ML_DTRSYL – Solves the real Sylvester matrix equation for quasi-triangular matrices A and B

Block SymbolLicensing group: MATRIX

Function Description
The output references yA, yB and yC are always set to the corresponding input references uA, uB and uC. If HLD = on then nothing is computed otherwise the LAPACK function DTRSYL is called internally:

DTRSYL(sTRANA, sTRANB, M, N, uA, LDA, uB, LDB, uC, LDC, scale, info);

where parameters of DTRSYL are set in the following way:

Integer inputs trana and tranb are mapped to strings sTRANA and sTRANB: ${0, 1} \to "N"$ , ${2} \to "T"$ and ${3} \to "C"$ .
M is number of rows of the matrix referenced by uA.
N is number of columns of the matrix referenced by uB.
LDA, LDB and LDC are leading dimensions of matrices referenced by uA, uB and uC.
scale is returned scaling factor to avoid overflow.
info is return code from the function DTRSYL.

The error flag E is set to on if:

the reference uA or uB or uC is not defined (i.e. input uA or uB or uC is not connected),
trana or tranb is less than 0 or greater than 3
number of columns of the matrix referenced by uA is not equal to M
number of rows of the matrix referenced by uB is not equal to N
number of rows of the matrix referenced by uC is not equal to N or number of columns of this matrix is not equal to M,
the call of the function DTRSYL returns error using the function XERBLA, see the system log.

See LAPACK documentation [7] for more details.

Inputs

uA	Input reference to matrix A	Reference
uB	Input reference to matrix B	Reference
uC	Input reference to matrix C	Reference
trana	Transposition of matrix A $↓$ 0 $↑$ 3 $⊙$ 0.00E+00	Long (I32)
tranb	Transposition of matrix B $↓$ 0 $↑$ 3 $⊙$ 0.00E+00	Long (I32)
isgn	Sign in the equation (1 or -1) $↓$ -1 $↑$ 1 $⊙$ 0.00E+00	Long (I32)
HLD	Hold	Bool

Outputs

yA	Output reference to matrix A	Reference
yB	Output reference to matrix B	Reference
yC	Output reference to matrix C	Reference
scale	Scale	Double (F64)
E	Error indicator	Bool
info	LAPACK function result info. If info = -i, the i=th argument had an illegal value	Long (I32)

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