def test_derivative_by_array():
from sympy.abc import i, j, t, x, y, z
bexpr = x*y**2*exp(z)*log(t)
sexpr = sin(bexpr)
cexpr = cos(bexpr)
a = Array([sexpr])
assert derive_by_array(sexpr, t) == x*y**2*exp(z)*cos(x*y**2*exp(z)*log(t))/t
assert derive_by_array(sexpr, [x, y, z]) == Array([bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr, bexpr*cexpr])
assert derive_by_array(a, [x, y, z]) == Array([[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr], [bexpr*cexpr]])
assert derive_by_array(sexpr, [[x, y], [z, t]]) == Array([[bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr], [bexpr*cexpr, bexpr/log(t)/t*cexpr]])
assert derive_by_array(a, [[x, y], [z, t]]) == Array([[[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr]], [[bexpr*cexpr], [bexpr/log(t)/t*cexpr]]])
assert derive_by_array([[x, y], [z, t]], [x, y]) == Array([[[1, 0], [0, 0]], [[0, 1], [0, 0]]])
assert derive_by_array([[x, y], [z, t]], [[x, y], [z, t]]) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]],
[[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
assert diff(sexpr, t) == x*y**2*exp(z)*cos(x*y**2*exp(z)*log(t))/t
assert diff(sexpr, Array([x, y, z])) == Array([bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr, bexpr*cexpr])
assert diff(a, Array([x, y, z])) == Array([[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr], [bexpr*cexpr]])
assert diff(sexpr, Array([[x, y], [z, t]])) == Array([[bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr], [bexpr*cexpr, bexpr/log(t)/t*cexpr]])
assert diff(a, Array([[x, y], [z, t]])) == Array([[[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr]], [[bexpr*cexpr], [bexpr/log(t)/t*cexpr]]])
assert diff(Array([[x, y], [z, t]]), Array([x, y])) == Array([[[1, 0], [0, 0]], [[0, 1], [0, 0]]])
assert diff(Array([[x, y], [z, t]]), Array([[x, y], [z, t]])) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]],
[[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
# test for large scale sparse array
for SparseArrayType in [ImmutableSparseNDimArray, MutableSparseNDimArray]:
b = MutableSparseNDimArray({0:i, 1:j}, (10000, 20000))
assert derive_by_array(b, i) == ImmutableSparseNDimArray({0: 1}, (10000, 20000))
assert derive_by_array(b, (i, j)) == ImmutableSparseNDimArray({0: 1, 200000001: 1}, (2, 10000, 20000))
def test_derivative_by_array():
from sympy.abc import a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z
bexpr = x * y**2 * exp(z) * log(t)
sexpr = sin(bexpr)
cexpr = cos(bexpr)
a = Array([sexpr])
assert derive_by_array(
sexpr, t) == x * y**2 * exp(z) * cos(x * y**2 * exp(z) * log(t)) / t
assert derive_by_array(sexpr, [x, y, z]) == Array(
[bexpr / x * cexpr, 2 * y * bexpr / y**2 * cexpr, bexpr * cexpr])
assert derive_by_array(a,
[x, y, z]) == Array([[bexpr / x * cexpr],
[2 * y * bexpr / y**2 * cexpr],
[bexpr * cexpr]])
assert derive_by_array(sexpr, [[x, y], [z, t]]) == Array(
[[bexpr / x * cexpr, 2 * y * bexpr / y**2 * cexpr],
[bexpr * cexpr, bexpr / log(t) / t * cexpr]])
assert derive_by_array(a, [[x, y], [z, t]]) == Array(
[[[bexpr / x * cexpr], [2 * y * bexpr / y**2 * cexpr]],
[[bexpr * cexpr], [bexpr / log(t) / t * cexpr]]])
assert derive_by_array([[x, y], [z, t]], [x, y]) == Array([[[1, 0], [0,
0]],
[[0, 1], [0,
0]]])
assert derive_by_array([[x, y], [z, t]],
[[x, y], [z, t]]) == Array([[[[1, 0], [0, 0]],
[[0, 1], [0, 0]]],
[[[0, 0], [1, 0]],
[[0, 0], [0, 1]]]])
def test_derivative_by_array():
from sympy.abc import a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z
bexpr = x*y**2*exp(z)*log(t)
sexpr = sin(bexpr)
cexpr = cos(bexpr)
a = Array([sexpr])
assert derive_by_array(sexpr, t) == x*y**2*exp(z)*cos(x*y**2*exp(z)*log(t))/t
assert derive_by_array(sexpr, [x, y, z]) == Array([bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr, bexpr*cexpr])
assert derive_by_array(a, [x, y, z]) == Array([[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr], [bexpr*cexpr]])
assert derive_by_array(sexpr, [[x, y], [z, t]]) == Array([[bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr], [bexpr*cexpr, bexpr/log(t)/t*cexpr]])
assert derive_by_array(a, [[x, y], [z, t]]) == Array([[[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr]], [[bexpr*cexpr], [bexpr/log(t)/t*cexpr]]])
assert derive_by_array([[x, y], [z, t]], [x, y]) == Array([[[1, 0], [0, 0]], [[0, 1], [0, 0]]])
assert derive_by_array([[x, y], [z, t]], [[x, y], [z, t]]) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]],
[[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])