/
det.py
109 lines (89 loc) · 3.55 KB
/
det.py
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import numpy
import chainer
from chainer.backends import cuda
from chainer import function_node
import chainer.functions
from chainer.functions.math import matmul
from chainer import utils
from chainer.utils import type_check
def _det_gpu(b):
# We do a batched LU decomposition on the GPU to compute
# and compute the determinant by multiplying the diagonal.
# Change the shape of the array to be size=1 minibatch if necessary.
# Also copy the matrix as the elments will be modified in-place.
a = matmul._as_batch_mat(b).copy()
n = a.shape[1]
n_matrices = len(a)
# Pivot array
p = cuda.cupy.zeros((n_matrices, n), dtype='int32')
# Output array
# These arrays hold information on the execution success
# or if the matrix was singular.
info = cuda.cupy.zeros(n_matrices, dtype=numpy.intp)
ap = matmul._mat_ptrs(a)
_, lda = matmul._get_ld(a)
cuda.cublas.sgetrfBatched(cuda.Device().cublas_handle, n, ap.data.ptr, lda,
p.data.ptr, info.data.ptr, n_matrices)
det = cuda.cupy.prod(a.diagonal(axis1=1, axis2=2), axis=1)
# The determinant is equal to the product of the diagonal entries
# of `a` where the sign of `a` is flipped depending on whether
# the pivot array is equal to its index.
rng = cuda.cupy.arange(1, n + 1, dtype='int32')
parity = cuda.cupy.sum(p != rng, axis=1) % 2
sign = 1. - 2. * parity.astype('float32')
return det * sign, info
class BatchDet(function_node.FunctionNode):
@property
def label(self):
return 'det'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x',))
a_type, = in_types
type_check.expect(a_type.dtype.kind == 'f')
# Only a minibatch of 2D array shapes allowed.
type_check.expect(a_type.ndim == 3)
# Matrix inversion only allowed for square matrices
# so assert the last two dimensions are equal.
type_check.expect(a_type.shape[-1] == a_type.shape[-2])
def forward_cpu(self, x):
self.retain_inputs((0,))
self.retain_outputs((0,))
detx = utils.force_array(numpy.linalg.det(x[0]))
return detx,
def forward_gpu(self, x):
self.retain_inputs((0,))
self.retain_outputs((0,))
detx, _ = _det_gpu(x[0])
return detx,
def backward(self, indexes, gy):
x, = self.get_retained_inputs()
detx, = self.get_retained_outputs()
gy, = gy
inv_x = chainer.functions.batch_inv(
chainer.functions.transpose(x, (0, 2, 1)))
gy = chainer.functions.broadcast_to(gy[:, None, None], inv_x.shape)
detx = chainer.functions.broadcast_to(detx[:, None, None], inv_x.shape)
grad = gy * detx * inv_x
return grad,
def batch_det(a):
"""Computes the determinant of a batch of square matrices.
Args:
a (Variable): Input array to compute the determinant for.
The first dimension should iterate over each matrix and be
of the batchsize.
Returns:
~chainer.Variable: vector of determinants for every matrix
in the batch.
"""
return BatchDet().apply((a,))[0]
def det(a):
"""Computes the determinant of a single square matrix.
Args:
a (Variable): Input array to compute the determinant for.
Returns:
~chainer.Variable: Scalar determinant of the matrix a.
"""
shape = (1, a.shape[0], a.shape[1])
batched_a = chainer.functions.reshape(a, shape)
batched_det = BatchDet().apply((batched_a,))[0]
return chainer.functions.reshape(batched_det, ())