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Nachschlagewerk MQL5Matrizen und VektorenOpenBLASFactored CalculationsCholeskyCondNumReciprocal 

CholeskyCondNumReciprocal

Estimates the reciprocal of the condition number of a real symmetric or complex Hermitian positive-definite matrix A using the LLT factorization computed by FactorizationCholesky. LAPACK function POCON.

Computing for type matrix<double>

bool  matrix::CholeskyCondNumReciprocal(
   double          anorm,         // matrix norm value
   double&         rcond          // condition number reciprocal
   );

Computing for type matrix<float>

bool  matrixf::CholeskyCondNumReciprocal(
   float           anorm,         // matrix norm value
   float&          rcond          // condition number reciprocal
   );

Computing for type matrix<complex>

bool  matrixc::CholeskyCondNumReciprocal(
   double          anorm,         // matrix norm value
   double&         rcond          // condition number reciprocal
   );

Computing for type matrix<complexf>

bool  matrixcf::CholeskyCondNumReciprocal(
   float           anorm,         // matrix norm value
   float&          rcond          // condition number reciprocal
   );

Parameters

anorm

[in]  Matrix one-norm value. Norm value can be obtained with MatrixNormSy of the original matrix A.

rcond

[out] An estimate of the reciprocal of the condition number. The routine sets rcond=0 if the estimate underflows; in this case the matrix is singular (to working precision). However, anytime rcond is small compared to 1.0, for the working precision, the matrix may be poorly conditioned or even singular.

 

Return Value

Return true if successful, otherwise false in case of an error.

Note

This method is applied to the matrix L obtained as result of FactorizationCholesky method.

The computed rcond is never less than r (the reciprocal of the true condition number) and in practice is nearly always less than 10r. A call to this routine involves solving a number of systems of linear equations A*x = b; the number is usually 4 or 5 and never more than 11