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BlockType BV block-orthogonalization types |
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MatMultType BV mat-mult types |
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OrthogBlockType BV block-orthogonalization types |
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OrthogRefineType BV orthogonalization refinement types |
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OrthogType BV orthogonalization types |
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RefineType BV orthogonalization refinement types |
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Type BV type |
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a new object with type S, a subtype of T |
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Inherited from Inherited from |
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Inherited from Inherited from |
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Multiplies a vector with the matrix associated to the bilinear form. Parameters
NotesIf the bilinear form has no associated matrix this function copies the vector. |
Copies a basis vector object into another one. Parameters
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Copies the values from one of the columns to another one. Parameters
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Copies one of the columns of a basis vectors object into a Vec. Parameters
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Creates the BV object. Parameters
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Creates a basis vectors object from a dense Mat object. Parameters
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Creates a new Mat object of dense type and copies the contents of the BV object. Returnsmat: the new matrix. |
Creates a new Vec object with the same type and dimensions as the columns of the basis vectors object. Returns
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Parameters
Returns
NotesThis 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). |
Computes multiple dot products of a column against all the column vectors of a BV. Parameters
Returns
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Computes multiple dot products of a vector against all the column vectors of a BV. Parameters
Returns
NotesThis 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. |
Creates a new BV object of the same type and dimensions as an existing one, but with possibly different number of columns. Parameters
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Returns the current active dimensions. Returns
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Returns a Vec object that contains the entries of the requested column of the basis vectors object. Parameters
Returns
NotesModifying the returned Vec will change the BV entries as well. |
Gets the tolerance to be used when checking a definite inner product. Returns
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Returns a Mat object of dense type that shares the memory of the basis vectors object. Returns
NotesThe 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. |
Gets the method used for the matMult() operation. Returns
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Retrieves the matrix representation of the inner product. Returnsmat: the matrix of the inner product |
Gets the number of constraints. Returns
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Gets the prefix used for searching for all BV options in the database. Returns
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Gets the orthogonalization settings from the BV object. Returns
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Gets the Returns
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Returns the local and global sizes, and the number of columns. Returns
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Gets the BV type of this object. Returns
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Insert a set of vectors as constraints. Parameters
Returns
NotesThe 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. |
Insert a vector into the specified column. Parameters
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Insert a set of vectors into specified columns. Parameters
Returns
NotesCopies 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. |
Computes the matrix-vector product for each column, Y = A*V. Parameters
Returns
NotesOnly 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. |
Computes the matrix-vector product for a specified column, storing the result in the next column: v_{j+1}=A*v_j. Parameters
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Computes the matrix-vector product with the conjugate transpose of a matrix for each column, Y=A^H*V. Parameters
Returns
NotesOnly 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(). |
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
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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
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Computes the projection of a matrix onto a subspace. M = Y^H A X Parameters
Returns
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Computes Y = beta*Y + alpha*X*Q. Parameters
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Computes y = beta*y + alpha*X*q, where y is the j-th column. Parameters
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Update a set of vectors as V(:,s:e-1) = V*Q(:,s:e-1). Parameters
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Computes y = beta*y + alpha*X*q. Parameters
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Computes the matrix norm of the BV. Parameters
Returnsnorm: float NotesAll 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(). |
Computes the matrix norm of the BV. Parameters
Returnsnorm: float NotesThe 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 all columns (except leading ones), that is, compute the QR decomposition. Parameters
NotesThe output satisfies V0 = V*R (where V0 represent the input V) and V'*V = I. |
Orthogonalize one of the column vectors with respect to the previous ones. Parameters
Returns
NotesThis 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. |
Orthogonalize a vector with respect to a set of vectors. Parameters
Returns
NotesThis 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. |
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
Returns
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Change the number of columns. Parameters
NotesInternal storage is reallocated. If copy is True, then the contents are copied to the leading part of the new space. |
Restore a column obtained with getColumn(). Parameters
NotesThe arguments must match the corresponding call to getColumn(). |
Restores the Mat obtained with getMat(). Parameters
NotesA 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. |
Multiply the entries by a scalar value. Parameters
NotesAll active columns (except the leading ones) are scaled. |
Scale column j by alpha Parameters
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Specify the columns that will be involved in operations. Parameters
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Sets the tolerance to be used when checking a definite inner product. Parameters
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Sets BV options from the options database. NotesTo see all options, run your program with the -help option.
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Specifies the method used for the matMult() operation. Parameters
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Sets the bilinear form to be used for inner products. Parameters
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Sets the number of constraints. Parameters
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Sets the prefix used for searching for all BV options in the database. Parameters
NotesA hyphen (-) must NOT be given at the beginning of the prefix name. The first character of all runtime options is AUTOMATICALLY the hyphen.
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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
NotesThe default settings work well for most problems. The parameter 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. |
Set the active columns of the BV to random numbers. NotesAll active columns (except the leading ones) are modified. |
Set one column of the BV to random numbers. Parameters
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Set the columns of a BV to random numbers, in a way that the generated matrix has a given condition number. Parameters
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Sets the Parameters
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Set the active columns of the BV to random numbers (with normal distribution). NotesAll active columns (except the leading ones) are modified. |
Set the entries of a BV to values 1 or -1 with equal probability. NotesAll active columns (except the leading ones) are modified. |
Sets the local and global sizes, and the number of columns. Parameters
NotesEither n or N (but not both) can be PETSc.DECIDE or None to have it automatically set. |
Sets the local and global sizes, and the number of columns. Local and global sizes are specified indirectly by passing a template vector. Parameters
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Selects the type for the BV object. Parameters
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Prints the BV data structure. Parameters
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