qmat.qdelta.diag

QDelta coefficients based on minimization approaches. In particular, generates the diagonal coefficients from [Caklovic et al., 2024].

Examples

>>> from qmat.qcoeff.collocation import Collocation
>>> coll = Collocation(nNodes=4, nodeType="LEGENDRE", quadType="RADAU-RIGHT")
>>>
>>> from qmat import genQDeltaCoeffs
>>> QDelta = genQDeltaCoeffs("MIN-SR-NS", nodes=coll.nodes)
>>>
>>> from qmat.qdelta.diag import MIN_SR_S, MIN_SR_FLEX
>>> minSRS= MIN_SR_S(coll.nNodes, coll.nodeType, coll.quadType)
>>> QDelta = minSRS.getQDelta()
>>> minSRFLEX = MIN_SR_FLEX(coll.nNodes, coll.nodeType, coll.quadType)
>>> QD1, QD2, QD3 = minSRFLEX.genCoeffs(k=[1,2,3])

Classes

MIN	Naive diagonal coefficients based on spectral radius optimization.
FromTable	Base (unregistered) class for diagonal coefficients stored in tables.
MIN3	Magic diagonal coefficients from [Speck, 2021].
MIN_VDHS	Diagonal coefficients from [van der Houwen & Sommeijer, 1991].
MIN_SR_NS	Diagonal MIN-SR-NS coefficients from [Caklovic et al., 2024].
MIN_SR_S	Diagonal MIN-SR-S coefficients from [Caklovic et al., 2024].
MIN_SR_FLEX	Diagonal MIN-SR-FLEX coefficients from [Caklovic et al., 2024]
Jumper	Diagonal coefficients allowing order jump
FlexJumper	Diagonal coefficients allowing order jump while still maintaining high stability
DNODES	Diagonal coefficients build on divided node (1 here)
DNODES2	Diagonal coefficients build on divided node (2 here)
DNODES3	Diagonal coefficients build on divided node (3 here)
DNODES4	Diagonal coefficients build on divided node (4 here)
DNODES5	Diagonal coefficients build on divided node (5 here)

Functions

check(k)	Utility function to check k parameter for k-dependent generators
registerTable(→ FromTable)

Module Contents

check(k)

Utility function to check k parameter for k-dependent generators

class MIN(Q, **kwargs)

Naive diagonal coefficients based on spectral radius optimization.

aliases = ['MIN-Speck']

rho(x)

computeQDelta(k=None)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

class FromTable(nNodes, nodeType, quadType, **kwargs)

Base (unregistered) class for diagonal coefficients stored in tables.

nNodes

nodeType

quadType

static extractParams(qGen: qmat.qcoeff.collocation.Collocation) → dict

Extract from a \(Q\)-generator object all parameters required to instantiate the \(Q_\Delta\)-generator

property size

Dimension of the approximated \(Q\)-coefficients (number of nodes)

computeQDelta(k=None)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

registerTable(cls: FromTable) → FromTable

class MIN3(nNodes, nodeType, quadType, **kwargs)

Magic diagonal coefficients from [Speck, 2021].

aliases = ['Magic_Numbers']

class MIN_VDHS(nNodes, nodeType, quadType, **kwargs)

Diagonal coefficients from [van der Houwen & Sommeijer, 1991].

aliases = ['VDHS']

class MIN_SR_NS(nodes, **kwargs)

Diagonal MIN-SR-NS coefficients from [Caklovic et al., 2024].

aliases = ['MIN-SR-NS', 'MIN_GT']

nodes

static extractParams(qGen: qmat.qdelta.QGenerator) → dict

Extract from a \(Q\)-generator object all parameters required to instantiate the \(Q_\Delta\)-generator

property size

Dimension of the approximated \(Q\)-coefficients (number of nodes)

computeQDelta(k=None)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

class MIN_SR_S(nNodes, nodeType, quadType, **kwargs)

Diagonal MIN-SR-S coefficients from [Caklovic et al., 2024].

Parameters:

• nNodes (int) – Number of nodes.

• nodeType (str) – Type of node distribution, see qmat.nodes.NodesGenerator for available types.

• quadType (str) – Quadrature type for the nodes, see qmat.nodes.NodesGenerator for available types.

• **kwargs – Additional parameters given during a generic call, not used by this class.

aliases = ['MIN-SR-S']

coll

nodeType

quadType

static extractParams(qGen: qmat.qcoeff.collocation.Collocation) → dict

Extract from a \(Q\)-generator object all parameters required to instantiate the \(Q_\Delta\)-generator

property size

Dimension of the approximated \(Q\)-coefficients (number of nodes)

computeCoeffs(M, a=None, b=None)

Compute diagonal coefficients for a given number of nodes M. If a and b are given, then it uses as initial guess:

>>> a * nodes**b / M

If a is not given, then do not care about b and uses as initial guess:

>>> nodes / M

Parameters:

• M (int) – Number of collocation nodes.

• a (float, optional) – a coefficient for the initial guess.

• b (float, optional) – b coefficient for the initial guess.

Returns:

• coeffs (array) – The diagonal coefficients.

• nodes (array) – The nodes associated to the current coefficients.

static fit(coeffs, nodes)

Function fitting given coefficients to a power law

computeQDelta(k=None)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

class MIN_SR_FLEX(nNodes, nodeType, quadType, **kwargs)

Diagonal MIN-SR-FLEX coefficients from [Caklovic et al., 2024]

Parameters:

• nNodes (int) – Number of nodes.

• nodeType (str) – Type of node distribution, see qmat.nodes.NodesGenerator for available types.

• quadType (str) – Quadrature type for the nodes, see qmat.nodes.NodesGenerator for available types.

• **kwargs – Additional parameters given during a generic call, not used by this class.

aliases = ['MIN-SR-FLEX']

computeQDelta(k=1)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

class Jumper(nodes, **kwargs)

Diagonal coefficients allowing order jump

aliases = ['JUMPER', 'FB']

computeQDelta(k=1)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

class FlexJumper(nodes, **kwargs)

Diagonal coefficients allowing order jump while still maintaining high stability

aliases = ['FLEX-JUMPER', 'FB2']

computeQDelta(k=1)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

class DNODES(nodes, **kwargs)

Diagonal coefficients build on divided node (1 here)

divider = 1

aliases = ['DNODES-1']

computeQDelta(k=None)

Compute and returns the \(Q_\Delta\) matrix, has to be implemented in the specialized class.

Parameters:

k (int, optional) – Iteration number of the approximation. The default is None.

Returns:

QDelta

Return type:

np.ndarray

class DNODES2(nodes, **kwargs)

Diagonal coefficients build on divided node (2 here)

divider = 2

aliases = ['DNODES-2']

class DNODES3(nodes, **kwargs)

Diagonal coefficients build on divided node (3 here)

divider = 3

aliases = ['DNODES-3']

class DNODES4(nodes, **kwargs)

Diagonal coefficients build on divided node (4 here)

divider = 4

aliases = ['DNODES-4']

class DNODES5(nodes, **kwargs)

Diagonal coefficients build on divided node (5 here)

divider = 5

aliases = ['DNODES-5']