Math

This submodule contains various mathematical functions. Most of them are imported directly from theano.tensor (see there for more details). Doing any kind of math with PyMC3 random variables, or defining custom likelihoods or priors requires you to use these theano expressions rather than NumPy or Python code.

dot(a, b)	Computes the dot product of two variables.
constant(x[, name, ndim, dtype])
flatten(x[, outdim])	Reshapes the variable x by keeping the first outdim-1 dimension size(s) of x the same, and making the last dimension size of x equal to the multiplication of its remaining dimension size(s).
zeros_like(model[, dtype, opt])	equivalent of numpy.zeros_like
ones_like(model[, dtype, opt])	equivalent of numpy.ones_like
stack(*tensors, **kwargs)	Stack tensors in sequence on given axis (default is 0).
concatenate(tensor_list[, axis])	Alias for `join`(axis, *tensor_list).
sum(input[, axis, dtype, keepdims, acc_dtype])	Computes the sum along the given axis(es) of a tensor input.
prod(input[, axis, dtype, keepdims, ...])	Computes the product along the given axis(es) of a tensor input.
lt	a < b
gt	a > b
le	a <= b
ge	a >= b
eq	a == b
neq	a != b
switch	if cond then ift else iff
clip	Clip x to be between min and max.
where	if cond then ift else iff
and_	bitwise a & b
or_	bitwise a | b
abs_	|`a`|
exp	e^`a`
log	base e logarithm of a
cos	cosine of a
sin	sine of a
tan	tangent of a
cosh	hyperbolic cosine of a
sinh	hyperbolic sine of a
tanh	hyperbolic tangent of a
sqr	square of a
sqrt	square root of a
erf	error function
erfinv	inverse error function
dot(a, b)	Computes the dot product of two variables.
maximum	elemwise maximum. See max for the maximum in one tensor
minimum	elemwise minimum. See min for the minimum in one tensor
sgn	sign of a
ceil	ceiling of a
floor	floor of a
det	Matrix determinant.
matrix_inverse	Computes the inverse of a matrix \(A\).
extract_diag	Return the diagonal of a matrix.
matrix_dot(*args)	Shorthand for product between several dots.
trace(X)	Returns the sum of diagonal elements of matrix X.
sigmoid	Generalizes a scalar op to tensors.
logsumexp(x[, axis])
invlogit(x[, eps])
logit(p)

class pymc3.math.LogDet

Compute the logarithm of the absolute determinant of a square matrix M, log(abs(det(M))) on the CPU. Avoids det(M) overflow/ underflow.

Note

Once PR #3959 (https://github.com/Theano/Theano/pull/3959/) by harpone is merged, this must be removed.

pymc3.math.expand_packed_triangular(n, packed, lower=True, diagonal_only=False)

Convert a packed triangular matrix into a two dimensional array.

Triangular matrices can be stored with better space efficiancy by storing the non-zero values in a one-dimensional array. We number the elements by row like this (for lower or upper triangular matrices):

[[0 - - -]     [[0 1 2 3]
 [1 2 - -]      [- 4 5 6]
 [3 4 5 -]      [- - 7 8]
 [6 7 8 9]]     [- - - 9]

Parameters:

• n (int) – The number of rows of the triangular matrix.
• packed (theano.vector) – The matrix in packed format.
• lower (bool, default=True) – If true, assume that the matrix is lower triangular.
• diagonal_only (bool) – If true, return only the diagonal of the matrix.

pymc3.math.tround(*args, **kwargs)

Temporary function to silence round warning in Theano. Please remove when the warning disappears.