### 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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