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- import numpy as np
- # numpy functions
- # additive log-ratio cl_transform
- def additive_log_ratio_transform(compositional):
- """Applies the additive log-ratio transform to compositional data."""
- compositional = compositional[:] + np.finfo(compositional.dtype).eps
- continuous = np.log(compositional[..., :-1] / compositional[..., -1, np.newaxis])
- return continuous
- # inverse additive log-ratio cl_transform
- def inverse_additive_log_ratio_transform(continuous):
- """Inverts the additive log-ratio transform, producing compositional data."""
- n = continuous.shape[0]
- compositional = np.hstack((np.exp(continuous), np.ones((n, 1))))
- compositional /= compositional.sum(axis=-1, keepdims=1)
- return compositional
- # centered log-ratio cl_transform
- def centered_log_ratio_transform(compositional):
- """Applies the centered log-ratio transform to compositional data."""
- continuous = np.log(compositional + np.finfo(compositional.dtype).eps)
- continuous -= continuous.mean(-1, keepdims=True)
- return continuous
- # inverse centered log-ratio cl_transform
- def inverse_centered_log_ratio_transform(continuous):
- """Inverts the centered log-ratio transform, producing compositional data."""
- compositional = np.exp(continuous)
- compositional /= compositional.sum(axis=-1, keepdims=1)
- return compositional
- # isometric log-ratio cl_transform
- def isometric_log_ratio_transform(compositional, projection_matrix):
- """Applies the isometric log-ratio transform to compositional data."""
- continuous = centered_log_ratio_transform(compositional)
- continuous = np.dot(continuous, projection_matrix)
- return continuous
- # inverse isometric log-ratio cl_transform
- def inverse_isometric_log_ratio_transform(continuous, projection_matrix):
- """Inverts the isometric log-ratio transform, producing compositional data."""
- continuous = np.dot(continuous, projection_matrix.T)
- compositional = inverse_centered_log_ratio_transform(continuous)
- return compositional
- # isometric log-ratio cl_transform
- def easy_isometric_log_ratio_transform(compositional):
- """Applies the isometric log-ratio transform to compositional data."""
- continuous = centered_log_ratio_transform(compositional)
- projection_matrix = make_projection_matrix(continuous.shape[1])
- continuous = np.dot(continuous, projection_matrix)
- return continuous
- # inverse isometric log-ratio cl_transform
- def easy_inverse_isometric_log_ratio_transform(continuous):
- """Inverts the isometric log-ratio transform, producing compositional data."""
- projection_matrix = make_projection_matrix(continuous.shape[1] + 1)
- continuous = np.dot(continuous, projection_matrix.T)
- compositional = inverse_centered_log_ratio_transform(continuous)
- return compositional
- # projection matrix for isometric log-ratio cl_transform
- def make_projection_matrix(dimension):
- """Creates the projection matrix for the the isometric log-ratio transform."""
- projection_matrix = np.zeros((dimension, dimension - 1), dtype=np.float32)
- for it in range(dimension - 1):
- i = it + 1
- projection_matrix[:i, it] = 1. / i
- projection_matrix[i, it] = -1
- projection_matrix[i + 1:, it] = 0
- projection_matrix[:, it] *= np.sqrt(i / (i + 1.))
- return projection_matrix
- # theano functions
- eps = np.finfo(np.float32).eps
- # additive log-ratio cl_transform
- def theano_additive_log_ratio_transform(compositional):
- """Applies the additive log-ratio transform to compositional data."""
- from theano import tensor as T
- compositional = compositional[:] + eps
- continuous = T.log(compositional[..., :-1] /
- compositional[..., -1].reshape(compositional.shape[:-1] + (1,)))
- return continuous
- # inverse additive log-ratio cl_transform
- def theano_inverse_additive_log_ratio_transform(continuous):
- """Inverts the additive log-ratio transform, producing compositional data."""
- from theano import tensor as T
- compositional = T.stack((T.exp(continuous), T.ones((continuous.shape[0], 1))), axis=continuous.ndim - 1)
- compositional /= compositional.sum(axis=-1, keepdims=1)
- return compositional
- # centered log-ratio cl_transform
- def theano_centered_log_ratio_transform(compositional):
- """Applies the centered log-ratio transform to compositional data."""
- from theano import tensor as T
- compositional = compositional[:] + eps
- continuous = T.log(compositional)
- continuous -= continuous.mean(-1, keepdims=True)
- return continuous
- # inverse centered log-ratio cl_transform
- def theano_inverse_centered_log_ratio_transform(continuous):
- """Inverts the centered log-ratio transform, producing compositional data."""
- from theano import tensor as T
- compositional = T.exp(continuous)
- compositional /= compositional.sum(axis=-1, keepdims=1)
- return compositional
- # isometric log-ratio cl_transform
- def theano_isometric_log_ratio_transform(compositional, projection_matrix):
- """Applies the isometric log-ratio transform to compositional data."""
- from theano import tensor as T
- continuous = theano_centered_log_ratio_transform(compositional)
- continuous = T.dot(continuous, projection_matrix)
- return continuous
- # inverse isometric log-ratio cl_transform
- def theano_inverse_isometric_log_ratio_transform(continuous, projection_matrix):
- """Inverts the isometric log-ratio transform, producing compositional data."""
- from theano import tensor as T
- continuous = T.dot(continuous, projection_matrix.T)
- compositional = theano_inverse_centered_log_ratio_transform(continuous)
- return compositional
- # tensorflow functions
- # additive log-ratio cl_transform
- def tf_additive_log_ratio_transform(compositional, name='alrt'):
- """Applies the additive log-ratio transform to compositional data."""
- import tensorflow as tf
- compositional = compositional + eps
- continuous = tf.log(compositional[..., :-1] /
- compositional[..., -1].reshape(compositional.shape[:-1] + (1,)), name=name)
- return continuous
- # inverse additive log-ratio cl_transform
- def tf_inverse_additive_log_ratio_transform(continuous, name='ialrt'):
- """Inverts the additive log-ratio transform, producing compositional data."""
- import tensorflow as tf
- compositional = tf.stack((tf.exp(continuous), tf.ones((continuous.shape[0], 1))), axis=tf.get_shape(continuous).ndim - 1)
- compositional /= tf.reduce_sum(compositional, axis=-1, keep_dims=True, name=name)
- return compositional
- # centered log-ratio cl_transform
- def tf_centered_log_ratio_transform(compositional, name='clrt'):
- """Applies the centered log-ratio transform to compositional data."""
- import tensorflow as tf
- compositional = compositional[:] + eps
- continuous = tf.log(compositional)
- continuous -= tf.reduce_mean(continuous, axis=-1, keep_dims=True)
- if name:
- continuous = tf.identity(continuous, name=name)
- return continuous
- # inverse centered log-ratio cl_transform
- def tf_inverse_centered_log_ratio_transform(continuous, name='iclrt'):
- """Inverts the centered log-ratio transform, producing compositional data."""
- import tensorflow as tf
- compositional = tf.exp(continuous)
- compositional /= tf.reduce_sum(compositional, axis=-1, keep_dims=True)
- if name:
- compositional = tf.identity(compositional, name=name)
- return compositional
- # isometric log-ratio cl_transform
- def tf_isometric_log_ratio_transform(compositional, projection_matrix, name='ilrt'):
- """Applies the isometric log-ratio transform to compositional data."""
- import tensorflow as tf
- continuous = tf_centered_log_ratio_transform(compositional, name=None)
- continuous = tf.matmul(continuous, projection_matrix, name=name)
- return continuous
- # inverse isometric log-ratio cl_transform
- def tf_inverse_isometric_log_ratio_transform(continuous, projection_matrix, name='iilrt'):
- """Inverts the isometric log-ratio transform, producing compositional data."""
- import tensorflow as tf
- continuous = tf.matmul(continuous, projection_matrix, transpose_b=True)
- compositional = tf_inverse_centered_log_ratio_transform(continuous, name=None)
- return tf.identity(compositional, name=name)
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