LAPACK

NAME¶

trsyl3 - trsyl3: Sylvester equation, level 3

SYNOPSIS¶

Functions¶

subroutine ctrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)
CTRSYL3 subroutine ztrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)
ZTRSYL3

Detailed Description¶

Function Documentation¶

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

TRANA



          TRANA is CHARACTER*1


          Specifies the option op(A):


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


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

TRANB



          TRANB is CHARACTER*1


          Specifies the option op(B):


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


          = 'C': op(B) = B**H (Conjugate 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 is INTEGER


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


          matrices X and C. M >= 0.



          N is INTEGER


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


          matrices X and C. N >= 0.



          A is COMPLEX array, dimension (LDA,M)


          The upper triangular matrix A.

LDA



          LDA is INTEGER


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



          B is COMPLEX array, dimension (LDB,N)


          The upper triangular matrix B.

LDB



          LDB is INTEGER


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



          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.

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.

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).

subroutine ztrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ldc, ) c, integer ldc, double precision scale, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)¶

ZTRSYL3