DTRSYL(1) LAPACK routine (version 3.2) DTRSYL(1)[top]NAMEDTRSYL - solves the real Sylvester matrix equationSYNOPSISSUBROUTINE 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, * )PURPOSEDTRSYL 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-diag‐ onal elements of opposite sign.ARGUMENTSTRANA (input) CHARACTER*1 Specifies the option op(A): = 'N': op(A) = A (No transpose) = 'T': op(A) = A**T (Transpose) = 'C': op(A) = A**H (Conjugate transpose = Transpose) TRANB (input) CHARACTER*1 Specifies the option op(B): = 'N': op(B) = B (No transpose) = 'T': op(B) = B**T (Transpose) = 'C': 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 matri‐ ces 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 =, 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). LAPACK routine (version 3.2) November 2008 DTRSYL(1)-i

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