-- LAPACK routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
DGGQRF computes a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B:
A = Q*R, B = Q*T*Z,
where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
matrix, and R and T assume one of the forms:
if N .GE. M, R = ( R11 ) M , or if N .LT. M, R = ( R11 R12 ) N,
( 0 ) N-M N M-N
M
where R11 is upper triangular, and
if N .LE. P, T = ( 0 T12 ) N, or if N .GT. P, T = ( T11 ) N-P,
P-N N ( T21 ) P
P
where T12 or T21 is upper triangular.
In particular, if B is square and nonsingular, the GQR factorization
of A and B implicitly gives the QR factorization of inv(B)*A:
inv(B)*A = Z'*(inv(T)*R)
where inv(B) denotes the inverse of the matrix B, and Z' denotes the
transpose of the matrix Z.
Inheritance Hierarchy Namespace: DotNumerics.LinearAlgebra.CSLapackAssembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax The DGGQRF type exposes the following members.
Constructors Methods | Name | Description |
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| Run |
Purpose
=======
DGGQRF computes a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B:
A = Q*R, B = Q*T*Z,
where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
matrix, and R and T assume one of the forms:
if N .GE. M, R = ( R11 ) M , or if N .LT. M, R = ( R11 R12 ) N,
( 0 ) N-M N M-N
M
where R11 is upper triangular, and
if N .LE. P, T = ( 0 T12 ) N, or if N .GT. P, T = ( T11 ) N-P,
P-N N ( T21 ) P
P
where T12 or T21 is upper triangular.
In particular, if B is square and nonsingular, the GQR factorization
of A and B implicitly gives the QR factorization of inv(B)*A:
inv(B)*A = Z'*(inv(T)*R)
where inv(B) denotes the inverse of the matrix B, and Z' denotes the
transpose of the matrix Z.
|
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