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## ctrsyl3()

subroutine ctrsyl3 | ( | character | trana,
|  | character | tranb,
|  | integer | isgn,
|  | integer | m,
|  | integer | n,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex, dimension( ldc, * ) | c,
|  | integer | ldc,
|  | real | scale,
|  | real, dimension( ldswork, * ) | swork,
|  | integer | ldswork,
|  | integer | info )

CTRSYL3

Purpose:

      !>
      !>  CTRSYL3 solves the complex Sylvester matrix equation:
      !>
      !>     op(A)*X + X*op(B) = scale*C or
      !>     op(A)*X - X*op(B) = scale*C,
      !>
      !>  where op(A) = A or A**H, and  A and B are both upper triangular. A is
      !>  M-by-M and B is N-by-N; the right hand side C and the solution X are
      !>  M-by-N; and scale is an output scale factor, set <= 1 to avoid
      !>  overflow in X.
      !>
      !>  This is the block version of the algorithm.
      !>

Parameters

  [in]

  TRANA

      !>          TRANA is CHARACTER*1
      !>          Specifies the option op(A):
      !>          = 'N': op(A) = A    (No transpose)
      !>          = 'C': op(A) = A**H (Conjugate transpose)
      !>

  [in]

  TRANB

      !>          TRANB is CHARACTER*1
      !>          Specifies the option op(B):
      !>          = 'N': op(B) = B    (No transpose)
      !>          = 'C': op(B) = B**H (Conjugate transpose)
      !>

  [in]

  ISGN

      !>          ISGN is INTEGER
      !>          Specifies the sign in the equation:
      !>          = +1: solve op(A)*X + X*op(B) = scale*C
      !>          = -1: solve op(A)*X - X*op(B) = scale*C
      !>

  [in]

  M

      !>          M is INTEGER
      !>          The order of the matrix A, and the number of rows in the
      !>          matrices X and C. M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix B, and the number of columns in the
      !>          matrices X and C. N >= 0.
      !>

  [in]

  A

      !>          A is COMPLEX array, dimension (LDA,M)
      !>          The upper triangular matrix A.
      !>

  [in]

  LDA

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

  [in]

  B

      !>          B is COMPLEX array, dimension (LDB,N)
      !>          The upper triangular matrix B.
      !>

  [in]

  LDB

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

  [in,out]

  C

      !>          C is COMPLEX array, dimension (LDC,N)
      !>          On entry, the M-by-N right hand side matrix C.
      !>          On exit, C is overwritten by the solution matrix X.
      !>

  [in]

  LDC

      !>          LDC is INTEGER
      !>          The leading dimension of the array C. LDC >= max(1,M)
      !>

  [out]

  SCALE

      !>          SCALE is REAL
      !>          The scale factor, scale, set <= 1 to avoid overflow in X.
      !>

  [out]

  SWORK

      !>          SWORK is REAL array, dimension (MAX(2, ROWS), MAX(1,COLS)).
      !>          On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS
      !>          and SWORK(2) returns the optimal COLS.
      !>

  [in]

  LDSWORK

      !>          LDSWORK is INTEGER
      !>          LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1)
      !>          and NB is the optimal block size.
      !>
      !>          If LDSWORK = -1, then a workspace query is assumed; the routine
      !>          only calculates the optimal dimensions of the SWORK matrix,
      !>          returns these values as the first and second entry of the SWORK
      !>          matrix, and no error message related LWORK is issued by XERBLA.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0: successful exit
      !>          < 0: if INFO = -i, the i-th argument had an illegal value
      !>          = 1: A and B have common or very close eigenvalues; perturbed
      !>               values were used to solve the equation (but the matrices
      !>               A and B are unchanged).
      !>