s + t
def test_sub():
"""subtraction of complexes, 64x"""
for s in numbers:
for t in numbers:
s - t
def test_mul():
"""multiplication of complexes, 64x"""
for s in numbers:
for t in numbers:
s * t
def test_div():
"""division of complexes, 64x"""
for s in numbers:
for t in numbers:
s / t
def test_pow():
"""complex integer power, 64x"""
for s in numbers:
for t in intnumbers:
s ** t
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_add, test_sub, test_mul,
test_div, test_pow])
n -= 1
def test_sum4():
""" sum(x**i/i,i=1..4), 100x
"""
n = 100
while n:
s = 0
i = 4
while i:
s += x**i/i
i -= 1
n -= 1
def test_inplace_sum4():
""" Add(x**i/i,i=1..4), 100x
"""
n = 100
while n:
Add(*[x**i/i for i in xrange(1,5)])
n -= 1
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_sum, test_inplace_sum,
test_sum40, test_inplace_sum40,
test_sum4, test_inplace_sum4,
test_negsum
])
"""division of small fractions and integers, 64x"""
for s in numbers:
for t in numbers:
s / t
def test_pow():
"""powers of small fractions and integers, 64x"""
for s in numbers:
for t in numbers:
s ** t
def test_mixed_symbolic():
"""Mixed arithmetic with symbols and small integers / fractions"""
a+x; a+x+b; a+x+x+x; a+x+b+x+c; a+x+x+b+x+c;
b+x; b+x+c; b+x+x+x; b+x+c+x+d; b+x+x+c+x+d;
c+x; c+x+b; c+x+x+x; c+x+d+x+e; c+x+x+d+x+e;
d+x; d+x+c; d+x+x+x; d+x+e+x+f; d+x+x+e+x+f;
a*x
a*x*a
a*x + b*x
a*x - b*x
a*x + b*x - a*x - b*x
a*x**2 + a*x + b*x**2 - a*x**2 - b*x**2
x/a + x/b + x/c
x/e + x/f + x/g
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_compare, test_equality, test_add, test_sub, test_mul,
test_div, test_pow, test_mixed_symbolic])
def test_compare_ne1():
""" not not (s1 == s2), s1 = expand((x+y+z)**10), s2 = expand((x+y+w)**10), 20x
"""
n = 20
while n:
not not (s1 == s2)
n -= 1
def test_compare_ne2():
""" not not (s1 == 1), s1 = expand((x+y+z)**10), 20x
"""
n = 20
while n:
not not (s1 == 1)
n -= 1
def test_compare_is():
""" not not (s1 is s1), s1 = expand((x+y+z)**10), 20x
"""
n = 20
while n:
not not (s1 is s1)
n -= 1
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_hash, test_compare_eq1, test_compare_eq2,
test_compare_eq3, test_compare_ne1, test_compare_ne2,
test_compare_is])
quad8.expand()
def test_high_3():
"""Expand large (1+x+y+z+a+b+c)**3"""
high3.expand()
def test_mixed_1():
"""Expand small mixed products, 8x"""
mixed1.expand(); mixed1.expand(); mixed1.expand()
mixed2.expand(); mixed2.expand();
mixed3.expand()
mixed4.expand()
mixed5.expand()
def test_mixed_2():
"""Expand large mixed product"""
mixed6.expand()
def test_nested():
"""Expand deeply nested expression"""
nested.expand()
if __name__=='__main__':
from func_timeit import run_tests
run_tests([
test_bin_1, test_bin_2, test_bin_3,
test_quad_1, test_quad_2,
test_mixed_1, test_mixed_2, test_nested,
test_high_3
])
while i:
ff = ff.integrate(x)
i -= 1
def test_integrate_defined1(f1=f1):
""" f.integrate((x,2,3)), 100x, f=4*x**3+sin(y)**2*x**2+x+1
"""
i = 100
while i:
f = f1.integrate((x, 2, 3))
i -= 1
def test_integrate_defined2(f1=f1):
""" r=f.integrate(x); r.subs(x,3)-r.subs(x,2), 100x, f=4*x**3+sin(y)**2*x**2+x+1
"""
i = 100
while i:
f = f1.integrate(x)
f = f.subs(x, 3) - f.subs(x, 2)
i -= 1
if __name__ == '__main__':
from func_timeit import run_tests
run_tests([
test_diff1, test_diff2, test_integrate, test_integrate_defined1,
test_integrate_defined2
])
"""
n = 101
while n:
n -= 1
Mul(x,n,y)
def test_Mul2():
""" x*i*y, i=0..100
"""
n = 101
while n:
n -= 1
x * n * y
def test_Div2():
""" x/i/y, i=0..100
"""
n = 101
while n:
n -= 1
x / n / y
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_Add, test_Add2, test_Sub2,
test_Mul, test_Mul2, test_Div2,
test_directadd5])
from sympycore import Symbol, Number
x,y,z = map(Symbol,'xyz')
e1 = ((x+2*y+3*z)**50).expand()
e2 = ((x+2*y+3*z)**2).expand()
#print len(e1.data)/len(e2.data) -> 221
def test_long():
"""str(e), e = expand((x+2*y+3*z)**50)"""
str(e1)
def test_short():
"""str(e), e = expand((x+2*y+3*z)**2), 221x"""
n = 221
while n:
n -= 1
str(e2)
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_long, test_short])
cos(n*pi/6)
e = 2 + 3*I
def test_complex_power():
""" evaluate (2+3*I)**1000, 10x
"""
n = 10
while n:
n -= 1
e ** 1000
re = 2 + 3*I/4
def test_rat_complex_power():
""" evaluate (2+3/4*I)**1000, 1x
"""
re ** 1000
def test_inverse_complex():
""" evaluate 1/(2+3/4*I), 100x
"""
n = 100
while n:
n -= 1
1/re
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_sin, test_cos, test_complex_power, test_rat_complex_power, test_inverse_complex])
def test_neg():
"""Negate a 15x20 random dense matrix."""
-a
def test_add():
"""Add two 15x20 random dense matricies."""
a + b
def test_sub():
"""Substract two 15x20 random dense matricies."""
a - b
def test_mul_coeff():
"""Multiply 15x20 random dense matrix with a number."""
a * 3
def test_div_coeff():
"""Divide 15x20 random dense matrix with a number."""
a / 3
def test_add_sparse():
"""Add two 15x20 random sparse int matricies."""
c + d
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_neg, test_add, test_sub, test_mul_coeff, test_div_coeff,
test_add_sparse])
from sympycore import Symbol, Number
x, y, z = map(Symbol, 'xyz')
e1 = ((x + 2 * y + 3 * z)**50).expand()
e2 = ((x + 2 * y + 3 * z)**2).expand()
#print len(e1.data)/len(e2.data) -> 221
def test_long():
"""str(e), e = expand((x+2*y+3*z)**50)"""
str(e1)
def test_short():
"""str(e), e = expand((x+2*y+3*z)**2), 221x"""
n = 221
while n:
n -= 1
str(e2)
if __name__ == '__main__':
from func_timeit import run_tests
run_tests([test_long, test_short])
""" f = f.integrate(), 100x, f=4*x**3+sin(y)**2*x**2+x+1
"""
i = 100
ff = f1
while i:
ff = ff.integrate(x)
i -= 1
def test_integrate_defined1(f1=f1):
""" f.integrate((x,2,3)), 100x, f=4*x**3+sin(y)**2*x**2+x+1
"""
i = 100
while i:
f = f1.integrate((x, 2, 3))
i -= 1
def test_integrate_defined2(f1=f1):
""" r=f.integrate(x); r.subs(x,3)-r.subs(x,2), 100x, f=4*x**3+sin(y)**2*x**2+x+1
"""
i = 100
while i:
f = f1.integrate(x)
f = f.subs(x, 3) - f.subs(x, 2)
i -= 1
if __name__=='__main__':
from func_timeit import run_tests
run_tests([test_diff1, test_diff2, test_integrate,
test_integrate_defined1, test_integrate_defined2
])
