STRSYL3 solves the real 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**T, and  A and B are both upper quasi-


  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.


  A and B must be in Schur canonical form (as returned by SHSEQR), that


  is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;


  each 2-by-2 diagonal block has its diagonal elements equal and its


  off-diagonal elements of opposite sign.


  This is the block version of the algorithm.

TRANA

          TRANA is CHARACTER*1


          Specifies the option op(A):


          = 'N': op(A) = A    (No transpose)


          = 'T': op(A) = A**T (Transpose)


          = 'C': op(A) = A**H (Conjugate transpose = Transpose)

TRANB

          TRANB is CHARACTER*1


          Specifies the option op(B):


          = 'N': op(B) = B    (No transpose)


          = 'T': op(B) = B**T (Transpose)


          = 'C': op(B) = B**H (Conjugate transpose = Transpose)

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

M

          M is INTEGER


          The order of the matrix A, and the number of rows in the


          matrices X and C. M >= 0.

N

          N is INTEGER


          The order of the matrix B, and the number of columns in the


          matrices X and C. N >= 0.

A

          A is REAL array, dimension (LDA,M)


          The upper quasi-triangular matrix A, in Schur canonical form.

LDA

          LDA is INTEGER


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

B

          B is REAL array, dimension (LDB,N)


          The upper quasi-triangular matrix B, in Schur canonical form.

LDB

          LDB is INTEGER


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

C

          C is REAL 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.

LDC

          LDC is INTEGER


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

SCALE

          SCALE is REAL


          The scale factor, scale, set <= 1 to avoid overflow in X.

IWORK

          IWORK is INTEGER array, dimension (MAX(1,LIWORK))


          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

          IWORK is INTEGER


          The dimension of the array IWORK. LIWORK >=  ((M + NB - 1) / NB + 1)


          + ((N + NB - 1) / NB + 1), where NB is the optimal block size.


          If LIWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal dimension of the IWORK array,


          returns this value as the first entry of the IWORK array, and


          no error message related to LIWORK is issued by XERBLA.

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.

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.

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).