diff --git a/docs/pyerrors/linalg.html b/docs/pyerrors/linalg.html index 5e92a4a9..9e1052fb 100644 --- a/docs/pyerrors/linalg.html +++ b/docs/pyerrors/linalg.html @@ -80,9 +80,6 @@
  • slogdet
    • -
  • - grad_eig -
    • @@ -106,9 +103,6 @@ import autograd.numpy as anp # Thinly-wrapped numpy from .obs import derived_observable, CObs, Obs, import_jackknife -from functools import partial -from autograd.extend import defvjp - def matmul(*operands): """Matrix multiply all operands. @@ -631,54 +625,6 @@ res_mat2.append(row) return (np.array(res_mat0) @ np.identity(mid_index), np.array(res_mat1) @ np.identity(mid_index), np.array(res_mat2) @ np.identity(shape[1])) - - -# This code block is directly taken from the current master branch of autograd and remains -# only until the new version is released on PyPi -_dot = partial(anp.einsum, '...ij,...jk->...ik') - - -# batched diag -def _diag(a): - return anp.eye(a.shape[-1]) * a - - -# batched diagonal, similar to matrix_diag in tensorflow -def _matrix_diag(a): - reps = anp.array(a.shape) - reps[:-1] = 1 - reps[-1] = a.shape[-1] - newshape = list(a.shape) + [a.shape[-1]] - return _diag(anp.tile(a, reps).reshape(newshape)) - -# https://arxiv.org/pdf/1701.00392.pdf Eq(4.77) -# Note the formula from Sec3.1 in https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf is incomplete - - -def grad_eig(ans, x): - """Gradient of a general square (complex valued) matrix""" - e, u = ans # eigenvalues as 1d array, eigenvectors in columns - n = e.shape[-1] - - def vjp(g): - ge, gu = g - ge = _matrix_diag(ge) - f = 1 / (e[..., anp.newaxis, :] - e[..., :, anp.newaxis] + 1.e-20) - f -= _diag(f) - ut = anp.swapaxes(u, -1, -2) - r1 = f * _dot(ut, gu) - r2 = -f * (_dot(_dot(ut, anp.conj(u)), anp.real(_dot(ut, gu)) * anp.eye(n))) - r = _dot(_dot(anp.linalg.inv(ut), ge + r1 + r2), ut) - if not anp.iscomplexobj(x): - r = anp.real(r) - # the derivative is still complex for real input (imaginary delta is allowed), real output - # but the derivative should be real in real input case when imaginary delta is forbidden - return r - return vjp - - -defvjp(anp.linalg.eig, grad_eig) -# End of the code block from autograd.master @@ -1184,45 +1130,6 @@ Obs valued. - -
    -
    #   - - - def - grad_eig(ans, x): -
    - -
    - View Source - 
    def grad_eig(ans, x):
-    """Gradient of a general square (complex valued) matrix"""
-    e, u = ans  # eigenvalues as 1d array, eigenvectors in columns
-    n = e.shape[-1]
-
-    def vjp(g):
-        ge, gu = g
-        ge = _matrix_diag(ge)
-        f = 1 / (e[..., anp.newaxis, :] - e[..., :, anp.newaxis] + 1.e-20)
-        f -= _diag(f)
-        ut = anp.swapaxes(u, -1, -2)
-        r1 = f * _dot(ut, gu)
-        r2 = -f * (_dot(_dot(ut, anp.conj(u)), anp.real(_dot(ut, gu)) * anp.eye(n)))
-        r = _dot(_dot(anp.linalg.inv(ut), ge + r1 + r2), ut)
-        if not anp.iscomplexobj(x):
-            r = anp.real(r)
-            # the derivative is still complex for real input (imaginary delta is allowed), real output
-            # but the derivative should be real in real input case when imaginary delta is forbidden
-        return r
-    return vjp
-
    - -
    - -

    Gradient of a general square (complex valued) matrix

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    - -