Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - solves the complex Sylvester matrix equation

**SYNOPSIS**

SUBROUTINE ZTRSYL( 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 COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )

**PURPOSE**

ZTRSYL solves the complex 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**H, and A and B are both upper 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.

**ARGUMENTS**

TRANA (input) CHARACTER*1 Specifies the option op(A): = 'N': op(A) = A (No transpose) = 'C': op(A) = A**H (Conjugate transpose) TRANB (input) CHARACTER*1 Specifies the option op(B): = 'N': op(B) = B (No transpose) = 'C': op(B) = B**H (Conjugate 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) COMPLEX*16 array, dimension (LDA,M) The upper triangular matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). B (input) COMPLEX*16 array, dimension (LDB,N) The upper triangular matrix B. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). C (input/output) COMPLEX*16 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). LAPACK routine (version 3.3.1) April 2011 ZTRSYL(3lapack)