dtrsyl (l)  Linux Manuals
dtrsyl: solves the real Sylvester matrix equation
NAME
DTRSYL  solves the real Sylvester matrix equationSYNOPSIS
 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
op(A)*X  X*op(B)
where op(A) = A or A**T, and A and B are both upper quasi triangular. A is MbyM and B is NbyN; the right hand side C and the solution X are MbyN; 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 1by1 and 2by2 diagonal blocks; each 2by2 diagonal block has its diagonal elements equal and its offdiagonal 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 quasitriangular 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 quasitriangular 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 MbyN 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 ith 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).