LAPACK

NAME¶

lasy2 - lasy2: Sylvester equation

SYNOPSIS¶

Functions¶

subroutine dlasy2 (ltranl, ltranr, isgn, n1, n2, tl, ldtl, tr, ldtr, b, ldb, scale, x, ldx, xnorm, info)
DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2. subroutine slasy2 (ltranl, ltranr, isgn, n1, n2, tl, ldtl, tr, ldtr, b, ldb, scale, x, ldx, xnorm, info)
SLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.

Detailed Description¶

Function Documentation¶

subroutine dlasy2 (logical ltranl, logical ltranr, integer isgn, integer n1, integer n2, double precision, dimension( ldtl, * ) tl, integer ldtl, double precision, dimension( ldtr, * ) tr, integer ldtr, double precision, dimension( ldb, * ) b, integer ldb, double precision scale, double precision, dimension( ldx, * ) x, integer ldx, double precision xnorm, integer info)¶

DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.

Purpose:



 DLASY2 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.

Parameters

LTRANL



          LTRANL is LOGICAL


          On entry, LTRANL specifies the op(TL):


             = .FALSE., op(TL) = TL,


             = .TRUE., op(TL) = TL**T.

LTRANR



          LTRANR is LOGICAL


          On entry, LTRANR specifies the op(TR):


            = .FALSE., op(TR) = TR,


            = .TRUE., op(TR) = TR**T.

ISGN



          ISGN is INTEGER


          On entry, ISGN specifies the sign of the equation


          as described before. ISGN may only be 1 or -1.



          N1 is INTEGER


          On entry, N1 specifies the order of matrix TL.


          N1 may only be 0, 1 or 2.



          N2 is INTEGER


          On entry, N2 specifies the order of matrix TR.


          N2 may only be 0, 1 or 2.



          TL is DOUBLE PRECISION array, dimension (LDTL,2)


          On entry, TL contains an N1 by N1 matrix.

LDTL



          LDTL is INTEGER


          The leading dimension of the matrix TL. LDTL >= max(1,N1).



          TR is DOUBLE PRECISION array, dimension (LDTR,2)


          On entry, TR contains an N2 by N2 matrix.

LDTR



          LDTR is INTEGER


          The leading dimension of the matrix TR. LDTR >= max(1,N2).



          B is DOUBLE PRECISION array, dimension (LDB,2)


          On entry, the N1 by N2 matrix B contains the right-hand


          side of the equation.

LDB



          LDB is INTEGER


          The leading dimension of the matrix B. LDB >= max(1,N1).

SCALE



          SCALE is DOUBLE PRECISION


          On exit, SCALE contains the scale factor. SCALE is chosen


          less than or equal to 1 to prevent the solution overflowing.



          X is DOUBLE PRECISION array, dimension (LDX,2)


          On exit, X contains the N1 by N2 solution.

LDX



          LDX is INTEGER


          The leading dimension of the matrix X. LDX >= max(1,N1).

XNORM



          XNORM is DOUBLE PRECISION


          On exit, XNORM is the infinity-norm of the solution.

INFO



          INFO is 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: In the interests of speed, this routine does not


                check the inputs for errors.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine slasy2 (logical ltranl, logical ltranr, integer isgn, integer n1, integer n2, real, dimension( ldtl, * ) tl, integer ldtl, real, dimension( ldtr, * ) tr, integer ldtr, real, dimension( ldb, * ) b, integer ldb, real scale, real, dimension( ldx, * ) x, integer ldx, real xnorm, integer info)¶

SLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.