### ML_DGECON – Estimates the reciprocal of the condition number of a general real matrix

Block SymbolLicensing group: MATRIX

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

DGECON(sINORM, N, uA, LDA, anorm, rcond, uWORK, uIWORK, info);

where parameters of DGECON are set in the following way:

• If $\mathtt{\text{INORM}}=\mathtt{\text{on}}$ then the string sINORM is set to "I" else it is set to "1".
• N is number of columns of the matrix referenced by uA.
• LDA is the leading dimension of the matrix referenced by uA.
• rcond is returned reciprocal value of the condition number of the matrix referenced by uA.
• info is return code from the function DGECON.

The error flag E is set to on if:

• the reference uA or uWORK or uIWORK is not defined (i.e. input uA or uWORK or uIWORK is not connected),
• the matrix referenced by uA is not square,
• number of elements of the vector referenced by uWORK is less than $4\ast \mathtt{\text{N}}$,
• number of elements of the integer vector referenced by uIWORK is less than N,
• the call of the function DGECON 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 uWORK Input reference to working vector WORK Reference uIWORK Input reference to integer working vector WORK Reference INORM Use Infinity-norm Bool anorm Norm of the original matrix A  $\odot$0.0 Double (F64) HLD Hold Bool

Outputs

 yA Output reference to matrix A Reference yWORK Output reference to working vector WORK Reference yIWORK Output reference to integer working vector WORK Reference rcond The reciprocal of the condition number of the matrix A Double (F64) 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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