slepc4py.SLEPc.DS#

class slepc4py.SLEPc.DS#

Bases: Object

DS.

Enumerations

MatType

To refer to one of the matrices stored internally in DS.

ParallelType

DS parallel types.

StateType

DS state types.

Type

DS type.

Methods Summary

allocate(ld)

Allocate memory for internal storage or matrices in DS.

appendOptionsPrefix([prefix])

Append to the prefix used for searching for all DS options in the database.

cond()

Compute the inf-norm condition number of the first matrix.

create([comm])

Create the DS object.

destroy()

Destroy the DS object.

duplicate()

Duplicate the DS object with the same type and dimensions.

getBlockSize()

Get the block size.

getCompact()

Get the compact storage flag.

getDimensions()

Get the current dimensions.

getExtraRow()

Get the extra row flag.

getGSVDDimensions()

Get the number of columns and rows of a DS of type GSVD.

getHSVDDimensions()

Get the number of columns of a DS of type HSVD.

getLeadingDimension()

Get the leading dimension of the allocated matrices.

getMat(matname)

Get the requested matrix as a sequential dense Mat object.

getMethod()

Get the method currently used in the DS.

getOptionsPrefix()

Get the prefix used for searching for all DS options in the database.

getPEPCoefficients()

Get the polynomial basis coefficients of a DS of type PEP.

getPEPDegree()

Get the polynomial degree of a DS of type PEP.

getParallel()

Get the mode of operation in parallel runs.

getRefined()

Get the refined vectors flag.

getSVDDimensions()

Get the number of columns of a DS of type SVD.

getState()

Get the current state.

getType()

Get the DS type of this object.

reset()

Reset the DS object.

restoreMat(matname, mat)

Restore the previously seized matrix.

setBlockSize(bs)

Set the block size.

setCompact(comp)

Set the matrices' compact storage flag.

setDimensions([n, l, k])

Set the matrices sizes in the DS object.

setExtraRow(ext)

Set a flag to indicate that the matrix has one extra row.

setFromOptions()

Set DS options from the options database.

setGSVDDimensions(m, p)

Set the number of columns and rows of a DS of type GSVD.

setHSVDDimensions(m)

Set the number of columns of a DS of type HSVD.

setIdentity(matname)

Set the identity on the active part of a matrix.

setMethod(meth)

Set the method to be used to solve the problem.

setOptionsPrefix([prefix])

Set the prefix used for searching for all DS options in the database.

setPEPCoefficients(pbc)

Set the polynomial basis coefficients of a DS of type PEP.

setPEPDegree(deg)

Set the polynomial degree of a DS of type PEP.

setParallel(pmode)

Set the mode of operation in parallel runs.

setRefined(ref)

Set a flag to indicate that refined vectors must be computed.

setSVDDimensions(m)

Set the number of columns of a DS of type SVD.

setState(state)

Set the state of the DS object.

setType(ds_type)

Set the type for the DS object.

solve()

Solve the problem.

truncate(n[, trim])

Truncate the system represented in the DS object.

updateExtraRow()

Ensure that the extra row gets up-to-date after a call to DS.solve().

vectors([matname])

Compute vectors associated to the dense system such as eigenvectors.

view([viewer])

Print the DS data structure.

Attributes Summary

block_size

The block size.

compact

Compact storage of matrices.

extra_row

If the matrix has one extra row.

method

The method to be used to solve the problem.

parallel

The mode of operation in parallel runs.

refined

If refined vectors must be computed.

state

The state of the DS object.

Methods Documentation

allocate(ld)#

Allocate memory for internal storage or matrices in DS.

Logically collective.

Parameters:

ld (int) – Leading dimension (maximum allowed dimension for the matrices, including the extra row if present).

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:245

appendOptionsPrefix(prefix=None)#

Append to the prefix used for searching for all DS options in the database.

Logically collective.

Parameters:

prefix (str | None) – The prefix string to prepend to all DS option requests.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:190

cond()#

Compute the inf-norm condition number of the first matrix.

Logically collective.

Returns:

Condition number.

Return type:

float

Source code at slepc4py/SLEPc/DS.pyx:654

create(comm=None)#

Create the DS object.

Collective.

Parameters:

comm (Comm | None) – MPI communicator; if not provided, it defaults to all processes.

Return type:

Self

Source code at slepc4py/SLEPc/DS.pyx:122

destroy()#

Destroy the DS object.

Collective.

Source code at slepc4py/SLEPc/DS.pyx:104

Return type:

Self

duplicate()#

Duplicate the DS object with the same type and dimensions.

Collective.

Source code at slepc4py/SLEPc/DS.pyx:233

Return type:

DS

getBlockSize()#

Get the block size.

Not collective.

Returns:

The block size.

Return type:

int

Source code at slepc4py/SLEPc/DS.pyx:409

getCompact()#

Get the compact storage flag.

Not collective.

Returns:

The flag.

Return type:

bool

Source code at slepc4py/SLEPc/DS.pyx:477

getDimensions()#

Get the current dimensions.

Not collective.

Returns:

  • n (int) – The new size.

  • l (int) – Number of locked (inactive) leading columns.

  • k (int) – Intermediate dimension (e.g., position of arrow).

  • t (int) – Truncated length.

Return type:

tuple[int, int, int, int]

Source code at slepc4py/SLEPc/DS.pyx:371

getExtraRow()#

Get the extra row flag.

Not collective.

Returns:

The flag.

Return type:

bool

Source code at slepc4py/SLEPc/DS.pyx:516

getGSVDDimensions()#

Get the number of columns and rows of a DS of type GSVD.

Not collective.

Returns:

  • m (int) – The number of columns.

  • p (int) – The number of rows for the second matrix.

Return type:

tuple[int, int]

Source code at slepc4py/SLEPc/DS.pyx:784

getHSVDDimensions()#

Get the number of columns of a DS of type HSVD.

Not collective.

Returns:

The number of columns.

Return type:

int

Source code at slepc4py/SLEPc/DS.pyx:752

getLeadingDimension()#

Get the leading dimension of the allocated matrices.

Not collective.

Returns:

Leading dimension (maximum allowed dimension for the matrices).

Return type:

int

Source code at slepc4py/SLEPc/DS.pyx:260

getMat(matname)#

Get the requested matrix as a sequential dense Mat object.

Not collective.

Parameters:

matname (MatType) – The requested matrix.

Returns:

The matrix.

Return type:

petsc4py.PETSc.Mat

Source code at slepc4py/SLEPc/DS.pyx:599

getMethod()#

Get the method currently used in the DS.

Not collective.

Returns:

Identifier of the method.

Return type:

int

Source code at slepc4py/SLEPc/DS.pyx:438

getOptionsPrefix()#

Get the prefix used for searching for all DS options in the database.

Not collective.

Returns:

The prefix string set for this DS object.

Return type:

str

Source code at slepc4py/SLEPc/DS.pyx:205

getPEPCoefficients()#

Get the polynomial basis coefficients of a DS of type PEP.

Not collective.

Returns:

Coefficients.

Return type:

ArrayReal

Source code at slepc4py/SLEPc/DS.pyx:847

getPEPDegree()#

Get the polynomial degree of a DS of type PEP.

Not collective.

Returns:

The polynomial degree.

Return type:

int

Source code at slepc4py/SLEPc/DS.pyx:816

getParallel()#

Get the mode of operation in parallel runs.

Not collective.

Returns:

The parallel mode.

Return type:

ParallelType

Source code at slepc4py/SLEPc/DS.pyx:329

getRefined()#

Get the refined vectors flag.

Not collective.

Returns:

The flag.

Return type:

bool

Source code at slepc4py/SLEPc/DS.pyx:556

getSVDDimensions()#

Get the number of columns of a DS of type SVD.

Not collective.

Returns:

The number of columns.

Return type:

int

Source code at slepc4py/SLEPc/DS.pyx:723

getState()#

Get the current state.

Not collective.

Returns:

The current state.

Return type:

StateType

Source code at slepc4py/SLEPc/DS.pyx:300

getType()#

Get the DS type of this object.

Not collective.

Returns:

The direct solver type currently being used.

Return type:

str

Source code at slepc4py/SLEPc/DS.pyx:154

reset()#

Reset the DS object.

Collective.

Source code at slepc4py/SLEPc/DS.pyx:114

Return type:

None

restoreMat(matname, mat)#

Restore the previously seized matrix.

Not collective.

Parameters:
Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:621

setBlockSize(bs)#

Set the block size.

Logically collective.

Parameters:

bs (int) – The block size.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:395

setCompact(comp)#

Set the matrices’ compact storage flag.

Logically collective.

Parameters:

comp (bool) – True means compact storage.

Return type:

None

Notes

Compact storage is used in some DS types such as DS.Type.HEP when the matrix is tridiagonal. This flag can be used to indicate whether the user provides the matrix entries via the compact form (the tridiagonal DS.MatType.T) or the non-compact one (DS.MatType.A).

The default is False.

Source code at slepc4py/SLEPc/DS.pyx:453

setDimensions(n=None, l=None, k=None)#

Set the matrices sizes in the DS object.

Logically collective.

Parameters:
  • n (int | None) – The new size.

  • l (int | None) – Number of locked (inactive) leading columns.

  • k (int | None) – Intermediate dimension (e.g., position of arrow).

Return type:

None

Notes

The internal arrays are not reallocated.

Source code at slepc4py/SLEPc/DS.pyx:344

setExtraRow(ext)#

Set a flag to indicate that the matrix has one extra row.

Logically collective.

Parameters:

ext (bool) – True if the matrix has extra row.

Return type:

None

Notes

In Krylov methods it is useful that the matrix representing the direct solver has one extra row, i.e., has dimension \((n+1) n\). If this flag is activated, all transformations applied to the right of the matrix also affect this additional row. In that case, \((n+1)\) must be less or equal than the leading dimension.

The default is False.

Source code at slepc4py/SLEPc/DS.pyx:492

setFromOptions()#

Set DS options from the options database.

Collective.

Notes

To see all options, run your program with the -help option.

Source code at slepc4py/SLEPc/DS.pyx:220

Return type:

None

setGSVDDimensions(m, p)#

Set the number of columns and rows of a DS of type GSVD.

Logically collective.

Parameters:
  • m (int) – The number of columns.

  • p (int) – The number of rows for the second matrix.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:767

setHSVDDimensions(m)#

Set the number of columns of a DS of type HSVD.

Logically collective.

Parameters:

m (int) – The number of columns.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:738

setIdentity(matname)#

Set the identity on the active part of a matrix.

Logically collective.

Parameters:

matname (MatType) – The requested matrix.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:638

setMethod(meth)#

Set the method to be used to solve the problem.

Logically collective.

Parameters:

meth (int) – An index identifying the method.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:424

setOptionsPrefix(prefix=None)#

Set the prefix used for searching for all DS options in the database.

Logically collective.

Parameters:

prefix (str | None) – The prefix string to prepend to all DS option requests.

Return type:

None

Notes

A hyphen (-) must NOT be given at the beginning of the prefix name. The first character of all runtime options is AUTOMATICALLY the hyphen.

Source code at slepc4py/SLEPc/DS.pyx:169

setPEPCoefficients(pbc)#

Set the polynomial basis coefficients of a DS of type PEP.

Logically collective.

Parameters:

pbc (Sequence[float]) – Coefficients.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:831

setPEPDegree(deg)#

Set the polynomial degree of a DS of type PEP.

Logically collective.

Parameters:

deg (int) – The polynomial degree.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:802

setParallel(pmode)#

Set the mode of operation in parallel runs.

Logically collective.

Parameters:

pmode (ParallelType) – The parallel mode.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:315

setRefined(ref)#

Set a flag to indicate that refined vectors must be computed.

Logically collective.

Parameters:

ref (bool) – True if refined vectors must be used.

Return type:

None

Notes

Normally the vectors returned in DS.MatType.X are eigenvectors of the projected matrix. With this flag activated, vectors() will return the right singular vector of the smallest singular value of matrix \(At - theta I\), where \(At\) is the extended \((n+1) times n\) matrix and \(theta\) is the Ritz value. This is used in the refined Ritz approximation.

The default is False.

Source code at slepc4py/SLEPc/DS.pyx:531

setSVDDimensions(m)#

Set the number of columns of a DS of type SVD.

Logically collective.

Parameters:

m (int) – The number of columns.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:709

setState(state)#

Set the state of the DS object.

Logically collective.

Parameters:

state (StateType) – The new state.

Return type:

None

Notes

The state indicates that the dense system is in an initial state (raw), in an intermediate state (such as tridiagonal, Hessenberg or Hessenberg-triangular), in a condensed state (such as diagonal, Schur or generalized Schur), or in a truncated state.

This function is normally used to return to the raw state when the condensed structure is destroyed.

Source code at slepc4py/SLEPc/DS.pyx:275

setType(ds_type)#

Set the type for the DS object.

Logically collective.

Parameters:

ds_type (Type | str) – The direct solver type to be used.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:139

solve()#

Solve the problem.

Logically collective.

Returns:

Eigenvalues or singular values.

Return type:

ArrayScalar

Source code at slepc4py/SLEPc/DS.pyx:669

truncate(n, trim=False)#

Truncate the system represented in the DS object.

Logically collective.

Parameters:
  • n (int) – The new size.

  • trim (bool) – A flag to indicate if the factorization must be trimmed.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:571

updateExtraRow()#

Ensure that the extra row gets up-to-date after a call to DS.solve().

Logically collective.

Perform all necessary operations so that the extra row gets up-to-date after a call to DS.solve().

Source code at slepc4py/SLEPc/DS.pyx:588

Return type:

None

vectors(matname=X)#

Compute vectors associated to the dense system such as eigenvectors.

Logically collective.

Parameters:

matname (DS.MatType enumerate) – The matrix, used to indicate which vectors are required.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:693

view(viewer=None)#

Print the DS data structure.

Collective.

Parameters:

viewer (Viewer | None) – Visualization context; if not provided, the standard output is used.

Return type:

None

Source code at slepc4py/SLEPc/DS.pyx:89

Attributes Documentation

block_size#

The block size.

Source code at slepc4py/SLEPc/DS.pyx:885

compact#

Compact storage of matrices.

Source code at slepc4py/SLEPc/DS.pyx:899

extra_row#

If the matrix has one extra row.

Source code at slepc4py/SLEPc/DS.pyx:906

method#

The method to be used to solve the problem.

Source code at slepc4py/SLEPc/DS.pyx:892

parallel#

The mode of operation in parallel runs.

Source code at slepc4py/SLEPc/DS.pyx:878

refined#

If refined vectors must be computed.

Source code at slepc4py/SLEPc/DS.pyx:913

state#

The state of the DS object.

Source code at slepc4py/SLEPc/DS.pyx:871