lasy2(3) Library Functions Manual 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. LAPACK Version 3.12.0 lasy2(3)