?lasy2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?lasy2

Solves the Sylvester matrix equation where the matrices are of order 1 or 2.

Syntax

call slasy2(ltranl, ltranr, isgn, n1, n2, tl, ldtl, tr, ldtr, b, ldb, scale, x, ldx,
            xnorm, info)

call dlasy2(ltranl, ltranr, isgn, n1, n2, tl, ldtl, tr, ldtr, b, ldb, scale, x, ldx,
            xnorm, info)

Include Files

mkl.fi

Description

The routine solves for the n1 -by- n2 matrix X , 1 ≤ n1 , n2 ≤ 2 , in

op(TL)*X + isgn*X*op(TR) = scale*B ,

where

TL is n1 -by- n1 ,

TR is n2 -by- n2 ,

B is n1 -by- n2 ,

and isgn = 1 or -1. op(T) = T or T^T , where T^T denotes the transpose of T .

Input Parameters

ltranl: LOGICAL . On entry, ltranl specifies the op(TL) : = .FALSE. , op(TL) = TL , = .TRUE. , op(TL) = (TL)^{T} .
ltranr: LOGICAL . On entry, ltranr specifies the op( TR ): = .FALSE. , op(TR) = TR , = .TRUE. , op(TR) = (TR)^{T} .
isgn: INTEGER . On entry, isgn specifies the sign of the equation as described before. isgn may only be 1 or -1.
n1: INTEGER . On entry, n1 specifies the order of matrix TL . n1 may only be 0, 1 or 2.
n2: INTEGER . On entry, n2 specifies the order of matrix TR . n2 may only be 0, 1 or 2.
tl: REAL for slasy2 DOUBLE PRECISION for dlasy2 . Array, DIMENSION ( ldtl ,2). On entry, tl contains an n1 -by- n1 matrix TL .
ldtl: INTEGER .The leading dimension of the matrix TL . ldtl≥ max(1,n1) .
tr: REAL for slasy2 DOUBLE PRECISION for dlasy2 . Array, DIMENSION ( ldtr ,2). On entry, tr contains an n2 -by- n2 matrix TR .
ldtr: INTEGER . The leading dimension of the matrix TR . ldtr≥ max(1,n2) .
b: REAL for slasy2 DOUBLE PRECISION for dlasy2 . Array, DIMENSION ( ldb ,2). On entry, the n1 -by- n2 matrix B contains the right-hand side of the equation.
ldb: INTEGER . The leading dimension of the matrix B . ldb≥ max(1,n1) .
ldx: INTEGER . The leading dimension of the output matrix X . ldx≥ max(1,n1) .

Output Parameters

scale: REAL for slasy2 DOUBLE PRECISION for dlasy2 . On exit, scale contains the scale factor. scale is chosen less than or equal to 1 to prevent the solution overflowing.
x: REAL for slasy2 DOUBLE PRECISION for dlasy2 . Array, DIMENSION ( ldx ,2). On exit, x contains the n1 -by- n2 solution.
xnorm: REAL for slasy2 DOUBLE PRECISION for dlasy2 . On exit, xnorm is the infinity-norm of the solution.

info

INTEGER . On exit, info is set to 0: successful exit. 1: TL and TR have too close eigenvalues, so TL or TR is perturbed to get a nonsingular equation.

NOTE:

For higher speed, this routine does not check the inputs for errors.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lasy2

Syntax

Include Files

Description

Input Parameters

Output Parameters