* Tests for symbolic differentiation, including various functions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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
const ex &d, unsigned nth=1)
{
ex ed = e.diff(x, nth);
- if ((ed - d).compare(ex(0)) != 0) {
+ if (!(ed - d).is_zero()) {
switch (nth) {
case 0:
clog << "zeroth ";
clog << nth << "th ";
}
clog << "derivative of " << e << " by " << x << " returned "
- << ed << " instead of " << d << endl;
+ << ed << " instead of " << d << endl;
clog << "returned:" << endl;
- ed.printtree(clog);
- clog << endl << "instead of" << endl;
- d.printtree(clog);
+ clog << tree << ed << "instead of\n" << d << dflt;
return 1;
}
}
// Simple (expanded) polynomials
-static unsigned exam_differentiation1(void)
+static unsigned exam_differentiation1()
{
unsigned result = 0;
symbol x("x"), y("y");
}
// Trigonometric functions
-static unsigned exam_differentiation2(void)
+static unsigned exam_differentiation2()
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
result += check_diff(e, x, d);
d = 2*b*pow(cos(e1),2)*pow(2*x*y + a, 2) + 4*b*y*e2*cos(e1)
- - 2*b*pow(e2,2)*pow(2*x*y + a, 2) - y*e2*pow(2*x*y + a, 2)
- + 2*pow(y,2)*cos(e1);
+ - 2*b*pow(e2,2)*pow(2*x*y + a, 2) - y*e2*pow(2*x*y + a, 2)
+ + 2*pow(y,2)*cos(e1);
result += check_diff(e, x, d, 2);
d = 2*b*e2*cos(e1)*pow(x, 2) + e2 + y*cos(e1)*pow(x, 2);
result += check_diff(e, y, d);
d = 2*b*pow(cos(e1),2)*pow(x,4) - 2*b*pow(e2,2)*pow(x,4)
- + 2*cos(e1)*pow(x,2) - y*e2*pow(x,4);
+ + 2*cos(e1)*pow(x,2) - y*e2*pow(x,4);
result += check_diff(e, y, d, 2);
// construct expression e to be diff'ed:
result += check_diff(e, x, d);
d = 2*b*pow(sin(e1),2)*pow(2*y*x + a,2) - 4*b*e2*sin(e1)*y
- - 2*b*pow(e2,2)*pow(2*y*x + a,2) - y*e2*pow(2*y*x + a,2)
- - 2*pow(y,2)*sin(e1);
+ - 2*b*pow(e2,2)*pow(2*y*x + a,2) - y*e2*pow(2*y*x + a,2)
+ - 2*pow(y,2)*sin(e1);
result += check_diff(e, x, d, 2);
d = -2*b*e2*sin(e1)*pow(x,2) + e2 - y*sin(e1)*pow(x, 2);
result += check_diff(e, y, d);
d = -2*b*pow(e2,2)*pow(x,4) + 2*b*pow(sin(e1),2)*pow(x,4)
- - 2*sin(e1)*pow(x,2) - y*e2*pow(x,4);
+ - 2*sin(e1)*pow(x,2) - y*e2*pow(x,4);
result += check_diff(e, y, d, 2);
return result;
}
// exp function
-static unsigned exam_differentiation3(void)
+static unsigned exam_differentiation3()
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
result += check_diff(e, x, d);
d = 4*b*pow(e2,2)*pow(2*y*x + a,2) + 4*b*pow(e2,2)*y
- + 2*pow(y,2)*e2 + y*e2*pow(2*y*x + a,2);
+ + 2*pow(y,2)*e2 + y*e2*pow(2*y*x + a,2);
result += check_diff(e, x, d, 2);
d = 2*b*pow(e2,2)*pow(x,2) + e2 + y*e2*pow(x,2);
}
// log functions
-static unsigned exam_differentiation4(void)
+static unsigned exam_differentiation4()
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
result += check_diff(e, x, d);
d = 2*b*pow((2*x*y + a),2)*pow(e1,-2) + 4*b*y*e2/e1
- - 2*b*e2*pow(2*x*y + a,2)*pow(e1,-2) + 2*pow(y,2)/e1
- - y*pow(2*x*y + a,2)*pow(e1,-2);
+ - 2*b*e2*pow(2*x*y + a,2)*pow(e1,-2) + 2*pow(y,2)/e1
+ - y*pow(2*x*y + a,2)*pow(e1,-2);
result += check_diff(e, x, d, 2);
d = 2*b*e2*pow(x,2)/e1 + e2 + y*pow(x,2)/e1;
result += check_diff(e, y, d);
d = 2*b*pow(x,4)*pow(e1,-2) - 2*b*e2*pow(e1,-2)*pow(x,4)
- + 2*pow(x,2)/e1 - y*pow(x,4)*pow(e1,-2);
+ + 2*pow(x,2)/e1 - y*pow(x,4)*pow(e1,-2);
result += check_diff(e, y, d, 2);
return result;
}
// Functions with two variables
-static unsigned exam_differentiation5(void)
+static unsigned exam_differentiation5()
{
unsigned result = 0;
symbol x("x"), y("y"), a("a"), b("b");
e1 = y*pow(x, 2) + a*x + b;
e2 = x*pow(y, 2) + b*y + a;
e = atan2(e1,e2);
- /*
- d = pow(y,2)*(-b-y*pow(x,2)-a*x)/(pow(b+y*pow(x,2)+a*x,2)+pow(x*pow(y,2)+b*y+a,2))
- +(2*y*x+a)/((x*pow(y,2)+b*y+a)*(1+pow(b*y*pow(x,2)+a*x,2)/pow(x*pow(y,2)+b*y+a,2)));
- */
- /*
- d = ((a+2*y*x)*pow(y*b+pow(y,2)*x+a,-1)-(a*x+b+y*pow(x,2))*
- pow(y*b+pow(y,2)*x+a,-2)*pow(y,2))*
- pow(1+pow(a*x+b+y*pow(x,2),2)*pow(y*b+pow(y,2)*x+a,-2),-1);
- */
- /*
- d = pow(1+pow(a*x+b+y*pow(x,2),2)*pow(y*b+pow(y,2)*x+a,-2),-1)
- *pow(y*b+pow(y,2)*x+a,-1)*(a+2*y*x)
- +pow(y,2)*(-a*x-b-y*pow(x,2))*
- pow(pow(y*b+pow(y,2)*x+a,2)+pow(a*x+b+y*pow(x,2),2),-1);
- */
+
d = pow(y,2)*pow(pow(b+y*pow(x,2)+x*a,2)+pow(y*b+pow(y,2)*x+a,2),-1)*
- (-b-y*pow(x,2)-x*a)+
- pow(pow(b+y*pow(x,2)+x*a,2)+pow(y*b+pow(y,2)*x+a,2),-1)*
- (y*b+pow(y,2)*x+a)*(2*y*x+a);
+ (-b-y*pow(x,2)-x*a)
+ +pow(pow(b+y*pow(x,2)+x*a,2)+pow(y*b+pow(y,2)*x+a,2),-1)*
+ (y*b+pow(y,2)*x+a)*(2*y*x+a);
result += check_diff(e, x, d);
return result;
}
// Series
-static unsigned exam_differentiation6(void)
+static unsigned exam_differentiation6()
{
symbol x("x");
ex e, d, ed;
ed = series_to_poly(ed);
d = series_to_poly(d);
- if ((ed - d).compare(ex(0)) != 0) {
+ if (!(ed - d).is_zero()) {
clog << "derivative of " << e << " by " << x << " returned "
- << ed << " instead of " << d << ")" << endl;
+ << ed << " instead of " << d << ")" << endl;
return 1;
}
return 0;
}
// Hashing can help a lot, if differentiation is done cleverly
-static unsigned exam_differentiation7(void)
+static unsigned exam_differentiation7()
{
symbol x("x");
ex P = x + pow(x,3);
ex e = (P.diff(x) / P).diff(x, 2);
ex d = 6/P - 18*x/pow(P,2) - 54*pow(x,3)/pow(P,2) + 2/pow(P,3)
- +18*pow(x,2)/pow(P,3) + 54*pow(x,4)/pow(P,3) + 54*pow(x,6)/pow(P,3);
+ +18*pow(x,2)/pow(P,3) + 54*pow(x,4)/pow(P,3) + 54*pow(x,6)/pow(P,3);
if (!(e-d).expand().is_zero()) {
clog << "expanded second derivative of " << (P.diff(x) / P) << " by " << x
- << " returned " << e.expand() << " instead of " << d << endl;
+ << " returned " << e.expand() << " instead of " << d << endl;
return 1;
}
if (e.nops() > 3) {
clog << "second derivative of " << (P.diff(x) / P) << " by " << x
- << " has " << e.nops() << " operands. "
- << "The result is still correct but not optimal: 3 are enough! "
- << "(Hint: maybe the product rule for objects of class mul should be more careful about assembling the result?)" << endl;
+ << " has " << e.nops() << " operands. "
+ << "The result is still correct but not optimal: 3 are enough! "
+ << "(Hint: maybe the product rule for objects of class mul should be more careful about assembling the result?)" << endl;
return 1;
}
return 0;
}
-unsigned exam_differentiation(void)
+unsigned exam_differentiation()
{
unsigned result = 0;