Table Of Contents
Table Of Contents

potri

mxnet.ndarray.linalg.potri(A=None, out=None, name=None, **kwargs)

Performs matrix inversion from a Cholesky factorization. Input is a tensor A of dimension n >= 2.

If n=2, A is a lower triangular matrix (entries of upper triangle are all zero) with positive diagonal. We compute:

out = A-T * A-1

In other words, if A is the Cholesky factor of a symmetric positive definite matrix B (obtained by potrf), then

out = B-1

If n>2, potri is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Note

Use this operator only if you are certain you need the inverse of B, and cannot use the Cholesky factor A (potrf), together with backsubstitution (trsm). The latter is numerically much safer, and also cheaper.

Examples:

// Single matrix inverse
A = [[2.0, 0], [0.5, 2.0]]
potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]

// Batch matrix inverse
A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
            [[0.06641, -0.01562], [-0.01562, 0,0625]]]

Defined in src/operator/tensor/la_op.cc:L259

Parameters:
  • A (NDArray) – Tensor of lower triangular matrices
  • out (NDArray, optional) – The output NDArray to hold the result.
Returns:

out – The output of this function.

Return type:

NDArray or list of NDArrays