SGESC2 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 SGETC2.

          N is INTEGER
          The order of the matrix A.

          A is REAL array, dimension (LDA,N)
          On entry, the  LU part of the factorization of the n-by-n
          matrix A computed by SGETC2:  A = P * L * U * Q

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

          RHS is REAL 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 owerflow in the solution.

 SGETC2 computes an LU factorization with 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 the Level 2 BLAS algorithm.

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

          A is REAL array, dimension (LDA, N)
          On entry, the n-by-n matrix A 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, i.e., 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 owerflow if
                we try to solve for x in Ax = b. So U is perturbed to
                avoid the overflow.

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

    SLANGE = ( 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 SLANGE as described
          above.

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

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

          A is REAL 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.

 SLAQGE 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 REAL 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.

 STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
 of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
 (A, B) by an orthogonal equivalence transformation.

 (A, B) must be in generalized real Schur canonical form (as returned
 by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
 diagonal blocks. B is upper triangular.

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

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

          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 REAL arrays, dimensions (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 REAL arrays, dimensions (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 REAL array, dimension (LDZ,N)
          On entry, if WANTQ = .TRUE., the orthogonal 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 REAL array, dimension (LDZ,N)
          On entry, if WANTZ =.TRUE., the orthogonal 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). 1 <= J1 <= N.

          N1 is INTEGER
          The order of the first block (A11, B11). N1 = 0, 1 or 2.

          N2 is INTEGER
          The order of the second block (A22, B22). N2 = 0, 1 or 2.

          WORK is REAL array, dimension (MAX(1,LWORK)).

          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >=  MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )

          INFO is INTEGER
            =0: Successful exit
            >0: If INFO = 1, the transformed matrix (A, B) would be
                too far from generalized Schur form; the blocks are
                not swapped and (A, B) and (Q, Z) are unchanged.
                The problem of swapping is too ill-conditioned.
            <0: If INFO = -16: LWORK is too small. Appropriate value
                for LWORK is returned in WORK(1).

  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.

  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
      Eigenvalues of a Regular Matrix Pair (A, B) and Condition
      Estimation: Theory, Algorithms and Software,
      Report UMINF - 94.04, Department of Computing Science, Umea
      University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
      Note 87. To appear in Numerical Algorithms, 1996.