def derive_by_array(expr, dx): r""" Derivative by arrays. Supports both arrays and scalars. Given the array `A_{i_1, \ldots, i_N}` and the array `X_{j_1, \ldots, j_M}` this function will return a new array `B` defined by `B_{j_1,\ldots,j_M,i_1,\ldots,i_N} := \frac{\partial A_{i_1,\ldots,i_N}}{\partial X_{j_1,\ldots,j_M}}` Examples ======== >>> from sympy import derive_by_array >>> from sympy.abc import x, y, z, t >>> from sympy import cos >>> derive_by_array(cos(x*t), x) -t*sin(t*x) >>> derive_by_array(cos(x*t), [x, y, z, t]) [-t*sin(t*x), 0, 0, -x*sin(t*x)] >>> derive_by_array([x, y**2*z], [[x, y], [z, t]]) [[[1, 0], [0, 2*y*z]], [[0, y**2], [0, 0]]] """ from sympy.matrices import MatrixBase from sympy.tensor.array import SparseNDimArray array_types = (Iterable, MatrixBase, NDimArray) if isinstance(dx, array_types): dx = ImmutableDenseNDimArray(dx) for i in dx: if not i._diff_wrt: raise ValueError("cannot derive by this array") if isinstance(expr, array_types): if isinstance(expr, NDimArray): expr = expr.as_immutable() else: expr = ImmutableDenseNDimArray(expr) if isinstance(dx, array_types): if isinstance(expr, SparseNDimArray): lp = len(expr) new_array = { k + i * lp: v for i, x in enumerate(Flatten(dx)) for k, v in expr.diff(x)._sparse_array.items() } else: new_array = [[y.diff(x) for y in Flatten(expr)] for x in Flatten(dx)] return type(expr)(new_array, dx.shape + expr.shape) else: return expr.diff(dx) else: if isinstance(dx, array_types): return ImmutableDenseNDimArray([expr.diff(i) for i in Flatten(dx)], dx.shape) else: return diff(expr, dx)
def derive_by_array(expr, dx): """ Derivative by arrays. Supports both arrays and scalars. Given the array `A_{i_1, \ldots, i_N}` and the array `X_{j_1, \ldots, j_M}` this function will return a new array `B` defined by `B_{j_1,\ldots,j_M,i_1,\ldots,i_N} := \frac{\partial A_{i_1,\ldots,i_N}}{\partial X_{j_1,\ldots,j_M}` Examples ======== >>> from sympy.tensor.array import derive_by_array >>> from sympy.abc import x, y, z, t >>> from sympy import cos >>> derive_by_array(cos(x*t), x) -t*sin(t*x) >>> derive_by_array(cos(x*t), [x, y, z, t]) [-t*sin(t*x), 0, 0, -x*sin(t*x)] >>> derive_by_array([x, y**2*z], [[x, y], [z, t]]) [[[1, 0], [0, 2*y*z]], [[0, y**2], [0, 0]]] """ array_types = (collections.Iterable, MatrixBase, NDimArray) if isinstance(dx, array_types): dx = ImmutableDenseNDimArray(dx) for i in dx: if not i._diff_wrt: raise ValueError("cannot derive by this array") if isinstance(expr, array_types): expr = ImmutableDenseNDimArray(expr) if isinstance(dx, array_types): new_array = [[y.diff(x) for y in expr] for x in dx] return type(expr)(new_array, dx.shape + expr.shape) else: return expr.diff(dx) else: if isinstance(dx, array_types): return ImmutableDenseNDimArray([expr.diff(i) for i in dx], dx.shape) else: return diff(expr, dx)
def derive_by_array(expr, dx): r""" Derivative by arrays. Supports both arrays and scalars. Given the array `A_{i_1, \ldots, i_N}` and the array `X_{j_1, \ldots, j_M}` this function will return a new array `B` defined by `B_{j_1,\ldots,j_M,i_1,\ldots,i_N} := \frac{\partial A_{i_1,\ldots,i_N}}{\partial X_{j_1,\ldots,j_M}}` Examples ======== >>> from sympy import derive_by_array >>> from sympy.abc import x, y, z, t >>> from sympy import cos >>> derive_by_array(cos(x*t), x) -t*sin(t*x) >>> derive_by_array(cos(x*t), [x, y, z, t]) [-t*sin(t*x), 0, 0, -x*sin(t*x)] >>> derive_by_array([x, y**2*z], [[x, y], [z, t]]) [[[1, 0], [0, 2*y*z]], [[0, y**2], [0, 0]]] """ from sympy.matrices import MatrixBase array_types = (collections.Iterable, MatrixBase, NDimArray) if isinstance(dx, array_types): dx = ImmutableDenseNDimArray(dx) for i in dx: if not i._diff_wrt: raise ValueError("cannot derive by this array") if isinstance(expr, array_types): expr = ImmutableDenseNDimArray(expr) if isinstance(dx, array_types): new_array = [[y.diff(x) for y in expr] for x in dx] return type(expr)(new_array, dx.shape + expr.shape) else: return expr.diff(dx) else: if isinstance(dx, array_types): return ImmutableDenseNDimArray([expr.diff(i) for i in dx], dx.shape) else: return diff(expr, dx)