CGGRQF man page on IRIX

Man page or keyword search:  
man Server   31559 pages
apropos Keyword Search (all sections)
Output format
IRIX logo
[printable version]



CGGRQF(3F)							    CGGRQF(3F)

NAME
     CGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and
     a P-by-N matrix B

SYNOPSIS
     SUBROUTINE CGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO
			)

	 INTEGER	INFO, LDA, LDB, LWORK, M, N, P

	 COMPLEX	A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB( * ), WORK(
			* )

PURPOSE
     CGGRQF 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 unitary matrix, Z is a P-by-P unitary matrix, and R
     and T assume one of the forms:

     if M <= N,	 R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,
		      N-M  M			       ( R21 ) N
							  N

     where R12 or R21 is upper triangular, and

     if P >= N,	 T = ( T11 ) N	,   or if P < 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
     conjugate transpose of the matrix Z.

ARGUMENTS
     M	     (input) INTEGER
	     The number of rows of the matrix A.  M >= 0.

     P	     (input) INTEGER
	     The number of rows of the matrix B.  P >= 0.

									Page 1

CGGRQF(3F)							    CGGRQF(3F)

     N	     (input) INTEGER
	     The number of columns of the matrices A and B. N >= 0.

     A	     (input/output) COMPLEX array, dimension (LDA,N)
	     On entry, the M-by-N matrix A.  On exit, if M <= N, the upper
	     triangle of the subarray A(1:M,N-M+1:N) contains the M-by-M upper
	     triangular matrix R; if M > N, the elements on and above the (M-
	     N)-th subdiagonal contain the M-by-N upper trapezoidal matrix R;
	     the remaining elements, with the array TAUA, represent the
	     unitary matrix Q as a product of elementary reflectors (see
	     Further Details).

     LDA     (input) INTEGER
	     The leading dimension of the array A. LDA >= max(1,M).

     TAUA    (output) COMPLEX array, dimension (min(M,N))
	     The scalar factors of the elementary reflectors which represent
	     the unitary matrix Q (see Further Details).  B
	     (input/output) COMPLEX 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 >= N); the elements below the
	     diagonal, with the array TAUB, represent the unitary matrix Z as
	     a product of elementary reflectors (see Further Details).	LDB
	     (input) INTEGER The leading dimension of the array B. LDB >=
	     max(1,P).

     TAUB    (output) COMPLEX array, dimension (min(P,N))
	     The scalar factors of the elementary reflectors which represent
	     the unitary matrix Z (see Further Details).  WORK
	     (workspace/output) COMPLEX array, dimension (LWORK) On exit, if
	     INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
	     The dimension of the array WORK. LWORK >= max(1,N,M,P).  For
	     optimum performance LWORK >= 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 CUNMRQ.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO=-i, the i-th argument had an illegal value.

FURTHER DETAILS
     The matrix Q is represented as a product of elementary reflectors

	Q = H(1) H(2) . . . H(k), where k = min(m,n).

     Each H(i) has the form

									Page 2

CGGRQF(3F)							    CGGRQF(3F)

	H(i) = I - taua * v * v'

     where taua is a complex scalar, and v is a complex vector with v(n-
     k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-
     k+i,1:n-k+i-1), and taua in TAUA(i).
     To form Q explicitly, use LAPACK subroutine CUNGRQ.
     To use Q to update another matrix, use LAPACK subroutine CUNMRQ.

     The matrix Z is represented as a product of elementary reflectors

	Z = H(1) H(2) . . . H(k), where k = min(p,n).

     Each H(i) has the form

	H(i) = I - taub * v * v'

     where taub is a complex scalar, and v is a complex vector with v(1:i-1) =
     0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i), and taub in
     TAUB(i).
     To form Z explicitly, use LAPACK subroutine CUNGQR.
     To use Z to update another matrix, use LAPACK subroutine CUNMQR.

									Page 3

[top]

List of man pages available for IRIX

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net