--- 
:name: zcgesv
:md5sum: bdec37d073bdd6753df626ef86ae37b2
:category: :subroutine
:arguments: 
- n: 
    :type: integer
    :intent: input
- nrhs: 
    :type: integer
    :intent: input
- a: 
    :type: doublecomplex
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- ipiv: 
    :type: integer
    :intent: output
    :dims: 
    - n
- b: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - ldb
    - nrhs
- ldb: 
    :type: integer
    :intent: input
- x: 
    :type: doublecomplex
    :intent: output
    :dims: 
    - ldx
    - nrhs
- ldx: 
    :type: integer
    :intent: input
- work: 
    :type: doublecomplex
    :intent: workspace
    :dims: 
    - n*nrhs
- swork: 
    :type: complex
    :intent: workspace
    :dims: 
    - n*(n+nrhs)
- rwork: 
    :type: doublereal
    :intent: workspace
    :dims: 
    - n
- iter: 
    :type: integer
    :intent: output
- info: 
    :type: integer
    :intent: output
:substitutions: 
  ldx: MAX(1,n)
:fortran_help: "      SUBROUTINE ZCGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  ZCGESV computes the solution to a complex system of linear equations\n\
  *     A * X = B,\n\
  *  where A is an N-by-N matrix and X and B are N-by-NRHS matrices.\n\
  *\n\
  *  ZCGESV first attempts to factorize the matrix in COMPLEX and use this\n\
  *  factorization within an iterative refinement procedure to produce a\n\
  *  solution with COMPLEX*16 normwise backward error quality (see below).\n\
  *  If the approach fails the method switches to a COMPLEX*16\n\
  *  factorization and solve.\n\
  *\n\
  *  The iterative refinement is not going to be a winning strategy if\n\
  *  the ratio COMPLEX performance over COMPLEX*16 performance is too\n\
  *  small. A reasonable strategy should take the number of right-hand\n\
  *  sides and the size of the matrix into account. This might be done\n\
  *  with a call to ILAENV in the future. Up to now, we always try\n\
  *  iterative refinement.\n\
  *\n\
  *  The iterative refinement process is stopped if\n\
  *      ITER > ITERMAX\n\
  *  or for all the RHS we have:\n\
  *      RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX\n\
  *  where\n\
  *      o ITER is the number of the current iteration in the iterative\n\
  *        refinement process\n\
  *      o RNRM is the infinity-norm of the residual\n\
  *      o XNRM is the infinity-norm of the solution\n\
  *      o ANRM is the infinity-operator-norm of the matrix A\n\
  *      o EPS is the machine epsilon returned by DLAMCH('Epsilon')\n\
  *  The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00\n\
  *  respectively.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The number of linear equations, i.e., the order of the\n\
  *          matrix A.  N >= 0.\n\
  *\n\
  *  NRHS    (input) INTEGER\n\
  *          The number of right hand sides, i.e., the number of columns\n\
  *          of the matrix B.  NRHS >= 0.\n\
  *\n\
  *  A       (input/output) COMPLEX*16 array,\n\
  *          dimension (LDA,N)\n\
  *          On entry, the N-by-N coefficient matrix A.\n\
  *          On exit, if iterative refinement has been successfully used\n\
  *          (INFO.EQ.0 and ITER.GE.0, see description below), then A is\n\
  *          unchanged, if double precision factorization has been used\n\
  *          (INFO.EQ.0 and ITER.LT.0, see description below), then the\n\
  *          array A contains the factors L and U from the factorization\n\
  *          A = P*L*U; the unit diagonal elements of L are not stored.\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of the array A.  LDA >= max(1,N).\n\
  *\n\
  *  IPIV    (output) INTEGER array, dimension (N)\n\
  *          The pivot indices that define the permutation matrix P;\n\
  *          row i of the matrix was interchanged with row IPIV(i).\n\
  *          Corresponds either to the single precision factorization\n\
  *          (if INFO.EQ.0 and ITER.GE.0) or the double precision\n\
  *          factorization (if INFO.EQ.0 and ITER.LT.0).\n\
  *\n\
  *  B       (input) COMPLEX*16 array, dimension (LDB,NRHS)\n\
  *          The N-by-NRHS right hand side matrix B.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *          The leading dimension of the array B.  LDB >= max(1,N).\n\
  *\n\
  *  X       (output) COMPLEX*16 array, dimension (LDX,NRHS)\n\
  *          If INFO = 0, the N-by-NRHS solution matrix X.\n\
  *\n\
  *  LDX     (input) INTEGER\n\
  *          The leading dimension of the array X.  LDX >= max(1,N).\n\
  *\n\
  *  WORK    (workspace) COMPLEX*16 array, dimension (N*NRHS)\n\
  *          This array is used to hold the residual vectors.\n\
  *\n\
  *  SWORK   (workspace) COMPLEX array, dimension (N*(N+NRHS))\n\
  *          This array is used to use the single precision matrix and the\n\
  *          right-hand sides or solutions in single precision.\n\
  *\n\
  *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)\n\
  *\n\
  *  ITER    (output) INTEGER\n\
  *          < 0: iterative refinement has failed, COMPLEX*16\n\
  *               factorization has been performed\n\
  *               -1 : the routine fell back to full precision for\n\
  *                    implementation- or machine-specific reasons\n\
  *               -2 : narrowing the precision induced an overflow,\n\
  *                    the routine fell back to full precision\n\
  *               -3 : failure of CGETRF\n\
  *               -31: stop the iterative refinement after the 30th\n\
  *                    iterations\n\
  *          > 0: iterative refinement has been successfully used.\n\
  *               Returns the number of iterations\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value\n\
  *          > 0:  if INFO = i, U(i,i) computed in COMPLEX*16 is exactly\n\
  *                zero.  The factorization has been completed, but the\n\
  *                factor U is exactly singular, so the solution\n\
  *                could not be computed.\n\
  *\n\
  *  =========\n\
  *\n"
