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134 lines (109 loc) · 4.49 KB
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# Copyright 2016 Intel Corporation
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Full Correlation Matrix Analysis (FCMA)
Correlation related high performance routines
"""
# Authors: Yida Wang
# (Intel Labs), 2017
import numpy as np
from . import cython_blas as blas # type: ignore
from scipy.stats.mstats import zscore
import math
__all__ = [
"compute_correlation",
]
def _normalize_for_correlation(data, axis, return_nans=False):
"""normalize the data before computing correlation
The data will be z-scored and divided by sqrt(n)
along the assigned axis
Parameters
----------
data: 2D array
axis: int
specify which dimension of the data should be normalized
return_nans: bool, default:False
If False, return zeros for NaNs; if True, return NaNs
Returns
-------
data: 2D array
the normalized data
"""
shape = data.shape
data = zscore(data, axis=axis, ddof=0)
# if zscore fails (standard deviation is zero),
# optionally set all values to be zero
if not return_nans:
data = np.nan_to_num(data)
data = data / math.sqrt(shape[axis])
return data
def compute_correlation(matrix1, matrix2, return_nans=False):
"""compute correlation between two sets of variables
Correlate the rows of matrix1 with the rows of matrix2.
If matrix1 == matrix2, it is auto-correlation computation
resulting in a symmetric correlation matrix.
The number of columns MUST agree between set1 and set2.
The correlation being computed here is
the Pearson's correlation coefficient, which can be expressed as
.. math:: corr(X, Y) = \\frac{cov(X, Y)}{\\sigma_X\\sigma_Y}
where cov(X, Y) is the covariance of variable X and Y, and
.. math:: \\sigma_X
is the standard deviation of variable X
Reducing the correlation computation to matrix multiplication
and using BLAS GEMM API wrapped by Scipy can speedup the numpy built-in
correlation computation (numpy.corrcoef) by one order of magnitude
.. math::
corr(X, Y)
&= \\frac{\\sum\\limits_{i=1}^n (x_i-\\bar{x})(y_i-\\bar{y})}{(n-1)
\\sqrt{\\frac{\\sum\\limits_{j=1}^n x_j^2-n\\bar{x}}{n-1}}
\\sqrt{\\frac{\\sum\\limits_{j=1}^{n} y_j^2-n\\bar{y}}{n-1}}}\\\\
&= \\sum\\limits_{i=1}^n(\\frac{(x_i-\\bar{x})}
{\\sqrt{\\sum\\limits_{j=1}^n x_j^2-n\\bar{x}}}
\\frac{(y_i-\\bar{y})}{\\sqrt{\\sum\\limits_{j=1}^n y_j^2-n\\bar{y}}})
By default (return_nans=False), returns zeros for vectors with NaNs.
If return_nans=True, convert zeros to NaNs (np.nan) in output.
Parameters
----------
matrix1: 2D array in shape [r1, c]
MUST be continuous and row-major
matrix2: 2D array in shape [r2, c]
MUST be continuous and row-major
return_nans: bool, default:False
If False, return zeros for NaNs; if True, return NaNs
Returns
-------
corr_data: 2D array in shape [r1, r2]
continuous and row-major in np.float32
"""
matrix1 = matrix1.astype(np.float32)
matrix2 = matrix2.astype(np.float32)
[r1, d1] = matrix1.shape
[r2, d2] = matrix2.shape
if d1 != d2:
raise ValueError('Dimension discrepancy')
# preprocess two components
matrix1 = _normalize_for_correlation(matrix1, 1,
return_nans=return_nans)
matrix2 = _normalize_for_correlation(matrix2, 1,
return_nans=return_nans)
corr_data = np.empty((r1, r2), dtype=np.float32, order='C')
# blas routine is column-major
blas.compute_single_matrix_multiplication('T', 'N',
r2, r1, d1,
1.0,
matrix2, d2,
matrix1, d1,
0.0,
corr_data,
r2)
return corr_data