### ML_DGELSD – Computes the minimum-norm solution to a real linear least squares problem

Block SymbolLicensing group: MATRIX

Function Description

The output references yA, yB, yS, yWORK and yIWORK are always set to the corresponding input
references uA, uB, uS, uWORK and uIWORK. If HLD = on then nothing is computed otherwise the
LAPACK function DGELSD is called internally:

DGELSD(M, N, NRHS, uA, LDA, uB, LDB, uS, rcond, irank,uWORK,

LWORK, uIWORK, info);

where parameters of DGELSD are set in the following way:

- M is number of rows of the matrix referenced by uA.
- N is number of columns of the matrix referenced by uA.
- NRHS is number of columns of the matrix referenced by uB.
- LDA and LDB are leading dimensions of the matrices referenced by uA and uB.
- irank is returned effective rank of the matrix referenced by uA.
- LWORK is number of elements in the vector referenced by uWORK.
- info is return code from the function DGELSD.

The error flag E is set to on if:

- the reference uA or uB or uS or uWORK or uIWORK is not defined (i.e. input uA or uB or uS or uWORK or uIWORK is not connected),
- the number of rows of the matrix referenced by uB is not equal to M,
- number of elements of any vector referenced by uS is less than the minimum of M and N,
- number of elements of the integer vector referenced by uIWORK is not sufficient (see details in the LAPACK documentation of the function DGELSD),
- the call of the function DGELSD returns error using the function XERBLA, see the return code info and system log.

See LAPACK documentation [7] for more details.

Inputs

uA | Input reference to matrix A | Reference |

uB | Input reference to matrix B | Reference |

uS | Input reference to vector of singular values | Reference |

uWORK | Input reference to working vector WORK | Reference |

uIWORK | Input reference to integer working vector WORK | Reference |

rcond | Used to determine the effective rank of A $\odot $0.0 | Double (F64) |

HLD | Hold | Bool |

Outputs

yA | Output reference to matrix A | Reference |

yB | Output reference to matrix B | Reference |

yS | Output reference to vector of singular values | Reference |

yWORK | Output reference to working vector WORK | Reference |

yIWORK | Output reference to integer working vector WORK | Reference |

irank | Effective rank of A | Long (I32) |

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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