* Here we examine manipulations on GiNaC's symbolic matrices. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2008 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
*
* 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
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <stdexcept>
-#include "exams.h"
+#include <iostream>
+#include "ginac.h"
+using namespace std;
+using namespace GiNaC;
-static unsigned matrix_determinants(void)
+static unsigned matrix_determinants()
{
- unsigned result = 0;
- ex det;
- 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");
-
- // check symbolic trivial matrix determinant
- m1.set(0,0,a);
- det = m1.determinant();
- if (det != a) {
- clog << "determinant of 1x1 matrix " << m1
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check generic dense symbolic 2x2 matrix determinant
- m2.set(0,0,a).set(0,1,b);
- m2.set(1,0,c).set(1,1,d);
- det = m2.determinant();
- if (det != (a*d-b*c)) {
- clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check generic dense symbolic 3x3 matrix determinant
- m3.set(0,0,a).set(0,1,b).set(0,2,c);
- m3.set(1,0,d).set(1,1,e).set(1,2,f);
- m3.set(2,0,g).set(2,1,h).set(2,2,i);
- det = m3.determinant();
- if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) {
- clog << "determinant of 3x3 matrix " << m3
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check dense numeric 3x3 matrix determinant
- m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3));
- m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2));
- m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2));
- det = m3.determinant();
- if (det != 42) {
- clog << "determinant of 3x3 matrix " << m3
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check dense symbolic 2x2 matrix determinant
- m2.set(0,0,a/(a-b)).set(0,1,1);
- m2.set(1,0,b/(a-b)).set(1,1,1);
- det = m2.determinant();
- if (det != 1) {
- if (det.normal() == 1) // only half wrong
- clog << "determinant of 2x2 matrix " << m2
- << " was returned unnormalized as " << det << endl;
- else // totally wrong
- clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
- ++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);
- m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
- ex p = m3.charpoly(a);
- if (p != 0) {
- clog << "charpoly of 3x3 matrix " << m3
- << " erroneously returned " << p << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ ex det;
+ 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");
+
+ // check symbolic trivial matrix determinant
+ m1.set(0,0,a);
+ det = m1.determinant();
+ if (det != a) {
+ clog << "determinant of 1x1 matrix " << m1
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check generic dense symbolic 2x2 matrix determinant
+ m2.set(0,0,a).set(0,1,b);
+ m2.set(1,0,c).set(1,1,d);
+ det = m2.determinant();
+ if (det != (a*d-b*c)) {
+ clog << "determinant of 2x2 matrix " << m2
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check generic dense symbolic 3x3 matrix determinant
+ m3.set(0,0,a).set(0,1,b).set(0,2,c);
+ m3.set(1,0,d).set(1,1,e).set(1,2,f);
+ m3.set(2,0,g).set(2,1,h).set(2,2,i);
+ det = m3.determinant();
+ if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) {
+ clog << "determinant of 3x3 matrix " << m3
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check dense numeric 3x3 matrix determinant
+ m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3));
+ m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2));
+ m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2));
+ det = m3.determinant();
+ if (det != 42) {
+ clog << "determinant of 3x3 matrix " << m3
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check dense symbolic 2x2 matrix determinant
+ m2.set(0,0,a/(a-b)).set(0,1,1);
+ m2.set(1,0,b/(a-b)).set(1,1,1);
+ det = m2.determinant();
+ if (det != 1) {
+ if (det.normal() == 1) // only half wrong
+ clog << "determinant of 2x2 matrix " << m2
+ << " was returned unnormalized as " << det << endl;
+ else // totally wrong
+ clog << "determinant of 2x2 matrix " << m2
+ << " erroneously returned " << det << endl;
+ ++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);
+ m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
+ ex p = m3.charpoly(a);
+ if (p != 0) {
+ clog << "charpoly of 3x3 matrix " << m3
+ << " erroneously returned " << p << endl;
+ ++result;
+ }
+
+ return result;
}
-static unsigned matrix_invert1(void)
+static unsigned matrix_invert1()
{
- unsigned result = 0;
- matrix m(1,1);
- symbol a("a");
-
- m.set(0,0,a);
- matrix m_i = m.inverse();
-
- if (m_i(0,0) != pow(a,-1)) {
- clog << "inversion of 1x1 matrix " << m
- << " erroneously returned " << m_i << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ matrix m(1,1);
+ symbol a("a");
+
+ m.set(0,0,a);
+ matrix m_i = m.inverse();
+
+ if (m_i(0,0) != pow(a,-1)) {
+ clog << "inversion of 1x1 matrix " << m
+ << " erroneously returned " << m_i << endl;
+ ++result;
+ }
+
+ return result;
}
-static unsigned matrix_invert2(void)
+static unsigned matrix_invert2()
{
- unsigned result = 0;
- matrix m(2,2);
- symbol a("a"), b("b"), c("c"), d("d");
- m.set(0,0,a).set(0,1,b);
- m.set(1,0,c).set(1,1,d);
- matrix m_i = m.inverse();
- ex det = m.determinant();
-
- if ((normal(m_i(0,0)*det) != d) ||
- (normal(m_i(0,1)*det) != -b) ||
- (normal(m_i(1,0)*det) != -c) ||
- (normal(m_i(1,1)*det) != a)) {
- clog << "inversion of 2x2 matrix " << m
- << " erroneously returned " << m_i << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ matrix m(2,2);
+ symbol a("a"), b("b"), c("c"), d("d");
+ m.set(0,0,a).set(0,1,b);
+ m.set(1,0,c).set(1,1,d);
+ matrix m_i = m.inverse();
+ ex det = m.determinant();
+
+ if ((normal(m_i(0,0)*det) != d) ||
+ (normal(m_i(0,1)*det) != -b) ||
+ (normal(m_i(1,0)*det) != -c) ||
+ (normal(m_i(1,1)*det) != a)) {
+ clog << "inversion of 2x2 matrix " << m
+ << " erroneously returned " << m_i << endl;
+ ++result;
+ }
+
+ return result;
}
-static unsigned matrix_invert3(void)
+static unsigned matrix_invert3()
{
- unsigned result = 0;
- matrix m(3,3);
- symbol a("a"), b("b"), c("c");
- symbol d("d"), e("e"), f("f");
- symbol g("g"), h("h"), i("i");
- m.set(0,0,a).set(0,1,b).set(0,2,c);
- m.set(1,0,d).set(1,1,e).set(1,2,f);
- m.set(2,0,g).set(2,1,h).set(2,2,i);
- matrix m_i = m.inverse();
- ex det = m.determinant();
-
- if ((normal(m_i(0,0)*det) != (e*i-f*h)) ||
- (normal(m_i(0,1)*det) != (c*h-b*i)) ||
- (normal(m_i(0,2)*det) != (b*f-c*e)) ||
- (normal(m_i(1,0)*det) != (f*g-d*i)) ||
- (normal(m_i(1,1)*det) != (a*i-c*g)) ||
- (normal(m_i(1,2)*det) != (c*d-a*f)) ||
- (normal(m_i(2,0)*det) != (d*h-e*g)) ||
- (normal(m_i(2,1)*det) != (b*g-a*h)) ||
- (normal(m_i(2,2)*det) != (a*e-b*d))) {
- clog << "inversion of 3x3 matrix " << m
- << " erroneously returned " << m_i << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ matrix m(3,3);
+ symbol a("a"), b("b"), c("c");
+ symbol d("d"), e("e"), f("f");
+ symbol g("g"), h("h"), i("i");
+ m.set(0,0,a).set(0,1,b).set(0,2,c);
+ m.set(1,0,d).set(1,1,e).set(1,2,f);
+ m.set(2,0,g).set(2,1,h).set(2,2,i);
+ matrix m_i = m.inverse();
+ ex det = m.determinant();
+
+ if ((normal(m_i(0,0)*det) != (e*i-f*h)) ||
+ (normal(m_i(0,1)*det) != (c*h-b*i)) ||
+ (normal(m_i(0,2)*det) != (b*f-c*e)) ||
+ (normal(m_i(1,0)*det) != (f*g-d*i)) ||
+ (normal(m_i(1,1)*det) != (a*i-c*g)) ||
+ (normal(m_i(1,2)*det) != (c*d-a*f)) ||
+ (normal(m_i(2,0)*det) != (d*h-e*g)) ||
+ (normal(m_i(2,1)*det) != (b*g-a*h)) ||
+ (normal(m_i(2,2)*det) != (a*e-b*d))) {
+ clog << "inversion of 3x3 matrix " << m
+ << " erroneously returned " << m_i << endl;
+ ++result;
+ }
+
+ return result;
}
-static unsigned matrix_solve2(void)
+static unsigned matrix_solve2()
{
- // check the solution of the multiple system A*X = B:
- // [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ]
- // [ 1 4 -2 ]*[ x1 y1 ] = [ 7 0 ]
- // [ a -2 2 ] [ x2 y2 ] [ a 4 ]
- unsigned result = 0;
- symbol a("a");
- symbol x0("x0"), x1("x1"), x2("x2");
- symbol y0("y0"), y1("y1"), y2("y2");
- matrix A(3,3);
- A.set(0,0,1).set(0,1,2).set(0,2,-1);
- A.set(1,0,1).set(1,1,4).set(1,2,-2);
- A.set(2,0,a).set(2,1,-2).set(2,2,2);
- matrix B(3,2);
- B.set(0,0,4).set(1,0,7).set(2,0,a);
- B.set(0,1,0).set(1,1,0).set(2,1,4);
- matrix X(3,2);
- X.set(0,0,x0).set(1,0,x1).set(2,0,x2);
- X.set(0,1,y0).set(1,1,y1).set(2,1,y2);
- matrix cmp(3,2);
- cmp.set(0,0,1).set(1,0,3).set(2,0,3);
- cmp.set(0,1,0).set(1,1,2).set(2,1,4);
- matrix sol(A.solve(X, B));
- for (unsigned ro=0; ro<3; ++ro)
- for (unsigned co=0; co<2; ++co)
- if (cmp(ro,co) != sol(ro,co))
- result = 1;
- if (result) {
- clog << "Solving " << A << " * " << X << " == " << B << endl
- << "erroneously returned " << sol << endl;
- }
-
- return result;
+ // check the solution of the multiple system A*X = B:
+ // [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ]
+ // [ 1 4 -2 ]*[ x1 y1 ] = [ 7 0 ]
+ // [ a -2 2 ] [ x2 y2 ] [ a 4 ]
+ unsigned result = 0;
+ symbol a("a");
+ symbol x0("x0"), x1("x1"), x2("x2");
+ symbol y0("y0"), y1("y1"), y2("y2");
+ matrix A(3,3);
+ A.set(0,0,1).set(0,1,2).set(0,2,-1);
+ A.set(1,0,1).set(1,1,4).set(1,2,-2);
+ A.set(2,0,a).set(2,1,-2).set(2,2,2);
+ matrix B(3,2);
+ B.set(0,0,4).set(1,0,7).set(2,0,a);
+ B.set(0,1,0).set(1,1,0).set(2,1,4);
+ matrix X(3,2);
+ X.set(0,0,x0).set(1,0,x1).set(2,0,x2);
+ X.set(0,1,y0).set(1,1,y1).set(2,1,y2);
+ matrix cmp(3,2);
+ cmp.set(0,0,1).set(1,0,3).set(2,0,3);
+ cmp.set(0,1,0).set(1,1,2).set(2,1,4);
+ matrix sol(A.solve(X, B));
+ for (unsigned ro=0; ro<3; ++ro)
+ for (unsigned co=0; co<2; ++co)
+ if (cmp(ro,co) != sol(ro,co))
+ result = 1;
+ if (result) {
+ clog << "Solving " << A << " * " << X << " == " << B << endl
+ << "erroneously returned " << sol << endl;
+ }
+
+ return result;
}
-static unsigned matrix_misc(void)
+static unsigned matrix_evalm()
{
- unsigned result = 0;
- matrix m1(2,2);
- symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f");
- m1.set(0,0,a).set(0,1,b);
- m1.set(1,0,c).set(1,1,d);
- ex tr = trace(m1);
-
- // check a simple trace
- if (tr.compare(a+d)) {
- clog << "trace of 2x2 matrix " << m1
- << " erroneously returned " << tr << endl;
- ++result;
- }
-
- // and two simple transpositions
- matrix m2 = transpose(m1);
- if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) {
- clog << "transpose of 2x2 matrix " << m1
- << " erroneously returned " << m2 << endl;
- ++result;
- }
- matrix m3(3,2);
- m3.set(0,0,a).set(0,1,b);
- m3.set(1,0,c).set(1,1,d);
- m3.set(2,0,e).set(2,1,f);
- if (transpose(transpose(m3)) != m3) {
- clog << "transposing 3x2 matrix " << m3 << " twice"
- << " erroneously returned " << transpose(transpose(m3)) << endl;
- ++result;
- }
-
- // produce a runtime-error by inverting a singular matrix and catch it
- matrix m4(2,2);
- matrix m5;
- bool caught = false;
- try {
- m5 = inverse(m4);
- } catch (std::runtime_error err) {
- caught = true;
- }
- if (!caught) {
- cerr << "singular 2x2 matrix " << m4
- << " erroneously inverted to " << m5 << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+
+ matrix S(2, 2, lst(
+ 1, 2,
+ 3, 4
+ )), T(2, 2, lst(
+ 1, 1,
+ 2, -1
+ )), R(2, 2, lst(
+ 27, 14,
+ 36, 26
+ ));
+
+ ex e = ((S + T) * (S + 2*T));
+ ex f = e.evalm();
+ if (!f.is_equal(R)) {
+ clog << "Evaluating " << e << " erroneously returned " << f << " instead of " << R << endl;
+ result++;
+ }
+
+ return result;
+}
+
+static unsigned matrix_rank()
+{
+ unsigned result = 0;
+ symbol x("x"), y("y");
+ matrix m(3,3);
+
+ // the zero matrix always has rank 0
+ if (m.rank() != 0) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ // a trivial rank one example
+ m = 1, 0, 0,
+ 2, 0, 0,
+ 3, 0, 0;
+ if (m.rank() != 1) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ // an example from Maple's help with rank two
+ m = x, 1, 0,
+ 0, 0, 1,
+ x*y, y, 1;
+ if (m.rank() != 2) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ // the 3x3 unit matrix has rank 3
+ m = ex_to<matrix>(unit_matrix(3,3));
+ if (m.rank() != 3) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned matrix_misc()
+{
+ unsigned result = 0;
+ matrix m1(2,2);
+ symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f");
+ m1.set(0,0,a).set(0,1,b);
+ m1.set(1,0,c).set(1,1,d);
+ ex tr = trace(m1);
+
+ // check a simple trace
+ if (tr.compare(a+d)) {
+ clog << "trace of 2x2 matrix " << m1
+ << " erroneously returned " << tr << endl;
+ ++result;
+ }
+
+ // and two simple transpositions
+ matrix m2 = transpose(m1);
+ if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) {
+ clog << "transpose of 2x2 matrix " << m1
+ << " erroneously returned " << m2 << endl;
+ ++result;
+ }
+ matrix m3(3,2);
+ m3.set(0,0,a).set(0,1,b);
+ m3.set(1,0,c).set(1,1,d);
+ m3.set(2,0,e).set(2,1,f);
+ if (transpose(transpose(m3)) != m3) {
+ clog << "transposing 3x2 matrix " << m3 << " twice"
+ << " erroneously returned " << transpose(transpose(m3)) << endl;
+ ++result;
+ }
+
+ // produce a runtime-error by inverting a singular matrix and catch it
+ matrix m4(2,2);
+ matrix m5;
+ bool caught = false;
+ try {
+ m5 = inverse(m4);
+ } catch (std::runtime_error err) {
+ caught = true;
+ }
+ if (!caught) {
+ cerr << "singular 2x2 matrix " << m4
+ << " erroneously inverted to " << m5 << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned exam_matrices()
+{
+ unsigned result = 0;
+
+ cout << "examining symbolic matrix manipulations" << flush;
+
+ result += matrix_determinants(); cout << '.' << flush;
+ result += matrix_invert1(); cout << '.' << flush;
+ result += matrix_invert2(); cout << '.' << flush;
+ result += matrix_invert3(); cout << '.' << flush;
+ result += matrix_solve2(); cout << '.' << flush;
+ result += matrix_evalm(); cout << "." << flush;
+ result += matrix_rank(); cout << "." << flush;
+ result += matrix_misc(); cout << '.' << flush;
+
+ return result;
}
-unsigned exam_matrices(void)
+int main(int argc, char** argv)
{
- unsigned result = 0;
-
- 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_solve2(); cout << '.' << flush;
- result += matrix_misc(); cout << '.' << flush;
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
-
- return result;
+ return exam_matrices();
}
git://www.ginac.de / ginac.git / blobdiff