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DGGQRFRun Method

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.

Namespace: DotNumerics.LinearAlgebra.CSLapack
Assembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
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public void Run(
	int N,
	int M,
	int P,
	ref double[] A,
	int offset_a,
	int LDA,
	ref double[] TAUA,
	int offset_taua,
	ref double[] B,
	int offset_b,
	int LDB,
	ref double[] TAUB,
	int offset_taub,
	ref double[] WORK,
	int offset_work,
	int LWORK,
	ref int INFO
)
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Parameters

N  Int32
(input) INTEGER The number of rows of the matrices A and B. N .GE. 0.
M  Int32
(input) INTEGER The number of columns of the matrix A. M .GE. 0.
P  Int32
(input) INTEGER The number of columns of the matrix B. P .GE. 0.
A  Double
= Q*R, B = Q*T*Z,
offset_a  Int32
 
LDA  Int32
(input) INTEGER The leading dimension of the array A. LDA .GE. max(1,N).
TAUA  Double
(output) DOUBLE PRECISION array, dimension (min(N,M)) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q (see Further Details).
offset_taua  Int32
 
B  Double
(input/output) DOUBLE PRECISION array, dimension (LDB,P) On entry, the N-by-P matrix B. On exit, if N .LE. P, the upper triangle of the subarray B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; if N .GT. P, the elements on and above the (N-P)-th subdiagonal contain the N-by-P upper trapezoidal matrix T; the remaining elements, with the array TAUB, represent the orthogonal matrix Z as a product of elementary reflectors (see Further Details).
offset_b  Int32
 
LDB  Int32
(input) INTEGER The leading dimension of the array B. LDB .GE. max(1,N).
TAUB  Double
(output) DOUBLE PRECISION array, dimension (min(N,P)) The scalar factors of the elementary reflectors which represent the orthogonal matrix Z (see Further Details).
offset_taub  Int32
 
WORK  Double
(workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
offset_work  Int32
 
LWORK  Int32
(input) INTEGER The dimension of the array WORK. LWORK .GE. max(1,N,M,P). For optimum performance LWORK .GE. max(N,M,P)*max(NB1,NB2,NB3), where NB1 is the optimal blocksize for the QR factorization of an N-by-M matrix, NB2 is the optimal blocksize for the RQ factorization of an N-by-P matrix, and NB3 is the optimal blocksize for a call of DORMQR. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO  Int32
(output) INTEGER = 0: successful exit .LT. 0: if INFO = -i, the i-th argument had an illegal value.
See Also