cgetc2

 CGESC2 solves a system of linear equations

           A * X = scale* RHS

 with a general N-by-N matrix A using the LU factorization with
 complete pivoting computed by CGETC2.

          N is INTEGER
          The number of columns of the matrix A.

          A is COMPLEX array, dimension (LDA, N)
          On entry, the  LU part of the factorization of the n-by-n
          matrix A computed by CGETC2:  A = P * L * U * Q

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1, N).

          RHS is COMPLEX array, dimension N.
          On entry, the right hand side vector b.
          On exit, the solution vector X.

          IPIV is INTEGER array, dimension (N).
          The pivot indices; for 1 <= i <= N, row i of the
          matrix has been interchanged with row IPIV(i).

          JPIV is INTEGER array, dimension (N).
          The pivot indices; for 1 <= j <= N, column j of the
          matrix has been interchanged with column JPIV(j).

          SCALE is REAL
           On exit, SCALE contains the scale factor. SCALE is chosen
           0 <= SCALE <= 1 to prevent overflow in the solution.

 CGETC2 computes an LU factorization, using complete pivoting, of the
 n-by-n matrix A. The factorization has the form A = P * L * U * Q,
 where P and Q are permutation matrices, L is lower triangular with
 unit diagonal elements and U is upper triangular.

 This is a level 1 BLAS version of the algorithm.

          N is INTEGER
          The order of the matrix A. N >= 0.

          A is COMPLEX array, dimension (LDA, N)
          On entry, the n-by-n matrix to be factored.
          On exit, the factors L and U from the factorization
          A = P*L*U*Q; the unit diagonal elements of L are not stored.
          If U(k, k) appears to be less than SMIN, U(k, k) is given the
          value of SMIN, giving a nonsingular perturbed system.

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1, N).

          IPIV is INTEGER array, dimension (N).
          The pivot indices; for 1 <= i <= N, row i of the
          matrix has been interchanged with row IPIV(i).

          JPIV is INTEGER array, dimension (N).
          The pivot indices; for 1 <= j <= N, column j of the
          matrix has been interchanged with column JPIV(j).

          INFO is INTEGER
           = 0: successful exit
           > 0: if INFO = k, U(k, k) is likely to produce overflow if
                one tries to solve for x in Ax = b. So U is perturbed
                to avoid the overflow.

 CLANGE  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 complex matrix A.

    CLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
             (
             ( norm1(A),         NORM = '1', 'O' or 'o'
             (
             ( normI(A),         NORM = 'I' or 'i'
             (
             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

 where  norm1  denotes the  one norm of a matrix (maximum column sum),
 normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
 normF  denotes the  Frobenius norm of a matrix (square root of sum of
 squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.

          NORM is CHARACTER*1
          Specifies the value to be returned in CLANGE as described
          above.

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.  When M = 0,
          CLANGE is set to zero.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.  When N = 0,
          CLANGE is set to zero.

          A is COMPLEX array, dimension (LDA,N)
          The m by n matrix A.

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(M,1).

          WORK is REAL array, dimension (MAX(1,LWORK)),
          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
          referenced.

 CLAQGE equilibrates a general M by N matrix A using the row and
 column scaling factors in the vectors R and C.

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          On entry, the M by N matrix A.
          On exit, the equilibrated matrix.  See EQUED for the form of
          the equilibrated matrix.

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(M,1).

          R is REAL array, dimension (M)
          The row scale factors for A.

          C is REAL array, dimension (N)
          The column scale factors for A.

          ROWCND is REAL
          Ratio of the smallest R(i) to the largest R(i).

          COLCND is REAL
          Ratio of the smallest C(i) to the largest C(i).

          AMAX is REAL
          Absolute value of largest matrix entry.

          EQUED is CHARACTER*1
          Specifies the form of equilibration that was done.
          = 'N':  No equilibration
          = 'R':  Row equilibration, i.e., A has been premultiplied by
                  diag(R).
          = 'C':  Column equilibration, i.e., A has been postmultiplied
                  by diag(C).
          = 'B':  Both row and column equilibration, i.e., A has been
                  replaced by diag(R) * A * diag(C).

  THRESH is a threshold value used to decide if row or column scaling
  should be done based on the ratio of the row or column scaling
  factors.  If ROWCND < THRESH, row scaling is done, and if
  COLCND < THRESH, column scaling is done.

  LARGE and SMALL are threshold values used to decide if row scaling
  should be done based on the absolute size of the largest matrix
  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.

 CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
 in an upper triangular matrix pair (A, B) by an unitary equivalence
 transformation.

 (A, B) must be in generalized Schur canonical form, that is, A and
 B are both upper triangular.

 Optionally, the matrices Q and Z of generalized Schur vectors are
 updated.

        Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
        Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H

          WANTQ is LOGICAL
          .TRUE. : update the left transformation matrix Q;
          .FALSE.: do not update Q.

          WANTZ is LOGICAL
          .TRUE. : update the right transformation matrix Z;
          .FALSE.: do not update Z.

          N is INTEGER
          The order of the matrices A and B. N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          On entry, the matrix A in the pair (A, B).
          On exit, the updated matrix A.

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).

          B is COMPLEX array, dimension (LDB,N)
          On entry, the matrix B in the pair (A, B).
          On exit, the updated matrix B.

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).

          Q is COMPLEX array, dimension (LDQ,N)
          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
          the updated matrix Q.
          Not referenced if WANTQ = .FALSE..

          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= 1;
          If WANTQ = .TRUE., LDQ >= N.

          Z is COMPLEX array, dimension (LDZ,N)
          If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
          the updated matrix Z.
          Not referenced if WANTZ = .FALSE..

          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= 1;
          If WANTZ = .TRUE., LDZ >= N.

          J1 is INTEGER
          The index to the first block (A11, B11).

          INFO is INTEGER
           =0:  Successful exit.
           =1:  The transformed matrix pair (A, B) would be too far
                from generalized Schur form; the problem is ill-
                conditioned.