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
from sympy.tensor.array import MutableSparseNDimArray, ImmutableSparseNDimArray
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
b = MutableSparseNDimArray.zeros(10000, 20000)
b[0, 0] = i
b[0, 1] = j
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))
sqrt(1.0 / 3.0), 1.0 / 3.0,
sqrt(1.0 / 3.0), 1.0 / 3.0
],
])
#--------------------------------------------------------------------
# Matrix modes_to_nodes
val_r_inv = val_r**(-1)
# Computes coordiantes modes
coords_modes_ = val_r_inv * coords_
coords_modes = lambdify(coords_, coords_modes_, "numpy")
# Initialized coordiantes
interp_coords_ = MutableSparseNDimArray.zeros(nnodes_ie, 3)
for inode in range(0, nnodes_ie):
for idir in range(0, 3):
interp_coords_[inode, idir] = val_i[inode, :] * coords_modes_[:, idir]
# Initialized jacobian
jacobian_ = MutableSparseNDimArray.zeros(3, 3, nnodes_ie)
for inode in range(0, nnodes_ie):
jacobian_[0, 0, inode] = ddxi_i[inode, :] * coords_modes_[:, 0]
jacobian_[0, 1, inode] = ddeta_i[inode, :] * coords_modes_[:, 0]
jacobian_[0, 2, inode] = ddzeta_i[inode, :] * coords_modes_[:, 0]
jacobian_[1, 0, inode] = ddxi_i[inode, :] * coords_modes_[:, 1]
jacobian_[1, 1, inode] = ddeta_i[inode, :] * coords_modes_[:, 1]
jacobian_[1, 2, inode] = ddzeta_i[inode, :] * coords_modes_[:, 1]
jacobian_[2, 0, inode] = ddxi_i[inode, :] * coords_modes_[:, 2]
jacobian_[2, 1, inode] = ddeta_i[inode, :] * coords_modes_[:, 2]