ZCGESV(3)

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zcgesv.f — okay bestie, this is the zcgesv.f(3) page from the Library Functions Manual, and it's all about ZCGESV, no cap. 💖

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✨ SYNOPSIS ✨

🧩 Functions/Subroutines

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)

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🦋 Function/Subroutine Documentation 🦋

subroutine ZCGESV (integer n, integer nrhs, complex*16, dimension( lda, * )
    a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(
    ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx,
    complex*16, dimension( n, * ) work, complex, dimension( * ) swork,
    double precision, dimension( * ) rwork, integer iter, integer info)

ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

🎯 Purpose

Okay so 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. Iconic.

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. iykyk 💅

The iterative refinement process is stopped if

ITER > ITERMAX

or for all the RHS we have:

RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX

where

• ITER is the number of the current iteration in the iterative refinement process
• RNRM is the infinity-norm of the residual
• XNRM is the infinity-norm of the solution
• ANRM is the infinity-operator-norm of the matrix A
• EPS is the machine epsilon returned by DLAMCH('Epsilon')

The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively. periodt. ✨

🧾 Parameters

• N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. 🫶
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 🌸
• A — 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 = 0 and ITER >= 0, see description below), then A is unchanged; if double precision factorization has been used (INFO = 0 and ITER < 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💖
• IPIV — 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 = 0 and ITER >= 0) or the double precision factorization (if INFO = 0 and ITER < 0). 🎀
• B — COMPLEX*16 array, dimension (LDB,NRHS). The N-by-NRHS right hand side matrix B. 🦋
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N). ⭐
• X — COMPLEX*16 array, dimension (LDX,NRHS). If INFO = 0, the N-by-NRHS solution matrix X. 👑
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N). 🌈
• WORK — COMPLEX*16 array, dimension (N,NRHS). This array is used to hold the residual vectors. 💜
• SWORK — 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 — DOUBLE PRECISION array, dimension (N). 🧚
• ITER — INTEGER. Here's the whole mood ring:

< 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 successfully used.
     Returns the number of iterations

• INFO — INTEGER. The receipts:

= 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.

🫶 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 199 of file zcgesv.f. ✨

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole zcgesv.f(3) page, bestie 💖 — source/version: LAPACK Version 3.12.0, from /home/abui...RC/zcgesv.f(3). 🎀