Click or drag to resize

DGGRQFRun Method

Purpose ======= DGGRQF computes a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B: A = R*Q, B = Z*T*Q, 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 M .LE. N, R = ( 0 R12 ) M, or if M .GT. N, R = ( R11 ) M-N, N-M M ( R21 ) N N where R12 or R21 is upper triangular, and if P .GE. N, T = ( T11 ) N , or if P .LT. N, T = ( T11 T12 ) P, ( 0 ) P-N P N-P N where T11 is upper triangular. In particular, if B is square and nonsingular, the GRQ factorization of A and B implicitly gives the RQ factorization of A*inv(B): A*inv(B) = (R*inv(T))*Z' 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
Copy
public void Run(
	int M,
	int P,
	int N,
	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
)
Request Example View Source

Parameters

M  Int32
(input) INTEGER The number of rows of the matrix A. M .GE. 0.
P  Int32
(input) INTEGER The number of rows of the matrix B. P .GE. 0.
N  Int32
(input) INTEGER The number of columns of the matrices A and B. N .GE. 0.
A  Double
= R*Q, B = Z*T*Q,
offset_a  Int32
 
LDA  Int32
(input) INTEGER The leading dimension of the array A. LDA .GE. max(1,M).
TAUA  Double
(output) DOUBLE PRECISION array, dimension (min(M,N)) 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,N) On entry, the P-by-N matrix B. On exit, the elements on and above the diagonal of the array contain the min(P,N)-by-N upper trapezoidal matrix T (T is upper triangular if P .GE. N); the elements below the diagonal, 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,P).
TAUB  Double
(output) DOUBLE PRECISION array, dimension (min(P,N)) 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 RQ factorization of an M-by-N matrix, NB2 is the optimal blocksize for the QR factorization of a P-by-N matrix, and NB3 is the optimal blocksize for a call of DORMRQ. 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 INF0= -i, the i-th argument had an illegal value.
See Also