--- /dev/null
+// check/matrix_checks.cpp
+
+/* Here we test manipulations on GiNaC's symbolic matrices. */
+
+#include "ginac.h"
+#include <stdexcept>
+
+static unsigned matrix_determinants(void)
+{
+ unsigned result = 0;
+ ex det;
+ matrix m1(1,1), m2(2,2), m3(3,3);
+ 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().expand();
+ 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,numeric(1));
+ m2.set(1,0,b/(a-b)).set(1,1,numeric(1));
+ det = m2.determinant(true);
+ if (det != 1) {
+ clog << "determinant of 2x2 matrix " << m2
+ << " 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)
+{
+ 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;
+ return 1;
+ }
+ return 0;
+}
+
+static unsigned matrix_invert2(void)
+{
+ 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().expand();
+
+ 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;
+ return 1;
+ }
+ return 0;
+}
+
+static unsigned matrix_invert3(void)
+{
+ 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().normal().expand();
+
+ 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;
+ return 1;
+ }
+ return 0;
+}
+
+static unsigned matrix_misc(void)
+{
+ 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 matrix_checks(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();
+
+ if (! result) {
+ cout << " passed ";
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed ";
+ }
+
+ return result;
+}
git://www.ginac.de / ginac.git / blobdiff