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OrthogRefineType IP orthogonalization refinement types |
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OrthogType IP orthogonalization types |
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RefineType IP orthogonalization refinement types |
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Type IP 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. |
Creates the IP object. Parameters
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Retrieves the matrix representation of the inner produc Returnsmat: the matrix of the inner product |
Gets the prefix used for searching for all IP options in the database. Returns
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Gets the orthogonalization settings from the IP object. Returns
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Gets the IP type of this object. Returns
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Computes the inner product of two vectors. Parameters
Returns
NotesThis function will usually compute the standard dot product, (x,y)=y^H x. However this behaviour may be different if changed via setMatrix(). This allows use of other inner products such as the indefinite product y^T x for complex symmetric problems or the B-inner product for positive definite B, (x,y)_B=y^H Bx. |
Computes the norm of a vector as the square root of the inner product (x,x) as defined by innerProduct(). Parameters
Returns
NotesThis function will usually compute the 2-norm of a vector, ||x||_2. But this behaviour may be different if using a non-standard inner product changed via setMatrix(). For example, if using the B-inner product for positive definite B`, ``(x,y)_B=y^H Bx, then the computed norm is ||x||_B = sqrt( x^H Bx ). |
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 VS. On exit, v0 = [V v]*H, where v0 is the original vector v. This routine does not normalize the resulting vector. |
Sets IP options from the options database. NotesTo see all options, run your program with the -help option.
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Sets the bilinear form to be used for inner products. Parameters
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Sets the prefix used for searching for all IP 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 type of orthogonalization technique to be used (classical or modified Gram-Schmidt with or without refinement). Parameters
NotesThe default settings work well for most problems. The parameter When using several processors, IP.OrthogType.MGS is likely to result in bad scalability. |
Selects the type for the IP object. Parameters
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Prints the IP data structure. Parameters
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