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| from mpmath import * | |
| def test_sumem(): | |
| mp.dps = 15 | |
| assert sumem(lambda k: 1/k**2.5, [50, 100]).ae(0.0012524505324784962) | |
| assert sumem(lambda k: k**4 + 3*k + 1, [10, 100]).ae(2050333103) | |
| def test_nsum(): | |
| mp.dps = 15 | |
| assert nsum(lambda x: x**2, [1, 3]) == 14 | |
| assert nsum(lambda k: 1/factorial(k), [0, inf]).ae(e) | |
| assert nsum(lambda k: (-1)**(k+1) / k, [1, inf]).ae(log(2)) | |
| assert nsum(lambda k: (-1)**(k+1) / k**2, [1, inf]).ae(pi**2 / 12) | |
| assert nsum(lambda k: (-1)**k / log(k), [2, inf]).ae(0.9242998972229388) | |
| assert nsum(lambda k: 1/k**2, [1, inf]).ae(pi**2 / 6) | |
| assert nsum(lambda k: 2**k/fac(k), [0, inf]).ae(exp(2)) | |
| assert nsum(lambda k: 1/k**2, [4, inf], method='e').ae(0.2838229557371153) | |
| assert abs(fp.nsum(lambda k: 1/k**4, [1, fp.inf]) - 1.082323233711138) < 1e-5 | |
| assert abs(fp.nsum(lambda k: 1/k**4, [1, fp.inf], method='e') - 1.082323233711138) < 1e-4 | |
| def test_nprod(): | |
| mp.dps = 15 | |
| assert nprod(lambda k: exp(1/k**2), [1,inf], method='r').ae(exp(pi**2/6)) | |
| assert nprod(lambda x: x**2, [1, 3]) == 36 | |
| def test_fsum(): | |
| mp.dps = 15 | |
| assert fsum([]) == 0 | |
| assert fsum([-4]) == -4 | |
| assert fsum([2,3]) == 5 | |
| assert fsum([1e-100,1]) == 1 | |
| assert fsum([1,1e-100]) == 1 | |
| assert fsum([1e100,1]) == 1e100 | |
| assert fsum([1,1e100]) == 1e100 | |
| assert fsum([1e-100,0]) == 1e-100 | |
| assert fsum([1e-100,1e100,1e-100]) == 1e100 | |
| assert fsum([2,1+1j,1]) == 4+1j | |
| assert fsum([2,inf,3]) == inf | |
| assert fsum([2,-1], absolute=1) == 3 | |
| assert fsum([2,-1], squared=1) == 5 | |
| assert fsum([1,1+j], squared=1) == 1+2j | |
| assert fsum([1,3+4j], absolute=1) == 6 | |
| assert fsum([1,2+3j], absolute=1, squared=1) == 14 | |
| assert isnan(fsum([inf,-inf])) | |
| assert fsum([inf,-inf], absolute=1) == inf | |
| assert fsum([inf,-inf], squared=1) == inf | |
| assert fsum([inf,-inf], absolute=1, squared=1) == inf | |
| assert iv.fsum([1,mpi(2,3)]) == mpi(3,4) | |
| def test_fprod(): | |
| mp.dps = 15 | |
| assert fprod([]) == 1 | |
| assert fprod([2,3]) == 6 | |