3.8.3. horton.matrix.cholesky – Cholesky decomposition of four-index objects¶

class horton.matrix.cholesky.CholeskyFourIndex(nbasis, nvec=None, array=None, array2=None)¶

Bases: horton.matrix.base.FourIndex

Arguments:

nbasis

The number of basis functions.

Optional arguments:

nvec

The number of (2-index) Cholesky vectors.

array

The array with Cholesky vectors, shape = (nvec, nbasis, nbasis).

array2

The second set of Cholesky vectors, if different from the first.

Either nvec or array must be given (or both).

assign(other)¶

Assign with the contents of another object

Arguments:

other

Another CholeskyFourIndex object.

assign_four_index_transform(ao_integrals, exp0, exp1=None, exp2=None, exp3=None, method='tensordot')¶

Perform four index transformation.

Arguments:

oa_integrals

A CholeskyFourIndex with integrals in atomic orbitals.

exp0

A DenseExpansion object with molecular orbitals

Optional arguments:

exp1, exp2, exp3

Can be provided to transform each index differently. See parse_four_index_transform_exps for details.

method

Either einsum or tensordot (default).

change_basis_signs(signs)¶

Correct for different sign conventions of the basis functions.

clear()¶

Reset all elements to zero.

contract_two_to_four(subscripts, two, out=None, factor=1.0, clear=True)¶

Contracts with a two-index object to obtain a four-index object.

Arguments:

subscripts

Any of abcd,cd->acbd, abcd,cd->acdb, abcd,cb->acdb, abcd,cb->acbd, abcd,ab->acbd, abcd,ab->acdb, abcd,ad->acbd, abcd,ad->acdb, abcd,ad->abcd, abcd,ad->abdc, abcd,bd->abcd, abcd,bd->abdc, abcd,bc->abdc, abcd,bc->abcd, abcd,ac->abcd, abcd,ac->abdc

two

An instance of DenseTwoIndex.

Optional arguments:

out, factor, clear

See DenseLinalgFactory.einsum()

contract_two_to_two(subscripts, two, out=None, factor=1.0, clear=True)¶

Contract self with a two-index to obtain a two-index.

Arguments:

subscripts

Any of abcd,bd->ac (direct), abcd,cb->ad (exchange)

two

The input two-index object. (DenseTwoIndex)

Optional arguments:

out, factor, clear

See DenseLinalgFactory.einsum()

copy()¶

Return a copy of the current four-index operator

decouple_array2()¶

Allocates a second Cholesky vector if not done yet

classmethod from_hdf5(grp)¶

Construct an instance from data previously stored in an h5py.Group.

Arguments:

grp

An h5py.Group object.

get_dense()¶

Return the DenseFourIndex equivalent. ONLY FOR TESTING. SUPER SLOW.

get_element(i, j, k, l)¶

Return a matrix element

iadd(other, factor)¶

This method is not supported due to the Cholesky decomposition.

iadd_exchange()¶

In-place addition of its own exchange contribution

is_symmetric(symmetry=2, rtol=1e-05, atol=1e-08)¶

Check the symmetry of the array.

Optional arguments:

symmetry

The symmetry to check. See Handling of index symmetry for more details.

rtol and atol

relative and absolute tolerance. See to np.allclose.

iscale(factor)¶

In-place multiplication with a scalar

Arguments:

factor

A scalar factor.

itranspose()¶

In-place transpose: 0,1,2,3 -> 1,0,3,2

new()¶

Return a new four-index object with the same nbasis

permute_basis(permutation)¶

Reorder the coefficients for a given permutation of basis functions.

randomize()¶

Fill with random normal data

reset_array2()¶

Deallocates the second cholesky vector and sets it to match the first.

set_element(i, j, k, l, value)¶

This method is not supported due to the Cholesky decomposition.

slice_to_three(subscripts, out=None, factor=1.0, clear=True)¶

Returns a three-index contraction of the four-index object.

Arguments:

subscripts

Any of abcc->bac, abcc->abc, abcb->abc, abbc->abc

Optional arguments:

out, factor, clear

See DenseLinalgFactory.einsum()

slice_to_two(subscripts, out=None, factor=1.0, clear=True)¶

Returns a two-index contraction of the four-index object.

Arguments:

subscripts

Any of aabb->ab, abab->ab, abba->ab

Optional arguments:

out, factor, clear

See DenseLinalgFactory.einsum()

sum()¶

Return the sum of all elements. EXPENSIVE!

symmetrize(symmetry=8)¶

to_hdf5(grp)¶

Dump this object in an h5py.Group

Arguments:

grp

An h5py.Group object.

is_decoupled¶

nbasis¶

The number of basis functions

ndim¶

The number of axes in the N-index object.

nvec¶

The number of Cholesky vectors

shape¶

The shape of the object

class horton.matrix.cholesky.CholeskyLinalgFactory(default_nbasis=None)¶

Bases: horton.matrix.dense.DenseLinalgFactory

Optional arguments:

default_nbasis

The default basis size when constructing new operators/expansions.

create_expansion(nbasis=None, nfn=None)¶

Create a DenseExpansion with defaults from the LinalgFactory

Optional arguments:

nbasis

The number of basis functions. When not given, the default_nbasis value of the DenseLinalgFactory instance will be used.

nfn

The number of orbitals. When not given, the default_nbasis value of the DenseLinalgFactory instance will be used.

create_four_index(nbasis=None, nvec=None, array=None, array2=None)¶

Create a DenseFourIndex with defaults from the LinalgFactory

Optional arguments:

nbasis

The number of basis functions. When not given, the default_nbasis value of the DenseLinalgFactory instance will be used.

create_one_index(nbasis=None)¶

Create a DenseOneIndex with defaults from the LinalgFactory

Optional arguments:

nbasis

The number of basis functions. When not given, the default_nbasis value of the DenseLinalgFactory instance will be used.

create_three_index(nbasis=None, nbasis1=None, nbasis2=None)¶

Create a DenseThreeIndex with defaults from the LinalgFactory

Optional arguments:

nbasis

The number of basis functions. When not given, the default_nbasis value of the DenseLinalgFactory instance will be used.

create_two_index(nbasis=None, nbasis1=None)¶

Create a DenseTwoIndex with defaults from the LinalgFactory

Optional arguments:

nbasis

The number of basis functions. When not given, the default_nbasis value of the DenseLinalgFactory instance will be used.

nbasis1

The number of basis functions for the second axis if it differes from nbasis.

einsum(subscripts, out, factor, clear, *operands)¶

einsum wrapper for DenseNBody objects

Arguments:

subscripts

The usual subscripts argument for the einsum function, except that the format is slightly limited. All indexes must be explicitly stated. If the output argument is a scalar, -> may not be present. In all other cases, -> must be present.

out

An output DenseNBody object. This argument is not allowed when the result is a scalar.

factor

Multiply the contraction by a scalar factor.

clear

When set to False, the output argument is not zeroed before adding the contraction.

operands

A list where each element is (i) a DenseNBody object or (ii) a two-tuple of DenseNBody object and ranges to select for slicing. The ranges must be a tuple of integers of the form (begin0, end0, begin1, end1, ...) where the number of (begin, end) pairs depends on the dimensionality of the corresponding tensor.

Returns: the out object. When the out argument is given, this is returned with in-place modifications.

from_hdf5(grp)¶

Construct an instance from data previously stored in an h5py.Group.

Arguments:

grp

An h5py.Group object.

set_default_nbasis(nbasis)¶

tensordot(a, b, axes, out=None, factor=1.0, clear=True)¶

tensordot wrapper for dense n-index objects.

Arguments:

a, b, axes

See documentation of numpy.tensordot

Optional arguments:

out

The output argument, an instance of one of the Dense?Index classes.

to_hdf5(grp)¶

Write a LinalgFactory to an HDF5 group

Argument:

grp

A h5py.Group instance to write to.