### 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 $\downarrow $0 $\uparrow $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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