- 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;
+ symbol a("a"), b("b"), c("c"), d("d");
+ matrix m = {{a, b},
+ {c, 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()
+{
+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c");
+ symbol d("d"), e("e"), f("f");
+ symbol g("g"), h("h"), i("i");
+ matrix m = {{a, b, c},
+ {d, e, f},
+ {g, h, 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()
+{
+ // 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 = {{1, 2, -1},
+ {1, 4, -2},
+ {a, -2, 2}};
+ matrix B = {{4, 0},
+ {7, 0},
+ {a, 4}};
+ matrix X = {{x0 ,y0},
+ {x1, y1},
+ {x2, y2}};
+ matrix cmp = {{1, 0},
+ {3, 2},
+ {3, 4}};
+ matrix sol(A.solve(X, B));
+ if (cmp != sol) {
+ clog << "Solving " << A << " * " << X << " == " << B << endl
+ << "erroneously returned " << sol << endl;
+ result = 1;
+ }
+
+ return result;