| QR Class |
Inheritance HierarchyNamespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
SyntaxThe QR type exposes the following members.
ConstructorsMethods| Name | Description | |
|---|---|---|
 | Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) |
| GetPermute |
Returns an int array containing information about the
permutation of the elements of the matrix during pivoting.
|
| GetQ |
The orthogonal or unitary matrix Q.
|
| GetR |
The upper trapezoidal matrix R.
|
| GetRank |
Returns the rank of the matrix used to construct this instance.
|
| GetRank(Double) |
Returns the rank of the matrix given an input tolerance.
|
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| Solve(Double) |
Returns the solution to the least-squares problem Ax = b.
|
| Solve(Double, Double) |
Returns the solution to the least-squares problem Ax = b using an
input tolerance.
|
| ToString | Returns a string that represents the current object. (Inherited from Object.) |
Properties| Name | Description | |
|---|---|---|
 | NumberOfProcessors |
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
|
RemarksClass QR computes the QR decomposition of a matrix using Householder transformations. It is based on the LINPACK routine SQRDC; see Dongarra et al. (1979).
QR determines an orthogonal matrix Q, a permutation matrix P, and an upper trapezoidal matrix R with diagonal elements of nonincreasing magnitude, such that AP = QR. The Householder transformation for column k is of the form
for 
, min(number of rows of
A, number of columns of A), where u has zeros in the first
k - 1 positions. The matrix Q is not produced directly by
QR. Instead the information needed to reconstruct the Householder
transformations is saved. If the matrix Q is needed explicitly,
use the Q property. This method accumulates Q from its factored form.
Before the decomposition is computed, initial columns are moved to the beginning of the array A and the final columns to the end. Both initial and final columns are frozen in place during the computation. Only free columns are pivoted. Pivoting is done on the free columns of largest reduced norm.
See Also