o 8Va@sdZddlmZmZmZmZddlmZmZddl m Z ddl m Z m Z ddlmZddlmZdddZdddZdddZdddZdddZd S)z Helpers for randomized testing )uniformRandom randrangerandint) is_sequenceas_int)Tuple)compI)Symbol) nsimplifyFNcCsFt||t||}}|s|t|St|d|dtt|d|dS)a Return a random complex number. To reduce chance of hitting branch cuts or anything, we guarantee b <= Im z <= d, a <= Re z <= c When rational is True, a rational approximation to a random number is obtained within specified tolerance, if any. T)rational tolerance)rr r )abcdrrABr8/usr/lib/python3/dist-packages/sympy/testing/randtest.pyrandom_complex_number s    rư>c sxt|||\}}}t|tr|gn|j|jB}tt|fdd|D}||} ||} t| | |S)a Test numerically that f and g agree when evaluated in the argument z. If z is None, all symbols will be tested. This routine does not test whether there are Floats present with precision higher than 15 digits so if there are, your results may not be what you expect due to round- off errors. Examples ======== >>> from sympy import sin, cos >>> from sympy.abc import x >>> from sympy.testing.randtest import verify_numerically as tn >>> tn(sin(x)**2 + cos(x)**2, 1, x) True csg|] }tqSr)r).0_rrrrrr 1sz&verify_numerically..) r isinstancer Z free_symbolslistzipsubsnr ) fgztolrrrrZrepsZz1Zz2rrrverify_numericallys " r*c CsPddlm}t||||}||||} ||||} t| | |S)a Test numerically that the symbolically computed derivative of f with respect to z is correct. This routine does not test whether there are Floats present with precision higher than 15 digits so if there are, your results may not be what you expect due to round-off errors. Examples ======== >>> from sympy import sin >>> from sympy.abc import x >>> from sympy.testing.randtest import test_derivative_numerically as td >>> td(sin(x), x) True r) Derivative)Zsympy.core.functionr+rZdiffr$Zdoit_numericallyr r%) r&r(r)rrrrr+Zz0f1f2rrrtest_derivative_numerically7s r.csV|durtSt|trt|jSt|r't|}|d|ffdd Std)aGReturn a randrange generator. ``seed`` can be o None - return randomly seeded generator o int - return a generator seeded with the int o list - the values to be returned will be taken from the list in the order given; the provided list is not modified. Examples ======== >>> from sympy.testing.randtest import _randrange >>> rr = _randrange() >>> rr(1000) # doctest: +SKIP 999 >>> rr = _randrange(3) >>> rr(1000) # doctest: +SKIP 238 >>> rr = _randrange([0, 5, 1, 3, 4]) >>> rr(3), rr(3) (0, 1) Ncs|dur d|}}t|t|}}||}|dkrtdz|}Wn ty/tdw||kr;|kr<|S|||S)Nrrz_randrange got empty rangez!_randrange sequence was too shortr ValueErrorpop IndexErrorrrseqwxgiverrr8ms    z_randrange..givez!_randrange got an unexpected seed)rr!intrrr"reverser0Zseedrr7r _randrangePs  r<csT|durtSt|trt|jSt|r&t|}||ffdd Std)aIReturn a randint generator. ``seed`` can be o None - return randomly seeded generator o int - return a generator seeded with the int o list - the values to be returned will be taken from the list in the order given; the provided list is not modified. Examples ======== >>> from sympy.testing.randtest import _randint >>> ri = _randint() >>> ri(1, 1000) # doctest: +SKIP 999 >>> ri = _randint(3) >>> ri(1, 1000) # doctest: +SKIP 238 >>> ri = _randint([0, 5, 1, 2, 4]) >>> ri(1, 3), ri(1, 3) (1, 2) Ncsrt|t|}}||}|dkrtdz|}Wn ty&tdw||kr2|kr3|S|||S)Nrz_randint got empty rangez_randint sequence was too shortr/r3r7rrr8s   z_randint..givez_randint got an unexpected seed)rr!r9rrr"r:r0r;rr7r_randints   r=)r rrrFN)Nrr rrr)rr rrr)N)__doc__ZrandomrrrrZsympy.core.compatibilityrrZsympy.core.containersrZsympy.core.numbersr r Zsympy.core.symbolr Zsympy.simplify.simplifyr rr*r.r<r=rrrrs       1