Package slepc4py :: Module SLEPc :: Class BV |
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# Class BV

BV

Nested Classes | [hide private]
| BlockType BV block-orthogonalization types
| MatMultType BV mat-mult types
| OrthogBlockType BV block-orthogonalization types
| OrthogRefineType BV orthogonalization refinement types
| OrthogType BV orthogonalization types
| RefineType BV orthogonalization refinement types
| Type BV type

Instance Methods | [hide private]
a new object with type S, a subtype of T |
__new__(S, ...) |
applyMatrix(self, Vec x, Vec y) Multiplies a vector with the matrix associated to the bilinear form. |
copy(self, BV result=None) Copies a basis vector object into another one. |
copyColumn(self, j, i) Copies the values from one of the columns to another one. |
copyVec(self, j, Vec v) Copies one of the columns of a basis vectors object into a Vec. |
create(self, comm=None) Creates the BV object. |
createFromMat(self, Mat A) Creates a basis vectors object from a dense Mat object. |
createMat(self) Creates a new Mat object of dense type and copies the contents of the BV object. |
createVec(self) Creates a new Vec object with the same type and dimensions as the columns of the basis vectors object. |
destroy(self) Destroys the BV object. |
dot(self, BV Y) M = Y^H*X (m_ij = y_i^H x_j) or M = Y^H*B*X |
dotColumn(self, j) Computes multiple dot products of a column against all the column vectors of a BV. |
dotVec(self, Vec v) Computes multiple dot products of a vector against all the column vectors of a BV. |
duplicate(self) Duplicate the BV object with the same type and dimensions. |
duplicateResize(self, m) Creates a new BV object of the same type and dimensions as an existing one, but with possibly different number of columns. |
getActiveColumns(self) Returns the current active dimensions. |
getColumn(self, j) Returns a Vec object that contains the entries of the requested column of the basis vectors object. |
getDefiniteTolerance(self) Gets the tolerance to be used when checking a definite inner product. |
getMat(self) Returns a Mat object of dense type that shares the memory of the basis vectors object. |
getMatMultMethod(self) Gets the method used for the matMult() operation. |
getMatrix(self) Retrieves the matrix representation of the inner product. |
getNumConstraints(self) Gets the number of constraints. |
getOptionsPrefix(self) Gets the prefix used for searching for all BV options in the database. |
getOrthogonalization(self) Gets the orthogonalization settings from the BV object. |
getRandomContext(self) Gets the `PETSc.Random` object associated with the BV. |
getSizes(self) Returns the local and global sizes, and the number of columns. |
getType(self) Gets the BV type of this object. |
insertConstraints(self, C) Insert a set of vectors as constraints. |
insertVec(self, j, Vec w) Insert a vector into the specified column. |
insertVecs(self, s, W, bool orth) Insert a set of vectors into specified columns. |
matMult(self, Mat A, BV Y=None) Computes the matrix-vector product for each column, Y = A*V. |
matMultColumn(self, Mat A, j) Computes the matrix-vector product for a specified column, storing the result in the next column: v_{j+1}=A*v_j. |
matMultHermitianTranspose(self, Mat A, BV Y=None) Computes the matrix-vector product with the conjugate transpose of a matrix for each column, Y=A^H*V. |
matMultHermitianTransposeColumn(self, Mat A, j) Computes the conjugate-transpose matrix-vector product for a specified column, storing the result in the next column: v_{j+1}=A^H*v_j. |
matMultTransposeColumn(self, Mat A, j) Computes the transpose matrix-vector product for a specified column, storing the result in the next column: v_{j+1}=A^T*v_j. |
matProject(self, Mat A, BV Y) Computes the projection of a matrix onto a subspace. |
mult(self, alpha, beta, BV X, Mat Q) Computes Y = beta*Y + alpha*X*Q. |
multColumn(self, alpha, beta, j, q) Computes y = beta*y + alpha*X*q, where y is the j-th column. |
multInPlace(self, Mat Q, s, e) Update a set of vectors as V(:,s:e-1) = V*Q(:,s:e-1). |
multVec(self, alpha, beta, Vec y, q) Computes y = beta*y + alpha*X*q. |
norm(self, norm_type=None) Computes the matrix norm of the BV. |
normColumn(self, int j, norm_type=None) Computes the matrix norm of the BV. |
orthogonalize(self, Mat R=None, **kargs) Orthogonalize all columns (except leading ones), that is, compute the QR decomposition. |
orthogonalizeColumn(self, j) Orthogonalize one of the column vectors with respect to the previous ones. |
orthogonalizeVec(self, Vec v) Orthogonalize a vector with respect to a set of vectors. |
orthonormalizeColumn(self, j, replace=False) Orthonormalize one of the column vectors with respect to the previous ones. |
resize(self, m, copy=True) Change the number of columns. |
restoreColumn(self, j, Vec v) Restore a column obtained with getColumn(). |
restoreMat(self, Mat A) Restores the Mat obtained with getMat(). |
scale(self, alpha) Multiply the entries by a scalar value. |
scaleColumn(self, j, alpha) Scale column j by alpha |
setActiveColumns(self, l, k) Specify the columns that will be involved in operations. |
setDefiniteTolerance(self, deftol) Sets the tolerance to be used when checking a definite inner product. |
setFromOptions(self) Sets BV options from the options database. |
setMatMultMethod(self, method) Specifies the method used for the matMult() operation. |
setMatrix(self, Mat mat, bool indef) Sets the bilinear form to be used for inner products. |
setNumConstraints(self, nc) Sets the number of constraints. |
setOptionsPrefix(self, prefix) Sets the prefix used for searching for all BV options in the database. |
setOrthogonalization(self, otype=None, refine=None, eta=None, block=None) Specifies the method used for the orthogonalization of vectors (classical or modified Gram-Schmidt with or without refinement), and for the block-orthogonalization (simultaneous orthogonalization of a set of vectors). |
setRandom(self) Set the active columns of the BV to random numbers. |
setRandomColumn(self, j) Set one column of the BV to random numbers. |
setRandomCond(self, condn) Set the columns of a BV to random numbers, in a way that the generated matrix has a given condition number. |
setRandomContext(self, Random rnd) Sets the `PETSc.Random` object associated with the BV, to be used in operations that need random numbers. |
setRandomNormal(self) Set the active columns of the BV to random numbers (with normal distribution). |
setRandomSign(self) Set the entries of a BV to values 1 or -1 with equal probability. |
setSizes(self, sizes, m) Sets the local and global sizes, and the number of columns. |
setSizesFromVec(self, Vec w, m) Sets the local and global sizes, and the number of columns. |
setType(self, bv_type) Selects the type for the BV object. |
view(self, Viewer viewer=None) Prints the BV data structure. |
Inherited from `petsc4py.PETSc.Object`: `__copy__`, `__deepcopy__`, `__eq__`, `__ge__`, `__gt__`, `__le__`, `__lt__`, `__ne__`, `__nonzero__`, `appendOptionsPrefix`, `compose`, `decRef`, `getAttr`, `getClassId`, `getClassName`, `getComm`, `getDict`, `getName`, `getRefCount`, `getTabLevel`, `incRef`, `incrementTabLevel`, `query`, `setAttr`, `setName`, `setTabLevel`, `stateGet`, `stateIncrease`, `stateSet`, `viewFromOptions` Inherited from `object`: `__delattr__`, `__format__`, `__getattribute__`, `__hash__`, `__init__`, `__reduce__`, `__reduce_ex__`, `__repr__`, `__setattr__`, `__sizeof__`, `__str__`, `__subclasshook__`

Properties | [hide private]
Inherited from `petsc4py.PETSc.Object`: `classid`, `comm`, `fortran`, `handle`, `klass`, `name`, `prefix`, `refcount`, `type` Inherited from `object`: `__class__`

Method Details | [hide private]

### __new__(S, ...) |
Returns: a new object with type S, a subtype of T Overrides: object.__new__

### applyMatrix(self, Vec x, Vec y) |
Multiplies a vector with the matrix associated to the bilinear form. # Parameters x: Vec The input vector. y: Vec The result vector. # Notes If the bilinear form has no associated matrix this function copies the vector.

### copy(self, BV result=None) |
Copies a basis vector object into another one. # Parameters result: BV, optional The copy.

### copyColumn(self, j, i) |
Copies the values from one of the columns to another one. # Parameters j: int The number of the source column. i: int The number of the destination column.

### copyVec(self, j, Vec v) |
Copies one of the columns of a basis vectors object into a Vec. # Parameters j: int The column number to be copied. v: Vec A vector.

### create(self, comm=None) |
Creates the BV object. # Parameters comm: Comm, optional MPI communicator; if not provided, it defaults to all processes.

### createFromMat(self, Mat A) |
Creates a basis vectors object from a dense Mat object. # Parameters A: Mat A dense tall-skinny matrix.

### createMat(self) |
Creates a new Mat object of dense type and copies the contents of the BV object. # Returns mat: the new matrix.

### createVec(self) |
Creates a new Vec object with the same type and dimensions as the columns of the basis vectors object. # Returns v: Vec New vector.

### destroy(self) |
Destroys the BV object. Overrides: petsc4py.PETSc.Object.destroy

### dot(self, BV Y) |
Computes the 'block-dot' product of two basis vectors objects. M = Y^H*X (m_ij = y_i^H x_j) or M = Y^H*B*X # Parameters Y: BV Left basis vectors, can be the same as self, giving M = X^H X. # Returns M: Mat The resulting matrix. # Notes This is the generalization of VecDot() for a collection of vectors, M = Y^H*X. The result is a matrix M whose entry m_ij is equal to y_i^H x_j (where y_i^H denotes the conjugate transpose of y_i). X and Y can be the same object. If a non-standard inner product has been specified with setMatrix(), then the result is M = Y^H*B*X. In this case, both X and Y must have the same associated matrix. Only rows (resp. columns) of M starting from ly (resp. lx) are computed, where ly (resp. lx) is the number of leading columns of Y (resp. X).

### dotColumn(self, j) |
Computes multiple dot products of a column against all the column vectors of a BV. # Parameters j: int The index of the column. # Returns m: array of scalars The computed values.

### dotVec(self, Vec v) |
Computes multiple dot products of a vector against all the column vectors of a BV. # Parameters v: Vec A vector. # Returns m: array of scalars The computed values. # Notes This is analogue to VecMDot(), but using BV to represent a collection of vectors. The result is m = X^H*y, so m_i is equal to x_j^H y. Note that here X is transposed as opposed to BVDot(). If a non-standard inner product has been specified with BVSetMatrix(), then the result is m = X^H*B*y.

### duplicateResize(self, m) |
Creates a new BV object of the same type and dimensions as an existing one, but with possibly different number of columns. # Parameters m: int The number of columns.

### getActiveColumns(self) |
Returns the current active dimensions. # Returns l: int The leading number of columns. k: int The active number of columns.

### getColumn(self, j) |
Returns a Vec object that contains the entries of the requested column of the basis vectors object. # Parameters j: int The index of the requested column. # Returns v: Vec The vector containing the jth column. # Notes Modifying the returned Vec will change the BV entries as well.

### getDefiniteTolerance(self) |
Gets the tolerance to be used when checking a definite inner product. # Returns deftol: float The tolerance.

### getMat(self) |
Returns a Mat object of dense type that shares the memory of the basis vectors object. # Returns A: Mat The matrix # Notes The returned matrix contains only the active columns. If the content of the Mat is modified, these changes are also done in the BV object. The user must call restoreMat() when no longer needed.

### getMatMultMethod(self) |
Gets the method used for the matMult() operation. # Returns method: BV.MatMultType enumerate The method for the matMult() operation.

### getMatrix(self) |
Retrieves the matrix representation of the inner product. # Returns mat: the matrix of the inner product

### getNumConstraints(self) |
Gets the number of constraints. # Returns nc: int The number of constraints.

### getOptionsPrefix(self) |
Gets the prefix used for searching for all BV options in the database. # Returns prefix: string The prefix string set for this BV object. Overrides: petsc4py.PETSc.Object.getOptionsPrefix

### getOrthogonalization(self) |
Gets the orthogonalization settings from the BV object. # Returns type: BV.OrthogType enumerate The type of orthogonalization technique. refine: BV.OrthogRefineType enumerate The type of refinement. eta: float Parameter for selective refinement (used when the the refinement type BV.OrthogRefineType.IFNEEDED). block: BV.OrthogBlockType enumerate The type of block orthogonalization .

### getRandomContext(self) |
Gets the `PETSc.Random` object associated with the BV. # Returns rnd: `PETSc.Random` The random number generator context.

### getSizes(self) |
Returns the local and global sizes, and the number of columns. # Returns sizes: two-tuple of int The local and global sizes `(n, N)`. m: int The number of columns.

### getType(self) |
Gets the BV type of this object. # Returns type: BV.Type enumerate The inner product type currently being used. Overrides: petsc4py.PETSc.Object.getType

### insertConstraints(self, C) |
Insert a set of vectors as constraints. # Parameters C: Vec or sequence of Vec. Set of vectors to be inserted as constraints. # Returns nc: int Number of linearly independent vectors. # Notes The constraints are relevant only during orthogonalization. Constraint vectors span a subspace that is deflated in every orthogonalization operation, so they are intended for removing those directions from the orthogonal basis computed in regular BV columns.

### insertVec(self, j, Vec w) |
Insert a vector into the specified column. # Parameters j: int The column to be overwritten. w: Vec The vector to be copied.

### insertVecs(self, s, W, bool orth) |
Insert a set of vectors into specified columns. # Parameters s: int The first column to be overwritten. W: Vec or sequence of Vec. Set of vectors to be copied. orth: Flag indicating if the vectors must be orthogonalized. # Returns m: int Number of linearly independent vectors. # Notes Copies the contents of vectors W into self(:,s:s+n), where n is the length of W. If orthogonalization flag is set then the vectors are copied one by one then orthogonalized against the previous one. If any are linearly dependent then it is discared and the value of m is decreased.

### matMult(self, Mat A, BV Y=None) |
Computes the matrix-vector product for each column, Y = A*V. # Parameters A: Mat The matrix. # Returns Y: BV The result. # Notes Only active columns (excluding the leading ones) are processed. It is possible to choose whether the computation is done column by column or using dense matrices using the options database keys: -bv_matmult_vecs -bv_matmult_mat The default is bv_matmult_mat.

### matMultColumn(self, Mat A, j) |
Computes the matrix-vector product for a specified column, storing the result in the next column: v_{j+1}=A*v_j. # Parameters A: Mat The matrix. j: int Index of column.

### matMultHermitianTranspose(self, Mat A, BV Y=None) |
Computes the matrix-vector product with the conjugate transpose of a matrix for each column, Y=A^H*V. # Parameters A: Mat The matrix. # Returns Y: BV The result. # Notes Only active columns (excluding the leading ones) are processed. As opoosed to matMult(), this operation is always done by column by column, with a sequence of calls to MatMultHermitianTranspose().

### matMultHermitianTransposeColumn(self, Mat A, j) |
Computes the conjugate-transpose matrix-vector product for a specified column, storing the result in the next column: v_{j+1}=A^H*v_j. # Parameters A: Mat The matrix. j: int Index of column.

### matMultTransposeColumn(self, Mat A, j) |
Computes the transpose matrix-vector product for a specified column, storing the result in the next column: v_{j+1}=A^T*v_j. # Parameters A: Mat The matrix. j: int Index of column.

### matProject(self, Mat A, BV Y) |
Computes the projection of a matrix onto a subspace. M = Y^H A X # Parameters A: Mat or None Matrix to be projected. Y: BV Left basis vectors, can be the same as self, giving M = X^H A X. # Returns M: Mat Projection of the matrix A onto the subspace.

### mult(self, alpha, beta, BV X, Mat Q) |
Computes Y = beta*Y + alpha*X*Q. # Parameters alpha: scalar Coefficient that multiplies X. beta: scalar Coefficient that multiplies Y. X: BV Input basis vectors. Q: Mat Input matrix.

### multColumn(self, alpha, beta, j, q) |
Computes y = beta*y + alpha*X*q, where y is the j-th column. # Parameters alpha: scalar Coefficient that multiplies X. beta: scalar Coefficient that multiplies y. j: int The column index. q: Array of scalar Input coefficients.

### multInPlace(self, Mat Q, s, e) |
Update a set of vectors as V(:,s:e-1) = V*Q(:,s:e-1). # Parameters Q: Mat A sequential dense matrix. s: int First column to be overwritten. e: int Last column to be overwritten.

### multVec(self, alpha, beta, Vec y, q) |
Computes y = beta*y + alpha*X*q. # Parameters alpha: scalar Coefficient that multiplies X. beta: scalar Coefficient that multiplies y. y: Vec Input/output vector. q: Array of scalar Input coefficients.

### norm(self, norm_type=None) |
Computes the matrix norm of the BV. # Parameters norm_type: `PETSC.NormType` enumerate The norm type. # Returns norm: float # Notes All active columns (except the leading ones) are considered as a matrix. The allowed norms are NORM_1, NORM_FROBENIUS, and NORM_INFINITY. This operation fails if a non-standard inner product has been specified with BVSetMatrix().

### normColumn(self, int j, norm_type=None) |
Computes the matrix norm of the BV. # Parameters j: int Index of column. norm_type: `PETSc.NormType` enumerate The norm type. # Returns norm: float # Notes The norm of V[j] is computed (NORM_1, NORM_2, or NORM_INFINITY). If a non-standard inner product has been specified with BVSetMatrix(), then the returned value is `sqrt(V[j]'* B*V[j])`, where B is the inner product matrix (argument 'type' is ignored).

### orthogonalize(self, Mat R=None, **kargs) |
Orthogonalize all columns (except leading ones), that is, compute the QR decomposition. # Parameters R: Mat, optional A sequential dense matrix. # Notes The output satisfies `V0 = V*R` (where V0 represent the input V) and `V'*V = I`.

### orthogonalizeColumn(self, j) |
Orthogonalize one of the column vectors with respect to the previous ones. # Parameters j: int Index of the column to be orthogonalized. # Returns norm: float The norm of the resulting vector. lindep: bool Flag indicating that refinement did not improve the quality of orthogonalization. # Notes This function applies an orthogonal projector to project vector `V[j]` onto the orthogonal complement of the span of the columns `V[0..j-1]`, where `V[.]` are the vectors of the BV. The columns `V[0..j-1]` are assumed to be mutually orthonormal. This routine does not normalize the resulting vector.

### orthogonalizeVec(self, Vec v) |
Orthogonalize a vector with respect to a set of vectors. # Parameters v: Vec Vector to be orthogonalized, modified on return. # Returns norm: float The norm of the resulting vector. lindep: bool Flag indicating that refinement did not improve the quality of orthogonalization. # Notes This function applies an orthogonal projector to project vector `v` onto the orthogonal complement of the span of the columns of the BV. This routine does not normalize the resulting vector.

### orthonormalizeColumn(self, j, replace=False) |
Orthonormalize one of the column vectors with respect to the previous ones. This is equivalent to a call to orthogonalizeColumn() followed by a call to scaleColumn() with the reciprocal of the norm. # Parameters j: int Index of the column to be orthonormalized. replace: bool, optional Whether it is allowed to set the vector randomly. # Returns norm: float The norm of the resulting vector. lindep: bool Flag indicating that refinement did not improve the quality of orthogonalization.

### resize(self, m, copy=True) |
Change the number of columns. # Parameters m: int The new number of columns. copy: bool A flag indicating whether current values should be kept. # Notes Internal storage is reallocated. If copy is True, then the contents are copied to the leading part of the new space.

### restoreColumn(self, j, Vec v) |
Restore a column obtained with getColumn(). # Parameters j: int The index of the requested column. v: Vec The vector obtained with getColumn(). # Notes The arguments must match the corresponding call to getColumn().

### restoreMat(self, Mat A) |
Restores the Mat obtained with getMat(). # Parameters A: Mat The matrix obtained with getMat(). # Notes A call to this function must match a previous call of getMat(). The effect is that the contents of the Mat are copied back to the BV internal data structures.

### scale(self, alpha) |
Multiply the entries by a scalar value. # Parameters alpha: float scaling factor. # Notes All active columns (except the leading ones) are scaled.

### scaleColumn(self, j, alpha) |
Scale column j by alpha # Parameters j: int column number to be scaled. alpha: float scaling factor.

### setActiveColumns(self, l, k) |
Specify the columns that will be involved in operations. # Parameters l: int The leading number of columns. k: int The active number of columns.

### setDefiniteTolerance(self, deftol) |
Sets the tolerance to be used when checking a definite inner product. # Parameters deftol: float The tolerance.

### setFromOptions(self) |
Sets BV options from the options database. # Notes To see all options, run your program with the `-help` option. Overrides: petsc4py.PETSc.Object.setFromOptions

### setMatMultMethod(self, method) |
Specifies the method used for the matMult() operation. # Parameters method: BV.MatMultType enumerate The method for the matMult() operation.

### setMatrix(self, Mat mat, bool indef) |
Sets the bilinear form to be used for inner products. # Parameters mat: Mat or None The matrix of the inner product. indef: bool, optional Whether the matrix is indefinite

### setNumConstraints(self, nc) |
Sets the number of constraints. # Parameters nc: int The number of constraints.

### setOptionsPrefix(self, prefix) |
Sets the prefix used for searching for all BV options in the database. # Parameters prefix: string The prefix string to prepend to all BV option requests. # 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. Overrides: petsc4py.PETSc.Object.setOptionsPrefix

### setOrthogonalization(self, otype=None, refine=None, eta=None, block=None) |
Specifies the method used for the orthogonalization of vectors (classical or modified Gram-Schmidt with or without refinement), and for the block-orthogonalization (simultaneous orthogonalization of a set of vectors). # Parameters otype: BV.OrthogType enumerate, optional The type of orthogonalization technique. refine: BV.OrthogRefineType enumerate, optional The type of refinement. eta: float, optional Parameter for selective refinement. block: BV.OrthogBlockType enumerate, optional The type of block orthogonalization. # Notes The default settings work well for most problems. The parameter `eta` should be a real value between `0` and `1` (or DEFAULT). The value of `eta` is used only when the refinement type is BV.OrthogRefineType.IFNEEDED. When using several processors, BV.OrthogType.MGS is likely to result in bad scalability. If the method set for block orthogonalization is GS, then the computation is done column by column with the vector orthogonalization.

### setRandom(self) |
Set the active columns of the BV to random numbers. # Notes All active columns (except the leading ones) are modified.

### setRandomColumn(self, j) |
Set one column of the BV to random numbers. # Parameters j: int Column number to be set.

### setRandomCond(self, condn) |
Set the columns of a BV to random numbers, in a way that the generated matrix has a given condition number. # Parameters condn: float Condition number.

### setRandomContext(self, Random rnd) |
Sets the `PETSc.Random` object associated with the BV, to be used in operations that need random numbers. # Parameters rnd: `PETSc.Random` The random number generator context.

### setRandomNormal(self) |
Set the active columns of the BV to random numbers (with normal distribution). # Notes All active columns (except the leading ones) are modified.

### setRandomSign(self) |
Set the entries of a BV to values 1 or -1 with equal probability. # Notes All active columns (except the leading ones) are modified.

### setSizes(self, sizes, m) |
Sets the local and global sizes, and the number of columns. # Parameters sizes: int or two-tuple of int The global size `N` or a two-tuple `(n, N)` with the local and global sizes. m: int The number of columns. # Notes Either `n` or `N` (but not both) can be `PETSc.DECIDE` or `None` to have it automatically set.

### setSizesFromVec(self, Vec w, m) |
Sets the local and global sizes, and the number of columns. Local and global sizes are specified indirectly by passing a template vector. # Parameters w: Vec The template vector. m: int The number of columns.

### setType(self, bv_type) |
Selects the type for the BV object. # Parameters bv_type: BV.Type enumerate The inner product type to be used.

### view(self, Viewer viewer=None) |
Prints the BV data structure. # Parameters viewer: Viewer, optional Visualization context; if not provided, the standard output is used. Overrides: petsc4py.PETSc.Object.view