lasy2(3)

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

    !>          N1 is INTEGER
    !>          On entry, N1 specifies the order of matrix TL.
    !>          N1 may only be 0, 1 or 2.
    !>

    N2

    !>          N2 is INTEGER
    !>          On entry, N2 specifies the order of matrix TR.
    !>          N2 may only be 0, 1 or 2.
    !>

    TL

    !>          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

    !>          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

    !>          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

    !>          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.

Definition at line 172 of file dlasy2.f.

  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.

Purpose:

    !>
    !> SLASY2 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

    !>          N1 is INTEGER
    !>          On entry, N1 specifies the order of matrix TL.
    !>          N1 may only be 0, 1 or 2.
    !>

    N2

    !>          N2 is INTEGER
    !>          On entry, N2 specifies the order of matrix TR.
    !>          N2 may only be 0, 1 or 2.
    !>

    TL

    !>          TL is REAL 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

    !>          TR is REAL 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

    !>          B is REAL 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 REAL
    !>          On exit, SCALE contains the scale factor. SCALE is chosen
    !>          less than or equal to 1 to prevent the solution overflowing.
    !>

    X

    !>          X is REAL 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 REAL
    !>          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.

Definition at line 172 of file slasy2.f.

Author

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