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

Generated automatically by Doxygen for LAPACK from the source code.