+
/** @file exam_matrices.cpp
*
* Here we examine manipulations on GiNaC's symbolic matrices. */
/*
- * GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2018 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
symbol g("g"), h("h"), i("i");
// check symbolic trivial matrix determinant
- m1.set(0,0,a);
+ m1 = matrix{{a}};
det = m1.determinant();
if (det != a) {
clog << "determinant of 1x1 matrix " << m1
}
// 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);
+ m2 = matrix{{a, b},
+ {c, d}};
det = m2.determinant();
if (det != (a*d-b*c)) {
clog << "determinant of 2x2 matrix " << m2
}
// 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);
+ m3 = matrix{{a, b, c},
+ {d, e, f},
+ {g, h, 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
}
// 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));
+ m3 = matrix{{0, -1, 3},
+ {3, -2, 2},
+ {3, 4, -2}};
det = m3.determinant();
if (det != 42) {
clog << "determinant of 3x3 matrix " << m3
}
// 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);
+ m2 = matrix{{a/(a-b), 1},
+ {b/(a-b), 1}};
det = m2.determinant();
if (det != 1) {
if (det.normal() == 1) // only half wrong
}
// 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);
+ m3 = matrix{{a, -2, 2},
+ {3, a-1, 2},
+ {3, 4, a-3}};
ex p = m3.charpoly(a);
if (p != 0) {
clog << "charpoly of 3x3 matrix " << m3
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 = {{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)) {
+ (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;
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 = {{a, b, c},
+ {d, e, f},
+ {g, h, i}};
matrix m_i = m.inverse();
ex det = m.determinant();
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 ]
+ // [ 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 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));
- 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) {
+ if (cmp != sol) {
clog << "Solving " << A << " * " << X << " == " << B << endl
<< "erroneously returned " << sol << endl;
+ result = 1;
+ }
+
+ return result;
+}
+
+static unsigned matrix_solve3()
+{
+ unsigned result = 0;
+ symbol x("x");
+ symbol t1("t1"), t2("t2"), t3("t3");
+ matrix A = {
+ {3+6*x, 6*(x+x*x)/(2+3*x), 0},
+ {-(2+7*x+6*x*x)/x, -2-2*x, 0},
+ {-2*(2+3*x)/(1+2*x), -6*x/(1+2*x), 1+4*x}
+ };
+ matrix B = {{0}, {0}, {0}};
+ matrix X = {{t1}, {t2}, {t3}};
+ for (auto algo : vector<int>({
+ solve_algo::gauss, solve_algo::divfree, solve_algo::bareiss, solve_algo::markowitz
+ })) {
+ matrix sol(A.solve(X, B, algo));
+ if (!normal((A*sol - B).evalm()).is_zero_matrix()) {
+ clog << "Solving " << A << " * " << X << " == " << B << " with algo=" << algo << endl
+ << "erroneously returned " << sol << endl;
+ result += 1;
+ }
}
-
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
- ));
+ matrix S {{1, 2},
+ {3, 4}};
+ matrix T {{1, 1},
+ {2, -1}};
+ matrix R {{27, 14},
+ {36, 26}};
ex e = ((S + T) * (S + 2*T));
ex f = e.evalm();
}
// a trivial rank one example
- m = 1, 0, 0,
- 2, 0, 0,
- 3, 0, 0;
+ 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;
+ 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;
return result;
}
+unsigned matrix_solve_nonnormal()
+{
+ symbol a("a"), b("b"), c("c"), x("x");
+ // This matrix has a non-normal zero element!
+ matrix mx {{1,0,0},
+ {0,1/(x+1)-(x-1)/(x*x-1),1},
+ {0,0,0}};
+ matrix zero {{0}, {0}, {0}};
+ matrix vars {{a}, {b}, {c}};
+ try {
+ matrix sol_gauss = mx.solve(vars, zero, solve_algo::gauss);
+ matrix sol_divfree = mx.solve(vars, zero, solve_algo::divfree);
+ matrix sol_bareiss = mx.solve(vars, zero, solve_algo::bareiss);
+ if (sol_gauss != sol_divfree || sol_gauss != sol_bareiss) {
+ clog << "different solutions while solving "
+ << mx << " * " << vars << " == " << zero << endl
+ << "gauss: " << sol_gauss << endl
+ << "divfree: " << sol_divfree << endl
+ << "bareiss: " << sol_bareiss << endl;
+ return 1;
+ }
+ } catch (const exception & e) {
+ clog << "exception thrown while solving "
+ << mx << " * " << vars << " == " << zero << endl;
+ return 1;
+ }
+ return 0;
+}
+
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);
+ matrix m1 = {{a, b},
+ {c, d}};
ex tr = trace(m1);
// check a simple trace
<< " 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);
+ matrix m3 = {{a, b},
+ {c, d},
+ {e, f}};
if (transpose(transpose(m3)) != m3) {
clog << "transposing 3x2 matrix " << m3 << " twice"
<< " erroneously returned " << transpose(transpose(m3)) << endl;
result += matrix_invert2(); cout << '.' << flush;
result += matrix_invert3(); cout << '.' << flush;
result += matrix_solve2(); cout << '.' << flush;
+ result += matrix_solve3(); cout << '.' << flush;
result += matrix_evalm(); cout << "." << flush;
result += matrix_rank(); cout << "." << flush;
+ result += matrix_solve_nonnormal(); cout << "." << flush;
result += matrix_misc(); cout << '.' << flush;
return result;
git://www.ginac.de / ginac.git / blobdiff