cggsvp3.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEcggsvp3.f
SYNOPSIS
Functions/Subroutinessubroutine cggsvp3 (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK, LWORK, INFO)
CGGSVP3
Function/Subroutine Documentation
subroutine cggsvp3 (character JOBU, character JOBV, character JOBQ, integer M, integer P, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, real TOLA, real TOLB, integer K, integer L, complex, dimension( ldu, * ) U, integer LDU, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( ldq, * ) Q, integer LDQ, integer, dimension( * ) IWORK, real, dimension( * ) RWORK, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer LWORK, integer INFO)CGGSVP3 Purpose: CGGSVP3 computes unitary matrices U, V and Q such that
N-K-L K L
U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )
N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )
N-K-L K L
V**H*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )
where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.
This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
CGGSVD3.Parameters: JOBU JOBU is CHARACTER*1
= 'U': Unitary matrix U is computed;
= 'N': U is not computed.
JOBV JOBV is CHARACTER*1
= 'V': Unitary matrix V is computed;
= 'N': V is not computed.
JOBQ JOBQ is CHARACTER*1
= 'Q': Unitary matrix Q is computed;
= 'N': Q is not computed.
M M is INTEGER
The number of rows of the matrix A. M >= 0.
P P is INTEGER
The number of rows of the matrix B. P >= 0.
N N is INTEGER
The number of columns of the matrices A and B. N >= 0.
A A is COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.
LDA LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B B is COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.
LDB LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).
TOLA TOLA is REAL
TOLB TOLB is REAL
TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MACHEPS,
TOLB = MAX(P,N)*norm(B)*MACHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.
K K is INTEGER
L L is INTEGER
On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A**H,B**H)**H.
U U is COMPLEX array, dimension (LDU,M)
If JOBU = 'U', U contains the unitary matrix U.
If JOBU = 'N', U is not referenced.
LDU LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = 'U'; LDU >= 1 otherwise.
V V is COMPLEX array, dimension (LDV,P)
If JOBV = 'V', V contains the unitary matrix V.
If JOBV = 'N', V is not referenced.
LDV LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = 'V'; LDV >= 1 otherwise.
Q Q is COMPLEX array, dimension (LDQ,N)
If JOBQ = 'Q', Q contains the unitary matrix Q.
If JOBQ = 'N', Q is not referenced.
LDQ LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK IWORK is INTEGER array, dimension (N)
RWORK RWORK is REAL array, dimension (2*N)
TAU TAU is COMPLEX array, dimension (N)
WORK WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK LWORK is INTEGER
The dimension of the array WORK.
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 INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: August 2015 Further Details: The subroutine uses LAPACK subroutine CGEQP3 for the QR factorization
with column pivoting to detect the effective numerical rank of the
a matrix. It may be replaced by a better rank determination strategy.
CGGSVP3 replaces the deprecated subroutine CGGSVP.Definition at line 280 of file cggsvp3.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
Data Size : 25,197 byte
man-cggsvp3.f.3Build : 2024-12-05, 20:55 :
Visitor Screen : x
Visitor Counter ( page / site ) : 2 / 184,108
Visitor ID : :
Visitor IP : 3.145.64.210 :
Visitor Provider : AMAZON-02 :
Provider Position ( lat x lon ) : 39.962500 x -83.006100 : x
Provider Accuracy Radius ( km ) : 1000 :
Provider City : Columbus :
Provider Province : Ohio , : ,
Provider Country : United States :
Provider Continent : North America :
Visitor Recorder : Version :
Visitor Recorder : Library :
Online Linux Manual Page : Version : Online Linux Manual Page - Fedora.40 - march=x86-64 - mtune=generic - 24.12.05
Online Linux Manual Page : Library : lib_c - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Online Linux Manual Page : Library : lib_m - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Data Base : Version : Online Linux Manual Page Database - 24.04.13 - march=x86-64 - mtune=generic - fedora-38
Data Base : Library : lib_c - 23.02.07 - march=x86-64 - mtune=generic - fedora.36
Very long time ago, I have the best tutor, Wenzel Svojanovsky . If someone knows the email address of Wenzel Svojanovsky , please send an email to johanes_gumabo@yahoo.co.id .
If error, please print screen and send to johanes_gumabo@yahoo.co.id
Under development. Support me via PayPal.