dtrsyl (l) - Linux Manuals

dtrsyl: solves the real Sylvester matrix equation

NAME

DTRSYL - solves the real Sylvester matrix equation

SYNOPSIS

SUBROUTINE DTRSYL(
TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO )

    
CHARACTER TRANA, TRANB

    
INTEGER INFO, ISGN, LDA, LDB, LDC, M, N

    
DOUBLE PRECISION SCALE

    
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE

DTRSYL solves the real Sylvester matrix equation:
op(A)*X + X*op(B) = scale*C or

op(A)*X - X*op(B) = scale*C,
where op(A) = A or A**T, and A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X.
A and B must be in Schur canonical form (as returned by DHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.

ARGUMENTS

TRANA (input) CHARACTER*1
Specifies the option op(A):
= aqNaq: op(A) = A (No transpose)
= aqTaq: op(A) = A**T (Transpose)
= aqCaq: op(A) = A**H (Conjugate transpose = Transpose)
TRANB (input) CHARACTER*1

Specifies the option op(B):
= aqNaq: op(B) = B (No transpose)
= aqTaq: op(B) = B**T (Transpose)
= aqCaq: op(B) = B**H (Conjugate transpose = Transpose)
ISGN (input) INTEGER

Specifies the sign in the equation:
= +1: solve op(A)*X + X*op(B) = scale*C
= -1: solve op(A)*X - X*op(B) = scale*C
M (input) INTEGER
The order of the matrix A, and the number of rows in the matrices X and C. M >= 0.
N (input) INTEGER
The order of the matrix B, and the number of columns in the matrices X and C. N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,M)
The upper quasi-triangular matrix A, in Schur canonical form.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input) DOUBLE PRECISION array, dimension (LDB,N)
The upper quasi-triangular matrix B, in Schur canonical form.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M)
SCALE (output) DOUBLE PRECISION
The scale factor, scale, set <= 1 to avoid overflow in X.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
= 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged).

Pages related to dtrsyl

  • dtrsyl (3)
  • dtrsen (l) - reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
  • dtrsm (l) - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
  • dtrsna (l) - estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
  • dtrsv (l) - solves one of the systems of equations A*x = b, or Aaq*x = b,
  • dtrcon (l) - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
  • dtrevc (l) - computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
  • dtrexc (l) - reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST