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 $⊙$ 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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