.TH DTRSYL 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DTRSYL - the real Sylvester matrix equation .SH SYNOPSIS .TP 19 SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO ) .TP 19 .ti +4 CHARACTER TRANA, TRANB .TP 19 .ti +4 INTEGER INFO, ISGN, LDA, LDB, LDC, M, N .TP 19 .ti +4 DOUBLE PRECISION SCALE .TP 19 .ti +4 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) .SH PURPOSE DTRSYL solves the real Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or .br op(A)*X - X*op(B) = scale*C, .br 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. .br 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. .br .SH ARGUMENTS .TP 8 TRANA (input) CHARACTER*1 Specifies the option op(A): .br = \(aqN\(aq: op(A) = A (No transpose) .br = \(aqT\(aq: op(A) = A**T (Transpose) .br = \(aqC\(aq: op(A) = A**H (Conjugate transpose = Transpose) .TP 8 TRANB (input) CHARACTER*1 .br Specifies the option op(B): .br = \(aqN\(aq: op(B) = B (No transpose) .br = \(aqT\(aq: op(B) = B**T (Transpose) .br = \(aqC\(aq: op(B) = B**H (Conjugate transpose = Transpose) .TP 8 ISGN (input) INTEGER .br Specifies the sign in the equation: .br = +1: solve op(A)*X + X*op(B) = scale*C .br = -1: solve op(A)*X - X*op(B) = scale*C .TP 8 M (input) INTEGER The order of the matrix A, and the number of rows in the matrices X and C. M >= 0. .TP 8 N (input) INTEGER The order of the matrix B, and the number of columns in the matrices X and C. N >= 0. .TP 8 A (input) DOUBLE PRECISION array, dimension (LDA,M) The upper quasi-triangular matrix A, in Schur canonical form. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). .TP 8 B (input) DOUBLE PRECISION array, dimension (LDB,N) The upper quasi-triangular matrix B, in Schur canonical form. .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 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. .TP 8 LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M) .TP 8 SCALE (output) DOUBLE PRECISION The scale factor, scale, set <= 1 to avoid overflow in X. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br = 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).