pseudo_inverse_svd_cm()

template<typename Scalar >

std::pair<DenseTensor<2, Scalar>, typename ScalarBase<Scalar>::type> syten::pseudo_inverse_svd_cm

(

DenseTensor< 2, Scalar > &&

input_cm

)

Takes a column-major input and pseudo-inverts it using a SVD.

Inverted singular values are broadened as \( \frac{s_i}{s_i^2 + \varepsilon} \) where \( \varepsilon \) is the largest singular value multiplied by SYTEN_SMALL_THRESHOLD.

The pseudo-inverse \( G \) of a matrix \( A \) is defined by its property that \( A \cdot G \cdot A = A \).

Returns

the pseudoinverse in row-major form and the ratio \( s_0 / s_i \) where \( s_i \) is the smallest singular value greater than the \( \varepsilon \) threshold.

References std::move(), overThreshold(), syten::STensorImpl::svd(), and SYTEN_SMALL_THRESHOLD.

Referenced by orthogonalise_solve_svd(), and pseudo_inverse_svd().

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