sym package

Unified wrapper for symbolic manipulation libraries in Python.

Submodules

sym.backend module

sym.backend.Backend(name=None, envvar='SYM_BACKEND', default='sympy')

Backend for the underlying symbolic manipulation packages

Parameters:

name: str (default: None)

Name of package e.g. ‘sympy’

envvar: str (default: ‘SYM_BACKEND’)

name of environment variable to read name from (when name is None)

default: str

name to use when the environment variable described by envvar is unset or empty (default: ‘sympy’)

Examples

>>> be = Backend('sympy')  # or e.g. 'symengine'
>>> x, y = map(be.Symbol, 'xy')
>>> exprs = [x + y + 1, x*y**2]
>>> lmb = be.Lambdify([x, y], exprs)
>>> import numpy as np
>>> lmb(np.arange(6.0).reshape((3, 2)))  
array([[   2.,    0.],
       [   6.,   18.],
       [  10.,  100.]])

sym.util module

sym.util.banded_jacobian(y, x, ml, mu)

Calculates a banded version of the jacobian

Compatible with the format requested by scipy.integrate.ode() (for SciPy >= v0.15).

Parameters:

y: array_like of expressions

x: array_like of symbols

ml: int

number of lower bands

mu: int

number of upper bands

Returns:

2D array of shape (1+ml+mu, len(y))

sym.util.check_transforms(fw, bw, symbs)

Verify validity of a pair of forward and backward transformations

Parameters:

fw: expression

forward transformation

bw: expression

backward transformation

symbs: iterable of symbols

the variables that are transformed

sym.util.linear_rref(A, b, backend)

Transform a linear system to reduced row-echelon form

Transforms both the matrix and right-hand side of a linear system of equations to reduced row echelon form

Parameters:

A: Matrix-like

iterable of rows

b: iterable

Returns:

A’, b’ - transformed versions

sym.util.sparse_jacobian_csc(y, x)

Calculates a compressed sparse column (CSC)

version of the jacobian

Parameters:

y: array_like of expressions

x: array_like of symbols

Returns:

jac_exprs: flattened list of expressions for nonzero entries of dy/dx in column-major order

colptrs: list of length len(y) + 1, where jac_exprs[colptrs[i]:colptrs[i+1]] are

the nonzero entries of column i in dy/dx

rowvals: list of length len(jac_exprs, denoting the row index in dy/dx for each

entry in jac_exprs

sym.util.sparse_jacobian_csr(y, x)

Calculates a compressed sparse row (CSR)

version of the jacobian

Parameters:

y: array_like of expressions

x: array_like of symbols

Returns:

jac_exprs: flattened list of expressions for nonzero entries of dy/dx in row-major order

rowptrs: list of length len(y) + 1, where jac_exprs[colptrs[i]:colptrs[i+1]] are

the nonzero entries of row i in dy/dx

colvals: list of length len(jac_exprs, denoting the column index in dy/dx for each

entry in jac_exprs