symmray.interface

Functional interface for symmray array objects.

Functions

conj(x, **kwargs)	Conjugate a symmray array.
gram(x[, axes])	Form dag(x) @ x, leaving axes open in both copies.
max(x)	Return the maximum value of a symmray array.
min(x)	Return the minimum value of a symmray array.
sum(x)	Return the sum of a symmray array.
all(x)	Check if all elements of a symmray array are true.
any(x)	Check if any elements of a symmray array are true.
isfinite(x)	Check if a symmray array contains only finite values.
finfo(dtype)	Return machine limits for a common floating-point dtype.
abs(x)	Return the absolute value of a symmray array.
sqrt(x)	Return the square root of a symmray array.
log(x)	Return the natural logarithm of a symmray array.
log2(x)	Return the base-2 logarithm of a symmray array.
log10(x)	Return the base-10 logarithm of a symmray array.
real(x)	Return the real part of a symmray array.
imag(x)	Return the imaginary part of a symmray array.
clip(x, a_min, a_max)	Clip the values of a symmray array.
squeeze(x[, axis])	Remove single-dimensional entries from shape of a symmray array.
expand_dims(x, axis)	Expand the shape of a symmray array.
reshape(a, newshape, **kwargs)	Reshape a symmray array, via fusing or unfusing.
tensordot(a, b[, axes])	Contract two symmray arrays along the specified axes.
_parse_tensordot_eq(eq)	Try to convert the two term einsum eq into tensordot axes and a
_parse_multiply_diagonal_eq(eq)	Check whether the two term einsum eq is a diagonal multiplication
einsum(*args, **kwargs)	Contract arrays with an einsum equation that names its output.
transpose(a[, axes])	Transpose a symmray array.
trace(a)	Return the trace of a symmray array.
take(a, indices, axis, **kwargs)	Take elements from a symmray array along an axis.
multiply_diagonal(x, v, axis)	Multiply a symmray array by a vector as if contracting a diagonal
ldmul(v, x)	Left multiply a symmray matrix x by a vector v.
rdmul(x, v)	Right multiply a symmray matrix x by a vector v.
lddiv(v, x)	Left divide a symmray matrix x by a vector v.
rddiv(x, v)	Right divide a symmray matrix x by a vector v.
align_axes(x, y, axes)	Align the axes of two symmray arrays (drop mis-matched charges)
fuse(x, *axes_groups)	Fuse multiple axes of a symmray array.

Module Contents

symmray.interface.conj(x, **kwargs)

Conjugate a symmray array.

symmray.interface.gram(x, axes=-1)

Form dag(x) @ x, leaving axes open in both copies.

See gram() for the fermionic sign convention.

symmray.interface.max(x)

Return the maximum value of a symmray array.

symmray.interface.min(x)

Return the minimum value of a symmray array.

symmray.interface.sum(x)

Return the sum of a symmray array.

symmray.interface.all(x)

Check if all elements of a symmray array are true.

symmray.interface.any(x)

Check if any elements of a symmray array are true.

symmray.interface.isfinite(x)

Check if a symmray array contains only finite values.

symmray.interface.finfo(dtype)

Return machine limits for a common floating-point dtype.

symmray.interface.abs(x)

Return the absolute value of a symmray array.

symmray.interface.sqrt(x)

Return the square root of a symmray array.

symmray.interface.log(x)

Return the natural logarithm of a symmray array.

symmray.interface.log2(x)

Return the base-2 logarithm of a symmray array.

symmray.interface.log10(x)

Return the base-10 logarithm of a symmray array.

symmray.interface.real(x)

Return the real part of a symmray array.

symmray.interface.imag(x)

Return the imaginary part of a symmray array.

symmray.interface.clip(x, a_min, a_max)

Clip the values of a symmray array.

symmray.interface.squeeze(x, axis=None)

Remove single-dimensional entries from shape of a symmray array.

symmray.interface.expand_dims(x, axis)

Expand the shape of a symmray array.

symmray.interface.reshape(a, newshape, **kwargs)

Reshape a symmray array, via fusing or unfusing.

symmray.interface.tensordot(a, b, axes=2, **kwargs)

Contract two symmray arrays along the specified axes.

Parameters:

• a (AbelianArray or FermionicArray) – First array to contract.

• b (AbelianArray or FermionicArray) – Second array to contract, with same type as a.

• axes (int or tuple of int, optional) – If an integer, the number of axes to contract. If a tuple, the axes to contract. Default is 2.

symmray.interface._parse_tensordot_eq(eq)

Try to convert the two term einsum eq into tensordot axes and a final output permutation.

Returns None if not possible, i.e. if the eq features batched, summed, or repeated indices, else a tuple (axes_a, axes_b, perm), where perm is a final permutation of the tensordot output axes, or None if not needed.

symmray.interface._parse_multiply_diagonal_eq(eq)

Check whether the two term einsum eq is a diagonal multiplication pattern, e.g. “i,ijkl->ijkl”, suitable for multiply_diagonal.

Returns None if it is not, else a tuple (which, axis, perm), where which is “left”, “right”, or “both” depending on which term(s) are vector-like, axis is the axis of the array term that the vector multiplies into, and perm is a final permutation of the array term axes, or None if not needed.

symmray.interface.einsum(*args, **kwargs)

Contract arrays with an einsum equation that names its output.

With one array, permute axes ("abc->cab") or trace pairs ("abcb->ca", "abab->"). Each output label must occur once. Each trace label must occur twice on indices with matching sizes and opposite dualness. A complete trace returns a scalar. Set preserve_array=True to return an array with no axes. Fermionic arrays include the signs from permuting and tracing axes.

Flat partial traces need a complete set of sector blocks and every charge on each input axis. Diagonal extraction, single-axis sums, and ellipses are unsupported.

With two arrays, pairwise contractions and outer products use tensordot. The result is reordered if the equation asks for it. A symmray vector can multiply along a shared axis, e.g. "i,ijkl->ijkl". Cotengra handles more than two arrays.

symmray.interface.transpose(a, axes=None, **kwargs)

Transpose a symmray array.

symmray.interface.trace(a)

Return the trace of a symmray array.

symmray.interface.take(a, indices, axis, **kwargs)

Take elements from a symmray array along an axis.

symmray.interface.multiply_diagonal(x, v, axis)

Multiply a symmray array by a vector as if contracting a diagonal matrix into one axis.

symmray.interface.ldmul(v, x)

Left multiply a symmray matrix x by a vector v.

symmray.interface.rdmul(x, v)

Right multiply a symmray matrix x by a vector v.

symmray.interface.lddiv(v, x)

Left divide a symmray matrix x by a vector v.

symmray.interface.rddiv(x, v)

Right divide a symmray matrix x by a vector v.

symmray.interface.align_axes(x, y, axes)

Align the axes of two symmray arrays (drop mis-matched charges) to prepare for contraction, explicit or implicit (e.g. decomposition that should match).

symmray.interface.fuse(x, *axes_groups)

Fuse multiple axes of a symmray array.