
+ for (unsigned i=0; i<col; ++i)
tmp.m[i*col+i] = _ex1();
- }
+
// create a copy of this matrix
matrix cpy(*this);
for (unsigned r1=0; r1<row; ++r1) {
return tmp;
}
+// superfluous helper function
void matrix::ffe_swap(unsigned r1, unsigned c1, unsigned r2 ,unsigned c2)
{
ensure_if_modifiable();
- ex tmp=ffe_get(r1,c1);
+ ex tmp = ffe_get(r1,c1);
ffe_set(r1,c1,ffe_get(r2,c2));
ffe_set(r2,c2,tmp);
}
+// superfluous helper function
void matrix::ffe_set(unsigned r, unsigned c, ex e)
{
set(r-1,c-1,e);
}
+// superfluous helper function
ex matrix::ffe_get(unsigned r, unsigned c) const
{
return operator()(r-1,c-1);
}
/** Solve a set of equations for an m x n matrix by fraction-free Gaussian
- * elimination. Based on algorithm 9.1 from 'Algorithms for Computer Algebra'
+ * elimination. Based on algorithm 9.1 from 'Algorithms for Computer Algebra'
* by Keith O. Geddes et al.
*
* @param vars n x p matrix
matrix matrix::fraction_free_elim(const matrix & vars,
const matrix & rhs) const
{
- if ((row != rhs.row) || (col != vars.row) || (rhs.col != vars.col)) {
- throw (std::logic_error("matrix::solve(): incompatible matrices"));
- }
+ // FIXME: implement a Sasaki-Murao scheme which avoids division at all!
+ if ((row != rhs.row) || (col != vars.row) || (rhs.col != vars.col))
+ throw (std::logic_error("matrix::fraction_free_elim(): incompatible matrices"));
- matrix a(*this); // make a copy of the matrix
- matrix b(rhs); // make a copy of the rhs vector
-
- /*
- cout << "before" << endl;
- cout << "a=" << a << endl;
- cout << "b=" << b << endl;
- */
+ matrix a(*this); // make a copy of the matrix
+ matrix b(rhs); // make a copy of the rhs vector
// given an m x n matrix a, reduce it to upper echelon form
- unsigned m=a.row;
- unsigned n=a.col;
- int sign=1;
- ex divisor=1;
- unsigned r=1;
+ unsigned m = a.row;
+ unsigned n = a.col;
+ int sign = 1;
+ ex divisor = 1;
+ unsigned r = 1;
// eliminate below row r, with pivot in column k
for (unsigned k=1; (k<=n)&&(r<=m); ++k) {
if (p<=m) {
if (p!=r) {
// switch rows p and r
- for (unsigned j=k; j<=n; ++j) {
+ for (unsigned j=k; j<=n; ++j)
a.ffe_swap(p,j,r,j);
- }
b.ffe_swap(p,1,r,1);
// keep track of sign changes due to row exchange
- sign=-sign;
+ sign = -sign;
}
for (unsigned i=r+1; i<=m; ++i) {
for (unsigned j=k+1; j<=n; ++j) {
b.ffe_set(i,1,b.ffe_get(i,1).normal() /*.normal() */ );
a.ffe_set(i,k,0);
}
- divisor=a.ffe_get(r,k);
+ divisor = a.ffe_get(r,k);
r++;
}
}
// optionally compute the determinant for square or augmented matrices
- // if (r==m+1) { det=sign*divisor; } else { det=0; }
+ // if (r==m+1) { det = sign*divisor; } else { det = 0; }
/*
for (unsigned r=1; r<=m; ++r) {
#ifdef DO_GINAC_ASSERT
// test if we really have an upper echelon matrix
- int zero_in_last_row=-1;
+ int zero_in_last_row = -1;
for (unsigned r=1; r<=m; ++r) {
int zero_in_this_row=0;
for (unsigned c=1; c<=n; ++c) {
- if (a.ffe_get(r,c).is_equal(_ex0())) {
+ if (a.ffe_get(r,c).is_equal(_ex0()))
zero_in_this_row++;
- } else {
+ else
break;
- }
}
GINAC_ASSERT((zero_in_this_row>zero_in_last_row)||(zero_in_this_row=n));
- zero_in_last_row=zero_in_this_row;
+ zero_in_last_row = zero_in_this_row;
}
#endif // def DO_GINAC_ASSERT
-
+
/*
cout << "after" << endl;
cout << "a=" << a << endl;
// assemble solution
matrix sol(n,1);
- unsigned last_assigned_sol=n+1;
+ unsigned last_assigned_sol = n+1;
for (unsigned r=m; r>0; --r) {
- unsigned first_non_zero=1;
- while ((first_non_zero<=n)&&(a.ffe_get(r,first_non_zero).is_zero())) {
+ unsigned first_non_zero = 1;
+ while ((first_non_zero<=n)&&(a.ffe_get(r,first_non_zero).is_zero()))
first_non_zero++;
- }
if (first_non_zero>n) {
// row consists only of zeroes, corresponding rhs must be 0 as well
if (!b.ffe_get(r,1).is_zero()) {
for (unsigned c=first_non_zero+1; c<=last_assigned_sol-1; ++c) {
sol.ffe_set(c,1,vars.ffe_get(c,1));
}
- ex e=b.ffe_get(r,1);
+ ex e = b.ffe_get(r,1);
for (unsigned c=first_non_zero+1; c<=n; ++c) {
e=e-a.ffe_get(r,c)*sol.ffe_get(c,1);
}
sol.ffe_set(first_non_zero,1,
(e/a.ffe_get(r,first_non_zero)).normal());
- last_assigned_sol=first_non_zero;
+ last_assigned_sol = first_non_zero;
}
}
// assign solutions for vars between 1 and
// last_assigned_sol-1: free parameters
- for (unsigned c=1; c<=last_assigned_sol-1; ++c) {
+ for (unsigned c=1; c<=last_assigned_sol-1; ++c)
sol.ffe_set(c,1,vars.ffe_get(c,1));
- }
-
- /*
- for (unsigned c=1; c<=n; ++c) {
- cout << vars.ffe_get(c,1) << "->" << sol.ffe_get(c,1) << endl;
- }
- */
-
- // cout << "sol=" << sol << endl;
#ifdef DO_GINAC_ASSERT
// test solution with echelon matrix
for (unsigned r=1; r<=m; ++r) {
- ex e=0;
- for (unsigned c=1; c<=n; ++c) {
- e=e+a.ffe_get(r,c)*sol.ffe_get(c,1);
- }
+ ex e = 0;
+ for (unsigned c=1; c<=n; ++c)
+ e = e+a.ffe_get(r,c)*sol.ffe_get(c,1);
if (!(e-b.ffe_get(r,1)).normal().is_zero()) {
cout << "e=" << e;
cout << "b.ffe_get(" << r<<",1)=" << b.ffe_get(r,1) << endl;
}
GINAC_ASSERT((e-b.ffe_get(r,1)).normal().is_zero());
}
-
+
// test solution with original matrix
for (unsigned r=1; r<=m; ++r) {
- ex e=0;
- for (unsigned c=1; c<=n; ++c) {
- e=e+ffe_get(r,c)*sol.ffe_get(c,1);
- }
+ ex e = 0;
+ for (unsigned c=1; c<=n; ++c)
+ e = e+ffe_get(r,c)*sol.ffe_get(c,1);
try {
- if (!(e-rhs.ffe_get(r,1)).normal().is_zero()) {
- cout << "e=" << e << endl;
- e.printtree(cout);
- ex en=e.normal();
- cout << "e.normal()=" << en << endl;
- en.printtree(cout);
- cout << "rhs.ffe_get(" << r<<",1)=" << rhs.ffe_get(r,1) << endl;
- cout << "diff=" << (e-rhs.ffe_get(r,1)).normal() << endl;
- }
+ if (!(e-rhs.ffe_get(r,1)).normal().is_zero()) {
+ cout << "e=" << e << endl;
+ e.printtree(cout);
+ ex en = e.normal();
+ cout << "e.normal()=" << en << endl;
+ en.printtree(cout);
+ cout << "rhs.ffe_get(" << r<<",1)=" << rhs.ffe_get(r,1) << endl;
+ cout << "diff=" << (e-rhs.ffe_get(r,1)).normal() << endl;
+ }
} catch (...) {
- ex xxx=e-rhs.ffe_get(r,1);
+ ex xxx = e - rhs.ffe_get(r,1);
cerr << "xxx=" << xxx << endl << endl;
}
GINAC_ASSERT((e-rhs.ffe_get(r,1)).normal().is_zero());
#endif // def DO_GINAC_ASSERT
return sol;
-}
+}
+
+/** Solve a set of equations for an m x n matrix.
+ *
+ * @param vars n x p matrix
+ * @param rhs m x p matrix
+ * @exception logic_error (incompatible matrices)
+ * @exception runtime_error (singular matrix) */
+matrix matrix::solve(const matrix & vars,
+ const matrix & rhs) const
+{
+ if ((row != rhs.row) || (col != vars.row) || (rhs.col != vars.col))
+ throw (std::logic_error("matrix::solve(): incompatible matrices"));
-/** Solve simultaneous set of equations. */
-matrix matrix::solve(const matrix & v) const
+ throw (std::runtime_error("FIXME: need implementation."));
+}
+
+/** Old and obsolete interface: */
+matrix matrix::old_solve(const matrix & v) const
{
- if (!(row == col && col == v.row)) {
+ if ((v.row != col) || (col != v.row))
throw (std::logic_error("matrix::solve(): incompatible matrices"));
- }
- // build the extended matrix of *this with v attached to the right
+ // build the augmented matrix of *this with v attached to the right
matrix tmp(row,col+v.col);
for (unsigned r=0; r<row; ++r) {
- for (unsigned c=0; c<col; ++c) {
- tmp.m[r*tmp.col+c] = m[r*col+c];
- }
- for (unsigned c=0; c<v.col; ++c) {
+ for (unsigned c=0; c<col; ++c)
+ tmp.m[r*tmp.col+c] = this->m[r*col+c];
+ for (unsigned c=0; c<v.col; ++c)
tmp.m[r*tmp.col+c+col] = v.m[r*v.col+c];
+ }
+ // cout << "augmented: " << tmp << endl;
+ tmp.gauss_elimination();
+ // cout << "degaussed: " << tmp << endl;
+ // assemble the solution matrix
+ exvector sol(v.row*v.col);
+ for (unsigned c=0; c<v.col; ++c) {
+ for (unsigned r=row; r>0; --r) {
+ for (unsigned i=r; i<col; ++i)
+ sol[(r-1)*v.col+c] -= tmp.m[(r-1)*tmp.col+i]*sol[i*v.col+c];
+ sol[(r-1)*v.col+c] += tmp.m[(r-1)*tmp.col+col+c];
+ sol[(r-1)*v.col+c] = (sol[(r-1)*v.col+c]/tmp.m[(r-1)*tmp.col+(r-1)]).normal();
}
}
+ return matrix(v.row, v.col, sol);
+}
+
+// protected
+
+/** Determinant of purely numeric matrix, using pivoting.
+ *
+ * @see matrix::determinant() */
+ex matrix::determinant_numeric(void) const
+{
+ matrix tmp(*this);
+ ex det = _ex1();
+ ex piv;
+
for (unsigned r1=0; r1<row; ++r1) {
int indx = tmp.pivot(r1);
- if (indx == -1) {
- throw (std::runtime_error("matrix::solve(): singular matrix"));
- }
- for (unsigned c=r1; c<tmp.col; ++c) {
- tmp.m[r1*tmp.col+c] /= tmp.m[r1*tmp.col+r1];
- }
+ if (indx == -1)
+ return _ex0();
+ if (indx != 0)
+ det *= _ex_1();
+ det = det * tmp.m[r1*col+r1];
for (unsigned r2=r1+1; r2<row; ++r2) {
- for (unsigned c=r1; c<tmp.col; ++c) {
- tmp.m[r2*tmp.col+c]
- -= tmp.m[r2*tmp.col+r1] * tmp.m[r1*tmp.col+c];
+ piv = tmp.m[r2*col+r1] / tmp.m[r1*col+r1];
+ for (unsigned c=r1+1; c<col; c++) {
+ tmp.m[r2*col+c] -= piv * tmp.m[r1*col+c];
}
}
}
+ return det;
+}
+
+/** Recursive determinant for small matrices having at least one symbolic
+ * entry. The basic algorithm, known as Laplace-expansion, is enhanced by
+ * some bookkeeping to avoid calculation of the same submatrices ("minors")
+ * more than once. According to W.M.Gentleman and S.C.Johnson this algorithm
+ * is better than elimination schemes for sparse multivariate polynomials and
+ * also for dense univariate polynomials once the dimesion becomes larger
+ * than 7.
+ *
+ * @see matrix::determinant() */
+ex matrix::determinant_symbolic_minor(void) const
+{
+ // for small matrices the algorithm does not make sense:
+ if (this->row==1)
+ return m[0];
+ if (this->row==2)
+ return (m[0]*m[3]-m[2]*m[1]);
+ if (this->row==3)
+ return ((m[4]*m[8]-m[5]*m[7])*m[0]-
+ (m[1]*m[8]-m[2]*m[7])*m[3]+
+ (m[1]*m[5]-m[4]*m[2])*m[6]);
- // assemble the solution matrix
- exvector sol(v.row*v.col);
- for (unsigned c=0; c<v.col; ++c) {
- for (unsigned r=col-1; r>=0; --r) {
- sol[r*v.col+c] = tmp[r*tmp.col+c];
- for (unsigned i=r+1; i<col; ++i) {
- sol[r*v.col+c]
- -= tmp[r*tmp.col+i] * sol[i*v.col+c];
+ // This algorithm can best be understood by looking at a naive
+ // implementation of Laplace-expansion, like this one:
+ // ex det;
+ // matrix minorM(this->row-1,this->col-1);
+ // for (unsigned r1=0; r1<this->row; ++r1) {
+ // // shortcut if element(r1,0) vanishes
+ // if (m[r1*col].is_zero())
+ // continue;
+ // // assemble the minor matrix
+ // for (unsigned r=0; r<minorM.rows(); ++r) {
+ // for (unsigned c=0; c<minorM.cols(); ++c) {
+ // if (r<r1)
+ // minorM.set(r,c,m[r*col+c+1]);
+ // else
+ // minorM.set(r,c,m[(r+1)*col+c+1]);
+ // }
+ // }
+ // // recurse down and care for sign:
+ // if (r1%2)
+ // det -= m[r1*col] * minorM.determinant_symbolic_minor();
+ // else
+ // det += m[r1*col] * minorM.determinant_symbolic_minor();
+ // }
+ // return det;
+ // What happens is that while proceeding down many of the minors are
+ // computed more than once. In particular, there are binomial(n,k)
+ // kxk minors and each one is computed factorial(n-k) times. Therefore
+ // it is reasonable to store the results of the minors. We proceed from
+ // right to left. At each column c we only need to retrieve the minors
+ // calculated in step c-1. We therefore only have to store at most
+ // 2*binomial(n,n/2) minors.
+
+ // we store our subminors in maps, keys being the rows they arise from
+ typedef map<vector<unsigned>,class ex> Rmap;
+ typedef map<vector<unsigned>,class ex>::value_type Rmap_value;
+ Rmap A, B;
+ ex det;
+ vector<unsigned> Pkey; // Unique flipper counter for partitioning into minors
+ Pkey.reserve(this->col);
+ vector<unsigned> Mkey; // key for minor determinant (a subpartition of Pkey)
+ Mkey.reserve(this->col-1);
+ // initialize A with last column:
+ for (unsigned r=0; r<this->col; ++r) {
+ Pkey.erase(Pkey.begin(),Pkey.end());
+ Pkey.push_back(r);
+ A.insert(Rmap_value(Pkey,m[this->col*r+this->col-1]));
+ }
+ // proceed from right to left through matrix
+ for (int c=this->col-2; c>=0; --c) {
+ Pkey.erase(Pkey.begin(),Pkey.end()); // don't change capacity
+ Mkey.erase(Mkey.begin(),Mkey.end());
+ for (unsigned i=0; i<this->col-c; ++i)
+ Pkey.push_back(i);
+ unsigned fc = 0; // controls logic for our strange flipper counter
+ do {
+ A.insert(Rmap_value(Pkey,_ex0()));
+ det = _ex0();
+ for (unsigned r=0; r<this->col-c; ++r) {
+ // maybe there is nothing to do?
+ if (m[Pkey[r]*this->col+c].is_zero())
+ continue;
+ // create the sorted key for all possible minors
+ Mkey.erase(Mkey.begin(),Mkey.end());
+ for (unsigned i=0; i<this->col-c; ++i)
+ if (i!=r)
+ Mkey.push_back(Pkey[i]);
+ // Fetch the minors and compute the new determinant
+ if (r%2)
+ det -= m[Pkey[r]*this->col+c]*A[Mkey];
+ else
+ det += m[Pkey[r]*this->col+c]*A[Mkey];
}
- }
+ // Store the new determinant at its place in B:
+ B.insert(Rmap_value(Pkey,det));
+ // increment our strange flipper counter
+ for (fc=this->col-c; fc>0; --fc) {
+ ++Pkey[fc-1];
+ if (Pkey[fc-1]<fc+c)
+ break;
+ }
+ if (fc<this->col-c)
+ for (unsigned j=fc; j<this->col-c; ++j)
+ Pkey[j] = Pkey[j-1]+1;
+ } while(fc);
+ // change the role of A and B:
+ A = B;
+ B.clear();
}
- return matrix(v.row, v.col, sol);
+
+ return det;
}
-// protected
+/** Determinant built by application of the full permutation group. This
+ * routine is only called internally by matrix::determinant(). */
+ex matrix::determinant_symbolic_perm(void) const
+{
+ if (rows()==1) // speed things up
+ return m[0];
+
+ ex det;
+ ex term;
+ vector<unsigned> sigma(col);
+ for (unsigned i=0; i<col; ++i)
+ sigma[i]=i;
+
+ do {
+ term = (*this)(sigma[0],0);
+ for (unsigned i=1; i<col; ++i)
+ term *= (*this)(sigma[i],i);
+ det += permutation_sign(sigma)*term;
+ } while (next_permutation(sigma.begin(), sigma.end()));
+
+ return det;
+}
+
+/** Perform the steps of an ordinary Gaussian elimination to bring the matrix
+ * into an upper echelon form.
+ *
+ * @return sign is 1 if an even number of rows was swapped, -1 if an odd
+ * number of rows was swapped and 0 if the matrix is singular. */
+int matrix::gauss_elimination(void)
+{
+ int sign = 1;
+ ensure_if_modifiable();
+ for (unsigned r1=0; r1<row-1; ++r1) {
+ int indx = pivot(r1);
+ if (indx == -1)
+ return 0; // Note: leaves *this in a messy state.
+ if (indx > 0)
+ sign = -sign;
+ for (unsigned r2=r1+1; r2<row; ++r2) {
+ for (unsigned c=r1+1; c<col; ++c)
+ this->m[r2*col+c] -= this->m[r2*col+r1]*this->m[r1*col+c]/this->m[r1*col+r1];
+ for (unsigned c=0; c<=r1; ++c)
+ this->m[r2*col+c] = _ex0();
+ }
+ }
+ return sign;
+}
/** Partial pivoting method.
- * Usual pivoting returns the index to the element with the largest absolute
- * value and swaps the current row with the one where the element was found.
- * Here it does the same with the first non-zero element. (This works fine,
- * but may be far from optimal for numerics.) */
-int matrix::pivot(unsigned ro)
+ * Usual pivoting (symbolic==false) returns the index to the element with the
+ * largest absolute value in column ro and swaps the current row with the one
+ * where the element was found. With (symbolic==true) it does the same thing
+ * with the first non-zero element.
+ *
+ * @param ro is the row to be inspected
+ * @param symbolic signal if we want the first non-zero element to be pivoted
+ * (true) or the one with the largest absolute value (false).
+ * @return 0 if no interchange occured, -1 if all are zero (usually signaling
+ * a degeneracy) and positive integer k means that rows ro and k were swapped.
+ */
+int matrix::pivot(unsigned ro, bool symbolic)
{
- unsigned k=ro;
+ unsigned k = ro;
- for (unsigned r=ro; r<row; ++r) {
- if (!m[r*col+ro].is_zero()) {
- k = r;
- break;
+ if (symbolic) { // search first non-zero
+ for (unsigned r=ro; r<row; ++r) {
+ if (!m[r*col+ro].is_zero()) {
+ k = r;
+ break;
+ }
+ }
+ } else { // search largest
+ numeric tmp(0);
+ numeric maxn(-1);
+ for (unsigned r=ro; r<row; ++r) {
+ GINAC_ASSERT(is_ex_of_type(m[r*col+ro],numeric));
+ if ((tmp = abs(ex_to_numeric(m[r*col+ro]))) > maxn &&
+ !tmp.is_zero()) {
+ maxn = tmp;
+ k = r;
+ }
}
}
- if (m[k*col+ro].is_zero()) {
+ if (m[k*col+ro].is_zero())
return -1;
- }
if (k!=ro) { // swap rows
+ ensure_if_modifiable();
for (unsigned c=0; c<col; ++c) {
m[k*col+c].swap(m[ro*col+c]);
}
GINAC_DECLARE_REGISTERED_CLASS(matrix, basic)
// friends
- friend ex determinant_numeric(const matrix & m);
- friend ex determinant_symbolic_perm(const matrix & m);
- friend ex determinant_symbolic_minor(const matrix & m);
-
+// (none)
// member functions
// default constructor, destructor, copy constructor, assignment operator
ex charpoly(const ex & lambda) const;
matrix inverse(void) const;
matrix fraction_free_elim(const matrix & vars, const matrix & v) const;
- matrix solve(const matrix & v) const;
+ matrix solve(const matrix & vars, const matrix & rhs) const;
+ matrix old_solve(const matrix & v) const; // FIXME: may be removed
protected:
- int pivot(unsigned ro);
+ ex determinant_numeric(void) const;
+ ex determinant_symbolic_minor(void) const;
+ ex determinant_symbolic_perm(void) const;
+ int gauss_elimination(void);
+ int fraction_free_elimination(void);
+ int pivot(unsigned ro, bool symbolic=true);
+private: // FIXME: these should be obsoleted
void ffe_swap(unsigned r1, unsigned c1, unsigned r2 ,unsigned c2);
void ffe_set(unsigned r, unsigned c, ex e);
ex ffe_get(unsigned r, unsigned c) const;
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#ifndef __GINAC_REMEMBER_H__
+#define __GINAC_REMEMBER_H__
+
#include <vector>
#include <list>
};
/** The remember table is organized like an n-fold associative cache
- in a microprocessor. The table has a width of 's' (which is rounded
+ in a microprocessor. The table has a width of 's' (which is rounded
to table_size, some power of 2 near 's', internally) and a depth of 'as'
(unless you choose that entries are never discarded). The place where
an entry is stored depends on the hashvalue of the parameters of the
#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
#endif // ndef NO_NAMESPACE_GINAC
+
+#endif // ndef __GINAC_REMEMBER_H__
}
}
+// Compute the sign of a permutation of a vector of things.
+template <typename T>
+int permutation_sign(vector<T> s)
+{
+ if (s.size() < 2)
+ return 0;
+ int sigma = 1;
+ for (typename vector<T>::iterator i=s.begin(); i!=s.end()-1; ++i) {
+ for (typename vector<T>::iterator j=i+1; j!=s.end(); ++j) {
+ if (*i == *j)
+ return 0;
+ if (*i > *j) {
+ iter_swap(i,j);
+ sigma = -sigma;
+ }
+ }
+ }
+ return sigma;
+}
+
// Collection of `construct on first use' wrappers for safely avoiding
// internal object replication without running into the `static
// initialization order fiasco'. This chest of numbers helps speed up
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
LATEX = @LATEX@
LEX = @LEX@
LIBGINACCINT = @LIBGINACCINT@
+LIBTERMCAP = @LIBTERMCAP@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
LT_AGE = @LT_AGE@
git://www.ginac.de / ginac.git / commitdiff