// check/matrix_checks.cpp

/* Here we test manipulations on GiNaC's symbolic matrices. */

#include <stdexcept>
#include <GiNaC/ginac.h>

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;
}