# dtrsyl3.f - Man Page

SRC/dtrsyl3.f

## Synopsis

### Functions/Subroutines

subroutine **dtrsyl3** (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)**DTRSYL3**

## Function/Subroutine Documentation

### subroutine dtrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldc, * ) c, integer ldc, double precision scale, integer, dimension( * ) iwork, integer liwork, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)

**DTRSYL3**

**Purpose**

DTRSYL3 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 DHSEQR), 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.

**Parameters***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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 **178** of file **dtrsyl3.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dtrsyl3(3) is an alias of dtrsyl3.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK