ZCGESV - Online Linux Manual PageSection : 1
Updated : November 2008
Source : LAPACK PROTOTYPE driver routine (version 3.2)
Note : LAPACK PROTOTYPE driver routine (version 3.2)
NAMEZCGESV - computes the solution to a complex system of linear equations A * X = B,
SYNOPSISSUBROUTINE ZCGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, + SWORK, RWORK, ITER, INFO ) INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS INTEGER IPIV( * ) DOUBLE PRECISION RWORK( * ) COMPLEX SWORK( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( N, * ), + X( LDX, * )
PURPOSEZCGESV computes the solution to a complex system of linear equations
A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. ZCGESV first attempts to factorize the matrix in COMPLEX and use this factorization within an iterative refinement procedure to produce a solution with COMPLEX*16 normwise backward error quality (see below). If the approach fails the method switches to a COMPLEX*16 factorization and solve.
The iterative refinement is not going to be a winning strategy if the ratio COMPLEX performance over COMPLEX*16 performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.
ARGUMENTSN (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input or input/ouptut) COMPLEX*16 array, dimension (LDA,N) On entry, the N-by-N coefficient matrix A. On exit, if iterative refinement has been successfully used (INFO.EQ.0 and ITER.GE.0, see description below), then A is unchanged, if double precision factorization has been used (INFO.EQ.0 and ITER.LT.0, see description below), then the array A contains the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). IPIV (output) INTEGER array, dimension (N) The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i). Corresponds either to the single precision factorization (if INFO.EQ.0 and ITER.GE.0) or the double precision factorization (if INFO.EQ.0 and ITER.LT.0). B (input) COMPLEX*16 array, dimension (LDB,NRHS) The N-by-NRHS right hand side matrix B. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). X (output) COMPLEX*16 array, dimension (LDX,NRHS) If INFO = 0, the N-by-NRHS solution matrix X. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). WORK (workspace) COMPLEX*16 array, dimension (N*NRHS) This array is used to hold the residual vectors. SWORK (workspace) COMPLEX array, dimension (N*(N+NRHS)) This array is used to use the single precision matrix and the right-hand sides or solutions in single precision. RWORK (workspace) DOUBLE PRECISION array, dimension (N) ITER (output) INTEGER < 0: iterative refinement has failed, COMPLEX*16 factorization has been performed -1 : the routine fell back to full precision for implementation- or machine-specific reasons -2 : narrowing the precision induced an overflow, the routine fell back to full precision -3 : failure of CGETRF
-31: stop the iterative refinement after the 30th iterations > 0: iterative refinement has been sucessfully used. Returns the number of iterations INFO (output) INTEGER = 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) computed in COMPLEX*16 is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. ========= 0
Johanes Gumabo
Data Size : 13,103 byte
man-zcgesv.lBuild : 2024-12-29, 07:25 :
Visitor Screen : x
Visitor Counter ( page / site ) : 2 / 256,533
Visitor ID : :
Visitor IP : 18.220.255.227 :
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 - 24.12.29
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.