dtrsylSolve the real Sylvester matrix equation op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C |
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Lapack documentation 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): = '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 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).
A |
Type: Real[:,:] Description: Upper quasi-triangular matrix |
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B |
Type: Real[:,:] Description: Upper quasi-triangular matrix |
C |
Type: Real[if tranA then size(A, 1) else size(A, 2),if tranB then size(B, 1) else size(B, 2)] Description: Right side of the Sylvester equation |
tranA |
Default Value: false Type: Boolean Description: = true, if op(A)=A' |
tranB |
Default Value: false Type: Boolean Description: = true, if op(B)=B' |
isgn |
Default Value: 1 Type: Integer Description: Specifies the sign in the equation, +1 or -1 |
X |
Default Value: C Type: Real[size(C, 1),size(C, 2)] Description: Solution of the Sylvester equation |
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scale |
Type: Real Description: Scale factor |
info |
Type: Integer |