### MB_DTRSV – Solves one of the system of equations A*x = b or A^T*x = b for triangular matrix A

Block SymbolLicensing group: STANDARD

Function Description
The output references yA and yX are always set to the corresponding input references uA and uX. If HLD = on then nothing is computed otherwise the BLAS function DTRSV is called internally:

DTRSV(sLUPLO, sTRANS, sNDIAG, N, uA, LDA, uX, INCX);

where parameters of DTRSV are set in the following way:

• If $\mathtt{\text{LUPLO}}=\mathtt{\text{on}}$ then the string sLUPLO is set to "L" else it is set to "U".
• Integer input trans is mapped to the string sTRANS: $\left\{0,1\right\}\to \mathtt{\text{"N"}}$, $\left\{2\right\}\to \mathtt{\text{"T"}}$ and $\left\{3\right\}\to \mathtt{\text{"C"}}$.
• If $\mathtt{\text{NDIAG}}=\mathtt{\text{on}}$ then the string sNDIAG is set to "N" else it is set to "U".
• N is number of rows and columns of the square matrix referenced by uA.
• LDA is the leading dimension of matrix referenced by uA.
• If the input $\mathtt{\text{incx}}\ne 0$ then INCX is set to incx else INCX is set to $1$.

The error flag E is set to on if:

• the reference uA or uX is not defined (i.e. input uA or uX is not connected),
• trans is less than 0 or greater than 3,
• matrix referenced by uA is not square,
• $\left(\mathtt{\text{N}}-1\right)\ast \mathtt{\text{|INCX|}}+1>\mathtt{\text{CNTX}}$, where CNTX is a number of the vector or matrix elements referenced by uX.
• the call of the function DTRMV returns error using the function XERBLA, see the system log.

See BLAS documentation [6] for more details.

Inputs

 uA Input reference to matrix A Reference uX Input reference to vector x Reference LUPLO Matrix A is a lower triangular matrix Bool trans Transposition of the input matrix  $↓$0 $↑$3 Long (I32) NDIAG Matrix A is not assumed to be unit triangular Bool incx Index increment of vector x  $\odot$0.00E+00 Long(I32) HLD Hold Bool

Outputs

 yA Output reference to matrix A Reference yX Output reference to vector x Reference E Error indicator Bool

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