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zcgesv.f(3) LAPACK zcgesv.f(3)

zcgesv.f -

subroutine zcgesv (N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO)
ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)
 ZCGESV 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.
          N is INTEGER
          The number of linear equations, i.e., the order of the
          matrix A.  N >= 0.
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
          A is 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 is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
          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 is COMPLEX*16 array, dimension (LDB,NRHS)
          The N-by-NRHS right hand side matrix B.
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
          X is COMPLEX*16 array, dimension (LDX,NRHS)
          If INFO = 0, the N-by-NRHS solution matrix X.
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
          WORK is COMPLEX*16 array, dimension (N*NRHS)
          This array is used to hold the residual vectors.
          SWORK is 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 is DOUBLE PRECISION array, dimension (N)
          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 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
          > 0: iterative refinement has been sucessfully used.
               Returns the number of iterations
          INFO is 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.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011
Definition at line 201 of file zcgesv.f.

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