X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_differentiation.cpp;h=ccb97dab9a8926c55598585ffd683ec5ffb36028;hp=1a5aabb114033840c5f0aab4767112be0e09258e;hb=2c22412269ccfb551a27fd8081712b46c243cbac;hpb=db5765dc91202851739e196ba11bfccb0b3fe7bc diff --git a/check/exam_differentiation.cpp b/check/exam_differentiation.cpp index 1a5aabb1..ccb97dab 100644 --- a/check/exam_differentiation.cpp +++ b/check/exam_differentiation.cpp @@ -3,7 +3,7 @@ * 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 @@ -23,274 +23,258 @@ #include "exams.h" static unsigned check_diff(const ex &e, const symbol &x, - const ex &d, unsigned nth=1) + const ex &d, unsigned nth=1) { - ex ed = e.diff(x, nth); - if ((ed - d).compare(ex(0)) != 0) { - switch (nth) { - case 0: - clog << "zeroth "; - break; - case 1: - break; - case 2: - clog << "second "; - break; - case 3: - clog << "third "; - break; - default: - clog << nth << "th "; - } - clog << "derivative of " << e << " by " << x << " returned " - << ed << " instead of " << d << endl; - clog << "returned:" << endl; - ed.printtree(clog); - clog << endl << "instead of" << endl; - d.printtree(clog); + ex ed = e.diff(x, nth); + if (!(ed - d).is_zero()) { + switch (nth) { + case 0: + clog << "zeroth "; + break; + case 1: + break; + case 2: + clog << "second "; + break; + case 3: + clog << "third "; + break; + default: + clog << nth << "th "; + } + clog << "derivative of " << e << " by " << x << " returned " + << ed << " instead of " << d << endl; + clog << "returned:" << endl; + clog << tree << ed << "instead of\n" << d << dflt; - return 1; - } - return 0; + return 1; + } + return 0; } // Simple (expanded) polynomials -static unsigned exam_differentiation1(void) +static unsigned exam_differentiation1() { - unsigned result = 0; - symbol x("x"), y("y"); - ex e1, e2, e, d; - - // construct bivariate polynomial e to be diff'ed: - e1 = pow(x, -2) * 3 + pow(x, -1) * 5 + 7 + x * 11 + pow(x, 2) * 13; - e2 = pow(y, -2) * 5 + pow(y, -1) * 7 + 11 + y * 13 + pow(y, 2) * 17; - e = (e1 * e2).expand(); - - // d e / dx: - d = ex("121-55/x^2-66/x^3-30/x^3/y^2-42/x^3/y-78/x^3*y-102/x^3*y^2-25/x^2/y^2-35/x^2/y-65/x^2*y-85/x^2*y^2+77/y+143*y+187*y^2+130*x/y^2+182/y*x+338*x*y+442*x*y^2+55/y^2+286*x",lst(x,y)); - result += check_diff(e, x, d); - - // d e / dy: - d = ex("91-30/x^2/y^3-21/x^2/y^2+39/x^2+102/x^2*y-50/x/y^3-35/x/y^2+65/x+170/x*y-77*x/y^2+143*x+374*x*y-130/y^3*x^2-91/y^2*x^2+169*x^2+442*x^2*y-110/y^3*x-70/y^3+238*y-49/y^2",lst(x,y)); - result += check_diff(e, y, d); - - // d^2 e / dx^2: - d = ex("286+90/x^4/y^2+126/x^4/y+234/x^4*y+306/x^4*y^2+50/x^3/y^2+70/x^3/y+130/x^3*y+170/x^3*y^2+130/y^2+182/y+338*y+442*y^2+198/x^4+110/x^3",lst(x,y)); - result += check_diff(e, x, d, 2); - - // d^2 e / dy^2: - d = ex("238+90/x^2/y^4+42/x^2/y^3+102/x^2+150/x/y^4+70/x/y^3+170/x+330*x/y^4+154*x/y^3+374*x+390*x^2/y^4+182*x^2/y^3+442*x^2+210/y^4+98/y^3",lst(x,y)); - result += check_diff(e, y, d, 2); - - return result; + unsigned result = 0; + symbol x("x"), y("y"); + ex e1, e2, e, d; + + // construct bivariate polynomial e to be diff'ed: + e1 = pow(x, -2) * 3 + pow(x, -1) * 5 + 7 + x * 11 + pow(x, 2) * 13; + e2 = pow(y, -2) * 5 + pow(y, -1) * 7 + 11 + y * 13 + pow(y, 2) * 17; + e = (e1 * e2).expand(); + + // d e / dx: + d = ex("121-55/x^2-66/x^3-30/x^3/y^2-42/x^3/y-78/x^3*y-102/x^3*y^2-25/x^2/y^2-35/x^2/y-65/x^2*y-85/x^2*y^2+77/y+143*y+187*y^2+130*x/y^2+182/y*x+338*x*y+442*x*y^2+55/y^2+286*x",lst(x,y)); + result += check_diff(e, x, d); + + // d e / dy: + d = ex("91-30/x^2/y^3-21/x^2/y^2+39/x^2+102/x^2*y-50/x/y^3-35/x/y^2+65/x+170/x*y-77*x/y^2+143*x+374*x*y-130/y^3*x^2-91/y^2*x^2+169*x^2+442*x^2*y-110/y^3*x-70/y^3+238*y-49/y^2",lst(x,y)); + result += check_diff(e, y, d); + + // d^2 e / dx^2: + d = ex("286+90/x^4/y^2+126/x^4/y+234/x^4*y+306/x^4*y^2+50/x^3/y^2+70/x^3/y+130/x^3*y+170/x^3*y^2+130/y^2+182/y+338*y+442*y^2+198/x^4+110/x^3",lst(x,y)); + result += check_diff(e, x, d, 2); + + // d^2 e / dy^2: + d = ex("238+90/x^2/y^4+42/x^2/y^3+102/x^2+150/x/y^4+70/x/y^3+170/x+330*x/y^4+154*x/y^3+374*x+390*x^2/y^4+182*x^2/y^3+442*x^2+210/y^4+98/y^3",lst(x,y)); + result += check_diff(e, y, d, 2); + + return result; } // Trigonometric functions -static unsigned exam_differentiation2(void) +static unsigned exam_differentiation2() { - unsigned result = 0; - symbol x("x"), y("y"), a("a"), b("b"); - ex e1, e2, e, d; - - // construct expression e to be diff'ed: - e1 = y*pow(x, 2) + a*x + b; - e2 = sin(e1); - e = b*pow(e2, 2) + y*e2 + a; - - d = 2*b*e2*cos(e1)*(2*x*y + a) + y*cos(e1)*(2*x*y + a); - 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); - 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); + unsigned result = 0; + symbol x("x"), y("y"), a("a"), b("b"); + ex e1, e2, e, d; + + // construct expression e to be diff'ed: + e1 = y*pow(x, 2) + a*x + b; + e2 = sin(e1); + e = b*pow(e2, 2) + y*e2 + a; + + d = 2*b*e2*cos(e1)*(2*x*y + a) + y*cos(e1)*(2*x*y + a); + 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); + 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); - result += check_diff(e, y, d, 2); - - // construct expression e to be diff'ed: - e2 = cos(e1); - e = b*pow(e2, 2) + y*e2 + a; - - d = -2*b*e2*sin(e1)*(2*x*y + a) - y*sin(e1)*(2*x*y + a); - 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); - 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); - result += check_diff(e, y, d, 2); + 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); + result += check_diff(e, y, d, 2); + + // construct expression e to be diff'ed: + e2 = cos(e1); + e = b*pow(e2, 2) + y*e2 + a; + + d = -2*b*e2*sin(e1)*(2*x*y + a) - y*sin(e1)*(2*x*y + a); + 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); + 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); + 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"); - ex e1, e2, e, d; + unsigned result = 0; + symbol x("x"), y("y"), a("a"), b("b"); + ex e1, e2, e, d; - // construct expression e to be diff'ed: - e1 = y*pow(x, 2) + a*x + b; - e2 = exp(e1); - e = b*pow(e2, 2) + y*e2 + a; - - d = 2*b*pow(e2, 2)*(2*x*y + a) + y*e2*(2*x*y + a); - 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); - result += check_diff(e, x, d, 2); - - d = 2*b*pow(e2,2)*pow(x,2) + e2 + y*e2*pow(x,2); - result += check_diff(e, y, d); - - d = 4*b*pow(e2,2)*pow(x,4) + 2*e2*pow(x,2) + y*e2*pow(x,4); - result += check_diff(e, y, d, 2); + // construct expression e to be diff'ed: + e1 = y*pow(x, 2) + a*x + b; + e2 = exp(e1); + e = b*pow(e2, 2) + y*e2 + a; + + d = 2*b*pow(e2, 2)*(2*x*y + a) + y*e2*(2*x*y + a); + 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); + result += check_diff(e, x, d, 2); + + d = 2*b*pow(e2,2)*pow(x,2) + e2 + y*e2*pow(x,2); + result += check_diff(e, y, d); + + d = 4*b*pow(e2,2)*pow(x,4) + 2*e2*pow(x,2) + y*e2*pow(x,4); + result += check_diff(e, y, d, 2); return result; } // log functions -static unsigned exam_differentiation4(void) +static unsigned exam_differentiation4() { - unsigned result = 0; - symbol x("x"), y("y"), a("a"), b("b"); - ex e1, e2, e, d; - - // construct expression e to be diff'ed: - e1 = y*pow(x, 2) + a*x + b; - e2 = log(e1); - e = b*pow(e2, 2) + y*e2 + a; - - d = 2*b*e2*(2*x*y + a)/e1 + y*(2*x*y + a)/e1; - 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); - 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); - result += check_diff(e, y, d, 2); + unsigned result = 0; + symbol x("x"), y("y"), a("a"), b("b"); + ex e1, e2, e, d; + + // construct expression e to be diff'ed: + e1 = y*pow(x, 2) + a*x + b; + e2 = log(e1); + e = b*pow(e2, 2) + y*e2 + a; + + d = 2*b*e2*(2*x*y + a)/e1 + y*(2*x*y + a)/e1; + 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); + 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); + 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"); - ex e1, e2, e, d; - - // test atan2 - 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); - result += check_diff(e, x, d); - - return result; + unsigned result = 0; + symbol x("x"), y("y"), a("a"), b("b"); + ex e1, e2, e, d; + + // test atan2 + e1 = y*pow(x, 2) + a*x + b; + e2 = x*pow(y, 2) + b*y + a; + e = atan2(e1,e2); + + 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); + 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; - - e = sin(x).series(x==0, 8); - d = cos(x).series(x==0, 7); - ed = e.diff(x); - ed = series_to_poly(ed); - d = series_to_poly(d); - - if ((ed - d).compare(ex(0)) != 0) { - clog << "derivative of " << e << " by " << x << " returned " - << ed << " instead of " << d << ")" << endl; - return 1; - } - return 0; + symbol x("x"); + ex e, d, ed; + + e = sin(x).series(x==0, 8); + d = cos(x).series(x==0, 7); + ed = e.diff(x); + ed = series_to_poly(ed); + d = series_to_poly(d); + + if (!(ed - d).is_zero()) { + clog << "derivative of " << e << " by " << x << " returned " + << 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); - - if (!(e-d).expand().is_zero()) { - clog << "expanded second derivative of " << (P.diff(x) / P) << " by " << x - << " 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; - return 1; - } - return 0; + 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); + + if (!(e-d).expand().is_zero()) { + clog << "expanded second derivative of " << (P.diff(x) / P) << " by " << x + << " 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; + return 1; + } + return 0; } -unsigned exam_differentiation(void) +unsigned exam_differentiation() { - unsigned result = 0; - - cout << "examining symbolic differentiation" << flush; - clog << "----------symbolic differentiation:" << endl; - - result += exam_differentiation1(); cout << '.' << flush; - result += exam_differentiation2(); cout << '.' << flush; - result += exam_differentiation3(); cout << '.' << flush; - result += exam_differentiation4(); cout << '.' << flush; - result += exam_differentiation5(); cout << '.' << flush; - result += exam_differentiation6(); cout << '.' << flush; - result += exam_differentiation7(); cout << '.' << flush; - - if (!result) { - cout << " passed " << endl; - clog << "(no output)" << endl; - } else { - cout << " failed " << endl; - } - return result; + unsigned result = 0; + + cout << "examining symbolic differentiation" << flush; + clog << "----------symbolic differentiation:" << endl; + + result += exam_differentiation1(); cout << '.' << flush; + result += exam_differentiation2(); cout << '.' << flush; + result += exam_differentiation3(); cout << '.' << flush; + result += exam_differentiation4(); cout << '.' << flush; + result += exam_differentiation5(); cout << '.' << flush; + result += exam_differentiation6(); cout << '.' << flush; + result += exam_differentiation7(); cout << '.' << flush; + + if (!result) { + cout << " passed " << endl; + clog << "(no output)" << endl; + } else { + cout << " failed " << endl; + } + return result; }