
NAMEzcgesv.f SYNOPSISFunctions/Subroutinessubroutine zcgesv (N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO) Function/Subroutine Documentationsubroutine zcgesv (integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, complex*16, dimension( n, * )WORK, complex, dimension( * )SWORK, double precision, dimension( * )RWORK, integerITER, integerINFO)ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement) Purpose:ZCGESV computes the solution to a complex system of linear equations A * X = B, where A is an NbyN matrix and X and B are NbyNRHS 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 righthand 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 infinitynorm of the residual o XNRM is the infinitynorm of the solution o ANRM is the infinityoperatornorm 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. N
Author:
N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the NbyN 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 LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).IPIV IPIV is 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 B is COMPLEX*16 array, dimension (LDB,NRHS) The NbyNRHS right hand side matrix B.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X X is COMPLEX*16 array, dimension (LDX,NRHS) If INFO = 0, the NbyNRHS solution matrix X.LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).WORK WORK is COMPLEX*16 array, dimension (N*NRHS) This array is used to hold the residual vectors.SWORK SWORK is COMPLEX array, dimension (N*(N+NRHS)) This array is used to use the single precision matrix and the righthand sides or solutions in single precision.RWORK RWORK is DOUBLE PRECISION array, dimension (N)ITER ITER is INTEGER < 0: iterative refinement has failed, COMPLEX*16 factorization has been performed 1 : the routine fell back to full precision for implementation or machinespecific 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 iterationsINFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith 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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 201 of file zcgesv.f.
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