hadamard_inv_diffdiff()

STensor syten::STensorImpl::hadamard_inv_diffdiff	(	STensor const &	s,
		STensor	x,
		SBasisId const &	j_basis,
		SBasisId const &	i_basis,
		bool	minus
	)

Given a diagonal square tensor s and a square tensor x, approximates \( x_i^j \left( \frac{1}{s_j - s_i} \pm \frac{1}{s_j + s_i} \right) \).

Parameters

s	diagonal input tensor whose diagonal differences are inverted
x	input tensor of which the Hadamard product is taken
j_basis	ID of the basis taken as the minuend in the difference
i_basis	ID of the basis taken as the subtrahend in the difference
minus	if true, select - in ±, if false, select +

Remarks

This function is necessary for the autodifferentiation of an SVD.

This function is not autodifferentiable.

References syten::STensorImpl::STensor::autodiff_enabled(), syten::STensorImpl::STensor::bi(), syten::STensorImpl::STensor::get(), SYTEN_ASSERT, SYTEN_ASSERT_MSG, and SYTEN_BROADENING_EPSILON.

Referenced by syten::STensorImpl::Autodiff::svd_adjoint_evaluator().

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