# dtrsyl.f - Man Page

SRC/dtrsyl.f

## Synopsis

### Functions/Subroutines

subroutine **dtrsyl** (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)**DTRSYL**

## Function/Subroutine Documentation

### subroutine dtrsyl (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 info)

**DTRSYL**

**Purpose:**

DTRSYL 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.

**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.

*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).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **162** of file **dtrsyl.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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