3.6.3. horton.matrix.cholesky – Cholesky decomposition of four-index objects¶
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class
horton.matrix.cholesky.CholeskyFourIndex(nbasis, nvec=None, array=None, array2=None)¶ Bases:
horton.matrix.base.FourIndexArguments:
- 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).
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__init__(nbasis, nvec=None, array=None, array2=None)¶ 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).
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assign(other)¶ Assign with the contents of another object
Arguments:
- other
- Another CholeskyFourIndex object.
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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_expsfor details. - method
- Either
einsumortensordot(default).
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change_basis_signs(signs)¶ Correct for different sign conventions of the basis functions.
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clear()¶ Reset all elements to zero.
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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()
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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()
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copy()¶ Return a copy of the current four-index operator
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decouple_array2()¶ Allocates a second Cholesky vector if not done yet
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classmethod
from_hdf5(grp)¶ Construct an instance from data previously stored in an h5py.Group.
Arguments:
- grp
- An h5py.Group object.
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get_dense()¶ Return the DenseFourIndex equivalent. ONLY FOR TESTING. SUPER SLOW.
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get_element(i, j, k, l)¶ Return a matrix element
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iadd(other, factor)¶ This method is not supported due to the Cholesky decomposition.
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iadd_exchange()¶ In-place addition of its own exchange contribution
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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.
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iscale(factor)¶ In-place multiplication with a scalar
Arguments:
- factor
- A scalar factor.
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itranspose()¶ In-place transpose:
0,1,2,3 -> 1,0,3,2
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new()¶ Return a new four-index object with the same nbasis
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permute_basis(permutation)¶ Reorder the coefficients for a given permutation of basis functions.
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randomize()¶ Fill with random normal data
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reset_array2()¶ Deallocates the second cholesky vector and sets it to match the first.
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set_element(i, j, k, l, value)¶ This method is not supported due to the Cholesky decomposition.
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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()
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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()
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sum()¶ Return the sum of all elements. EXPENSIVE!
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symmetrize(symmetry=8)¶
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to_hdf5(grp)¶ Dump this object in an h5py.Group
Arguments:
- grp
- An h5py.Group object.
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is_decoupled¶
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nbasis¶ The number of basis functions
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ndim¶ The number of axes in the N-index object.
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nvec¶ The number of Cholesky vectors
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shape¶ The shape of the object
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class
horton.matrix.cholesky.CholeskyLinalgFactory(default_nbasis=None)¶ Bases:
horton.matrix.dense.DenseLinalgFactoryOptional arguments:
- default_nbasis
- The default basis size when constructing new operators/expansions.
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__init__(default_nbasis=None)¶ Optional arguments:
- default_nbasis
- The default basis size when constructing new operators/expansions.
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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.
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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.
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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.
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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.
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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.
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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.
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from_hdf5(grp)¶ Construct an instance from data previously stored in an h5py.Group.
Arguments:
- grp
- An h5py.Group object.
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set_default_nbasis(nbasis)¶
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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.
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to_hdf5(grp)¶ Write a LinalgFactory to an HDF5 group
Argument:
- grp
- A h5py.Group instance to write to.