X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_matrices.cpp;h=ccf735ede4c2a58c4b73e5d91ca68c5ad177f45b;hp=a27d586ff97e09d7721ad80d7af2830c115a8afe;hb=7e7beee2c946694130a484c923f6af8391867495;hpb=fdf2f2da4e2b00870cd05c2ac9121de53e56ce3b

diff --git a/check/exam_matrices.cpp b/check/exam_matrices.cpp
index a27d586f..ccf735ed 100644
--- a/check/exam_matrices.cpp
+++ b/check/exam_matrices.cpp
@@ -3,7 +3,7 @@
  *  Here we examine manipulations on GiNaC's symbolic matrices. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 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
@@ -25,231 +25,294 @@
 
 static unsigned matrix_determinants(void)
 {
-    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,numeric(1));
-    m2.set(1,0,b/(a-b)).set(1,1,numeric(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)
 {
-    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)
 {
-    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)
 {
-    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)
+{
+	// 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_evalm(void)
+{
+	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_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 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(void)
 {
-    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_misc();  cout << '.' << flush;
-    
-    if (!result) {
-        cout << " passed " << endl;
-        clog << "(no output)" << endl;
-    } else {
-        cout << " failed " << endl;
-    }
-    
-    return result;
+	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_evalm();  cout << "." << flush;
+	result += matrix_misc();  cout << '.' << flush;
+	
+	if (!result) {
+		cout << " passed " << endl;
+		clog << "(no output)" << endl;
+	} else {
+		cout << " failed " << endl;
+	}
+	
+	return result;
 }