# ctrsyl3.f - Man Page

SRC/ctrsyl3.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine 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*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 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*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*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).

Definition at line **154** of file **ctrsyl3.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ctrsyl3(3) is an alias of ctrsyl3.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK