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| lasy2(3) | LAPACK | 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 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 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 172 of file slasy2.f.
Author
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