def pearsonr(x, y, axis=None):
'''
Calculates a Pearson correlation coefficient and the p-value for testing non-correlation.
The Pearson correlation coefficient measures the linear relationship between two datasets.
Strictly speaking, Pearson’s correlation requires that each dataset be normally distributed,
and not necessarily zero-mean. Like other correlation coefficients, this one varies between
-1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear
relationship. Positive correlations imply that as x increases, so does y. Negative
correlations imply that as x increases, y decreases.
The p-value roughly indicates the probability of an uncorrelated system producing datasets
that have a Pearson correlation at least as extreme as the one computed from these datasets.
The p-values are not entirely reliable but are probably reasonable for datasets larger than
500 or so.
:param x: (*array_like*) x data array.
:param y: (*array_like*) y data array.
:param axis: (*int*) By default, the index is into the flattened array, otherwise
along the specified axis.
:returns: Pearson’s correlation coefficient and 2-tailed p-value.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if axis is None:
r = StatsUtil.pearsonr(x.asarray(), y.asarray())
return r[0], r[1]
else:
r = StatsUtil.pearsonr(x.array, y.array, axis)
return MIArray(r[0]), MIArray(r[1])
def cov(m, y=None, rowvar=True, bias=False):
'''
Estimate a covariance matrix.
:param m: (*array_like*) A 1-D or 2-D array containing multiple variables and observations.
:param y: (*array_like*) Optional. An additional set of variables and observations. y has the same form as
that of m.
:param rowvar: (*boolean*) If ``rowvar`` is True (default), then each row represents a variable, with
observations in the columns. Otherwise, the relationship is transposed: each column represents a
variable, while the rows contain observations.
:param bias: (*boolean*) Default normalization (False) is by (N - 1), where N is the number of observations
given (unbiased estimate). If bias is True, then normalization is by N.
:returns: Covariance.
'''
if isinstance(m, list):
m = MIArray(ArrayUtil.array(m))
if rowvar == True and m.ndim == 2:
m = m.T
if y is None:
r = StatsUtil.cov(m.asarray(), not bias)
if isinstance(r, Array):
return MIArray(r)
else:
return r
else:
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if rowvar == True and y.ndim == 2:
y = y.T
r = StatsUtil.cov(m.asarray(), y.asarray(), not bias)
return MIArray(r)
def cov(m, y=None, rowvar=True, bias=False):
'''
Estimate a covariance matrix.
:param m: (*array_like*) A 1-D or 2-D array containing multiple variables and observations.
:param y: (*array_like*) Optional. An additional set of variables and observations. y has the same form as
that of m.
:param rowvar: (*boolean*) If ``rowvar`` is True (default), then each row represents a variable, with
observations in the columns. Otherwise, the relationship is transposed: each column represents a
variable, while the rows contain observations.
:param bias: (*boolean*) Default normalization (False) is by (N - 1), where N is the number of observations
given (unbiased estimate). If bias is True, then normalization is by N.
:returns: Covariance.
'''
if isinstance(m, list):
m = MIArray(ArrayUtil.array(m))
if rowvar == True and m.ndim == 2:
m = m.T
if y is None:
r = StatsUtil.cov(m.asarray(), not bias)
if isinstance(r, Array):
return MIArray(r)
else:
return r
else:
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if rowvar == True and y.ndim == 2:
y = y.T
r = StatsUtil.cov(m.asarray(), y.asarray(), not bias)
return MIArray(r)
def pearsonr(x, y):
'''
Calculates a Pearson correlation coefficient and the p-value for testing non-correlation.
The Pearson correlation coefficient measures the linear relationship between two datasets.
Strictly speaking, Pearson’s correlation requires that each dataset be normally distributed,
and not necessarily zero-mean. Like other correlation coefficients, this one varies between
-1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear
relationship. Positive correlations imply that as x increases, so does y. Negative
correlations imply that as x increases, y decreases.
The p-value roughly indicates the probability of an uncorrelated system producing datasets
that have a Pearson correlation at least as extreme as the one computed from these datasets.
The p-values are not entirely reliable but are probably reasonable for datasets larger than
500 or so.
:param x: (*array_like*) x data array.
:param y: (*array_like*) y data array.
:returns: Pearson’s correlation coefficient and 2-tailed p-value.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = StatsUtil.pearsonr(x.asarray(), y.asarray())
return r[0], r[1]
def __init__(self, x, y, z, kind='linear'):
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if isinstance(z, list):
z = MIArray(ArrayUtil.array(z))
self._func = InterpUtil.getBiInterpFunc(x.asarray(), y.asarray(), z.asarray())
def __init__(self, x, y, z):
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if isinstance(z, list):
z = MIArray(ArrayUtil.array(z))
self._func = InterpUtil.getBiInterpFunc(x.asarray(), y.asarray(),
z.asarray())
def mlinregress(y, x):
'''
Implements ordinary least squares (OLS) to estimate the parameters of a multiple linear
regression model.
:param y: (*array_like*) Y sample data - one dimension array.
:param x: (*array_like*) X sample data - two dimension array.
:returns: Estimated regression parameters and residuals.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = StatsUtil.multipleLineRegress_OLS(y.asarray(), x.asarray())
return MIArray(r[0]), MIArray(r[1])
def mlinregress(y, x):
'''
Implements ordinary least squares (OLS) to estimate the parameters of a multiple linear
regression model.
:param y: (*array_like*) Y sample data - one dimension array.
:param x: (*array_like*) X sample data - two dimension array.
:returns: Estimated regression parameters and residuals.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = StatsUtil.multipleLineRegress_OLS(y.asarray(), x.asarray())
return MIArray(r[0]), MIArray(r[1])
def covariance(x, y, bias=False):
'''
Calculate covariance of two array.
:param x: (*array_like*) A 1-D array containing multiple variables and observations.
:param y: (*array_like*) An additional set of variables and observations. y has the same form as
that of x.
:param bias: (*boolean*) Default normalization (False) is by (N - 1), where N is the number of observations
given (unbiased estimate). If bias is True, then normalization is by N.
returns: Covariance
'''
if isinstance(x, (list, tuple)):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, (list, tuple)):
y = MIArray(ArrayUtil.array(y))
r = StatsUtil.covariance(x.asarray(), y.asarray(), bias)
return r
def ttest_rel(a, b):
'''
Calculates the T-test on TWO RELATED samples of scores, a and b.
This is a two-sided test for the null hypothesis that 2 related or repeated samples
have identical average (expected) values.
:param a: (*array_like*) Sample data a.
:param b: (*array_like*) Sample data b.
:returns: t-statistic and p-value
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(a))
if isinstance(b, list):
b = MIArray(ArrayUtil.array(b))
r = StatsUtil.pairedTTest(a.asarray(), b.asarray())
return r[0], r[1]
def covariance(x, y, bias=False):
'''
Calculate covariance of two array.
:param x: (*array_like*) A 1-D array containing multiple variables and observations.
:param y: (*array_like*) An additional set of variables and observations. y has the same form as
that of x.
:param bias: (*boolean*) Default normalization (False) is by (N - 1), where N is the number of observations
given (unbiased estimate). If bias is True, then normalization is by N.
returns: Covariance
'''
if isinstance(x, (list, tuple)):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, (list, tuple)):
y = MIArray(ArrayUtil.array(y))
r = StatsUtil.covariance(x.asarray(), y.asarray(), bias)
return r
def ttest_rel(a, b):
'''
Calculates the T-test on TWO RELATED samples of scores, a and b.
This is a two-sided test for the null hypothesis that 2 related or repeated samples
have identical average (expected) values.
:param a: (*array_like*) Sample data a.
:param b: (*array_like*) Sample data b.
:returns: t-statistic and p-value
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(a))
if isinstance(b, list):
b = MIArray(ArrayUtil.array(b))
r = StatsUtil.pairedTTest(a.asarray(), b.asarray())
return r[0], r[1]
def ttest_ind(a, b):
'''
Calculates the T-test for the means of TWO INDEPENDENT samples of scores.
This is a two-sided test for the null hypothesis that 2 independent samples have
identical average (expected) values. This test assumes that the populations have
identical variances.
:param a: (*array_like*) Sample data a.
:param b: (*array_like*) Sample data b.
:returns: t-statistic and p-value
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(a))
if isinstance(b, list):
b = MIArray(ArrayUtil.array(b))
r = StatsUtil.tTest(a.asarray(), b.asarray())
return r[0], r[1]
def ttest_ind(a, b):
'''
Calculates the T-test for the means of TWO INDEPENDENT samples of scores.
This is a two-sided test for the null hypothesis that 2 independent samples have
identical average (expected) values. This test assumes that the populations have
identical variances.
:param a: (*array_like*) Sample data a.
:param b: (*array_like*) Sample data b.
:returns: t-statistic and p-value
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(a))
if isinstance(b, list):
b = MIArray(ArrayUtil.array(b))
r = StatsUtil.tTest(a.asarray(), b.asarray())
return r[0], r[1]
def polyfit(x, y, degree, func=False):
'''
Polynomail fitting.
:param x: (*array_like*) x data array.
:param y: (*array_like*) y data array.
:param func: (*boolean*) Return fit function (for predict function) or not. Default is ``False``.
:returns: Fitting parameters and function (optional).
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = FittingUtil.polyFit(x.asarray(), y.asarray(), degree)
if func:
return r[0], r[1], r[2]
else:
return r[0], r[1]
def linregress(x, y, outvdn=False):
'''
Calculate a linear least-squares regression for two sets of measurements.
:param x, y: (*array_like*) Two sets of measurements. Both arrays should have the same length.
:param outvdn: (*boolean*) Output validate data number or not. Default is False.
:returns: Result slope, intercept, relative coefficient, two-sided p-value for a hypothesis test
whose null hypothesis is that the slope is zero, standard error of the estimated gradient,
validate data number (remove NaN values).
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = ArrayMath.lineRegress(x.asarray(), y.asarray())
if outvdn:
return r[0], r[1], r[2], r[3], r[4], r[5]
else:
return r[0], r[1], r[2], r[3], r[4]
def __call__(self, x, y):
'''
Evaluate the interpolate vlaues.
:param x: (*array_like*) X to evaluate the interpolant at.
:param y: (*array_like*) Y to evaluate the interpolant at.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(x, (MIArray, DimArray)):
x = x.asarray()
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if isinstance(y, (MIArray, DimArray)):
y = y.asarray()
r = InterpUtil.evaluate(self._func, x, y)
if isinstance(r, float):
return r
else:
return MIArray(r)
def percentile(a, q, axis=None):
'''
Compute the qth percentile of the data along the specified axis.
:param a: (*array_like*) Input array.
:param q: (*float*) float in range of [0,100].
Percentile to compute, which must be between 0 and 100 inclusive.
:param axis: (*int*) Axis or axes along which the percentiles are computed. The default is
to compute the percentile along a flattened version of the array.
:returns: (*float*) qth percentile value.
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(x))
if axis is None:
r = StatsUtil.percentile(a.asarray(), q)
else:
r = StatsUtil.percentile(a.asarray(), q, axis)
r = MIArray(r)
return r
def percentile(a, q, axis=None):
'''
Compute the qth percentile of the data along the specified axis.
:param a: (*array_like*) Input array.
:param q: (*float*) float in range of [0,100].
Percentile to compute, which must be between 0 and 100 inclusive.
:param axis: (*int*) Axis or axes along which the percentiles are computed. The default is
to compute the percentile along a flattened version of the array.
:returns: (*float*) qth percentile value.
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(x))
if axis is None:
r = StatsUtil.percentile(a.asarray(), q)
else:
r = StatsUtil.percentile(a.asarray(), q, axis)
r = MIArray(r)
return r
def __call__(self, x, y):
'''
Evaluate the interpolate vlaues.
:param x: (*array_like*) X to evaluate the interpolant at.
:param y: (*array_like*) Y to evaluate the interpolant at.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(x, (MIArray, DimArray)):
x = x.asarray()
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if isinstance(y, (MIArray, DimArray)):
y = y.asarray()
r = InterpUtil.evaluate(self._func, x, y)
if isinstance(r, float):
return r
else:
return MIArray(r)
def linregress(x, y, outvdn=False):
'''
Calculate a linear least-squares regression for two sets of measurements.
:param x, y: (*array_like*) Two sets of measurements. Both arrays should have the same length.
:param outvdn: (*boolean*) Output validate data number or not. Default is False.
:returns: Result slope, intercept, relative coefficient, two-sided p-value for a hypothesis test
whose null hypothesis is that the slope is zero, standard error of the estimated gradient,
validate data number (remove NaN values).
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = ArrayMath.lineRegress(x.asarray(), y.asarray())
if outvdn:
return r[0], r[1], r[2], r[3], r[4], r[5]
else:
return r[0], r[1], r[2], r[3], r[4]
def kendalltau(x, y):
'''
Calculates Kendall's tau, a correlation measure for ordinal data.
Kendall's tau is a measure of the correspondence between two rankings.
Values close to 1 indicate strong agreement, values close to -1 indicate
strong disagreement. This is the 1945 "tau-b" version of Kendall's
tau [2]_, which can account for ties and which reduces to the 1938 "tau-a"
version [1]_ in absence of ties.
:param x: (*array_like*) x data array.
:param y: (*array_like*) y data array.
:returns: Correlation.
Notes
-----
The definition of Kendall's tau that is used is [2]_::
tau = (P - Q) / sqrt((P + Q + T) * (P + Q + U))
where P is the number of concordant pairs, Q the number of discordant
pairs, T the number of ties only in `x`, and U the number of ties only in
`y`. If a tie occurs for the same pair in both `x` and `y`, it is not
added to either T or U.
References
----------
.. [1] Maurice G. Kendall, "A New Measure of Rank Correlation", Biometrika
Vol. 30, No. 1/2, pp. 81-93, 1938.
.. [2] Maurice G. Kendall, "The treatment of ties in ranking problems",
Biometrika Vol. 33, No. 3, pp. 239-251. 1945.
.. [3] Gottfried E. Noether, "Elements of Nonparametric Statistics", John
Wiley & Sons, 1967.
.. [4] Peter M. Fenwick, "A new data structure for cumulative frequency
tables", Software: Practice and Experience, Vol. 24, No. 3,
pp. 327-336, 1994.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = StatsUtil.kendalltau(x.asarray(), y.asarray())
return r
def kendalltau(x, y):
'''
Calculates Kendall's tau, a correlation measure for ordinal data.
Kendall's tau is a measure of the correspondence between two rankings.
Values close to 1 indicate strong agreement, values close to -1 indicate
strong disagreement. This is the 1945 "tau-b" version of Kendall's
tau [2]_, which can account for ties and which reduces to the 1938 "tau-a"
version [1]_ in absence of ties.
:param x: (*array_like*) x data array.
:param y: (*array_like*) y data array.
:returns: Correlation.
Notes
-----
The definition of Kendall's tau that is used is [2]_::
tau = (P - Q) / sqrt((P + Q + T) * (P + Q + U))
where P is the number of concordant pairs, Q the number of discordant
pairs, T the number of ties only in `x`, and U the number of ties only in
`y`. If a tie occurs for the same pair in both `x` and `y`, it is not
added to either T or U.
References
----------
.. [1] Maurice G. Kendall, "A New Measure of Rank Correlation", Biometrika
Vol. 30, No. 1/2, pp. 81-93, 1938.
.. [2] Maurice G. Kendall, "The treatment of ties in ranking problems",
Biometrika Vol. 33, No. 3, pp. 239-251. 1945.
.. [3] Gottfried E. Noether, "Elements of Nonparametric Statistics", John
Wiley & Sons, 1967.
.. [4] Peter M. Fenwick, "A new data structure for cumulative frequency
tables", Software: Practice and Experience, Vol. 24, No. 3,
pp. 327-336, 1994.
'''
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
r = StatsUtil.kendalltau(x.asarray(), y.asarray())
return r
def reproject(a, x=None, y=None, fromproj=None, xp=None, yp=None, toproj=None, method='bilinear'):
"""
Project array
:param a: (*array_like*) Input array.
:param x: (*array_like*) Input x coordinates.
:param y: (*array_like*) Input y coordinates.
:param fromproj: (*ProjectionInfo*) Input projection.
:param xp: (*array_like*) Projected x coordinates.
:param yp: (*array_like*) Projected y coordinates.
:param toproj: (*ProjectionInfo*) Output projection.
:param method: Interpolation method: ``bilinear`` or ``neareast`` .
:returns: (*MIArray*) Projected array
"""
if isinstance(a, DimArray):
y = a.dimvalue(a.ndim - 2)
x = a.dimvalue(a.ndim - 1)
if fromproj is None:
fromproj = a.proj
if toproj is None:
toproj = KnownCoordinateSystems.geographic.world.WGS1984
if xp is None or yp is None:
pr = ArrayUtil.reproject(a.asarray(), x.aslist(), y.aslist(), fromproj, toproj)
r = pr[0]
return MIArray(r)
if method == 'bilinear':
method = ResampleMethods.Bilinear
else:
method = ResampleMethods.NearestNeighbor
if isinstance(xp, (list, tuple)):
xp = MIArray(xp)
if isinstance(yp, (list, tuple)):
yp = MIArray(yp)
xp, yp = ArrayUtil.meshgrid(xp.asarray(), yp.asarray())
r = ArrayUtil.reproject(a.asarray(), x.aslist(), y.aslist(), xp, yp, fromproj, toproj, method)
return MIArray(r)
def chisquare(f_obs, f_exp=None):
'''
Calculates a one-way chi square test.
The chi square test tests the null hypothesis that the categorical data has the
given frequencies.
:param f_obs: (*array_like*) Observed frequencies in each category.
:param f_exp: (*array_like*) Expected frequencies in each category. By default the categories
are assumed to be equally likely.
:returns: Chi-square statistic and p-value
'''
if isinstance(f_obs, list):
f_obs = MIArray(ArrayUtil.array(f_obs))
if f_exp is None:
n = len(f_obs)
f_exp = minum.ones(n) / n * f_obs.sum()
elif isinstance(f_exp, list):
f_exp = MIArray(ArrayUtil.array(f_exp))
r = StatsUtil.chiSquareTest(f_exp.asarray(), f_obs.asarray())
return r[0], r[1]
def chisquare(f_obs, f_exp=None):
'''
Calculates a one-way chi square test.
The chi square test tests the null hypothesis that the categorical data has the
given frequencies.
:param f_obs: (*array_like*) Observed frequencies in each category.
:param f_exp: (*array_like*) Expected frequencies in each category. By default the categories
are assumed to be equally likely.
:returns: Chi-square statistic and p-value
'''
if isinstance(f_obs, list):
f_obs = MIArray(ArrayUtil.array(f_obs))
if f_exp is None:
n = len(f_obs)
f_exp = minum.ones(n) / n * f_obs.sum()
elif isinstance(f_exp, list):
f_exp = MIArray(ArrayUtil.array(f_exp))
r = StatsUtil.chiSquareTest(f_exp.asarray(), f_obs.asarray())
return r[0], r[1]
def spearmanr(m, y=None, axis=0):
'''
Calculates a Spearman rank-order correlation coefficient.
The Spearman correlation is a nonparametric measure of the monotonicity of the relationship
between two datasets. Unlike the Pearson correlation, the Spearman correlation does not
assume that both datasets are normally distributed. Like other correlation coefficients,
this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1
imply an exact monotonic relationship. Positive correlations imply that as x increases, so
does y. Negative correlations imply that as x increases, y decreases.
:param m: (*array_like*) A 1-D or 2-D array containing multiple variables and observations.
:param y: (*array_like*) Optional. An additional set of variables and observations. y has the same form as
that of m.
:param axis: (*int*) If axis=0 (default), then each column represents a variable, with
observations in the rows. If axis=1, the relationship is transposed: each row represents
a variable, while the columns contain observations..
:returns: Spearman correlation matrix.
'''
if isinstance(m, list):
m = MIArray(ArrayUtil.array(m))
if axis == 1 and m.ndim == 2:
m = m.T
if y is None:
r = StatsUtil.spearmanr(m.asarray())
if isinstance(r, Array):
return MIArray(r)
else:
return r
else:
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if axis == 1 and y.ndim == 2:
y = y.T
r = StatsUtil.spearmanr(m.asarray(), y.asarray())
return MIArray(r)
def spearmanr(m, y=None, axis=0):
'''
Calculates a Spearman rank-order correlation coefficient.
The Spearman correlation is a nonparametric measure of the monotonicity of the relationship
between two datasets. Unlike the Pearson correlation, the Spearman correlation does not
assume that both datasets are normally distributed. Like other correlation coefficients,
this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1
imply an exact monotonic relationship. Positive correlations imply that as x increases, so
does y. Negative correlations imply that as x increases, y decreases.
:param m: (*array_like*) A 1-D or 2-D array containing multiple variables and observations.
:param y: (*array_like*) Optional. An additional set of variables and observations. y has the same form as
that of m.
:param axis: (*int*) If axis=0 (default), then each column represents a variable, with
observations in the rows. If axis=1, the relationship is transposed: each row represents
a variable, while the columns contain observations..
:returns: Spearman correlation matrix.
'''
if isinstance(m, list):
m = MIArray(ArrayUtil.array(m))
if axis == 1 and m.ndim == 2:
m = m.T
if y is None:
r = StatsUtil.spearmanr(m.asarray())
if isinstance(r, Array):
return MIArray(r)
else:
return r
else:
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
if axis == 1 and y.ndim == 2:
y = y.T
r = StatsUtil.spearmanr(m.asarray(), y.asarray())
return MIArray(r)
def predict(func, x):
'''
Predict y value using fitting function and x value.
:param func: (*Fitting function object*) Fitting function.
:param x: (*float*) x value.
:returns: (*float*) y value.
'''
if isinstance(x, (int, float, long)):
return func.predict(x)
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
return MIArray(FittingUtil.predict(x.asarray(), func))
def ttest_1samp(a, popmean):
'''
Calculate the T-test for the mean of ONE group of scores.
This is a two-sided test for the null hypothesis that the expected value (mean) of
a sample of independent observations a is equal to the given population mean, popmean.
:param a: (*array_like*) Sample observation.
:param popmean: (*float*) Expected value in null hypothesis.
:returns: t-statistic and p-value
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(x))
r = StatsUtil.tTest(a.asarray(), popmean)
return r[0], r[1]
def ttest_1samp(a, popmean):
'''
Calculate the T-test for the mean of ONE group of scores.
This is a two-sided test for the null hypothesis that the expected value (mean) of
a sample of independent observations a is equal to the given population mean, popmean.
:param a: (*array_like*) Sample observation.
:param popmean: (*float*) Expected value in null hypothesis.
:returns: t-statistic and p-value
'''
if isinstance(a, list):
a = MIArray(ArrayUtil.array(x))
r = StatsUtil.tTest(a.asarray(), popmean)
return r[0], r[1]
def chi2_contingency(observed):
'''
Chi-square test of independence of variables in a contingency table.
This function computes the chi-square statistic and p-value for the hypothesis test of
independence of the observed frequencies in the contingency table observed.
:param observed: (*array_like*) The contingency table. The table contains the observed
frequencies (i.e. number of occurrences) in each category. In the two-dimensional case,
the table is often described as an `R x C table`.
:returns: Chi-square statistic and p-value
'''
if isinstance(observed, list):
observed = MIArray(ArrayUtil.array(observed))
r = StatsUtil.chiSquareTest(observed.asarray())
return r[0], r[1]
def chi2_contingency(observed):
'''
Chi-square test of independence of variables in a contingency table.
This function computes the chi-square statistic and p-value for the hypothesis test of
independence of the observed frequencies in the contingency table observed.
:param observed: (*array_like*) The contingency table. The table contains the observed
frequencies (i.e. number of occurrences) in each category. In the two-dimensional case,
the table is often described as an `R x C table`.
:returns: Chi-square statistic and p-value
'''
if isinstance(observed, list):
observed = MIArray(ArrayUtil.array(observed))
r = StatsUtil.chiSquareTest(observed.asarray())
return r[0], r[1]
def polyval(p, x):
"""
Evaluate a polynomial at specific values.
If p is of length N, this function returns the value:
p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]
If x is a sequence, then p(x) is returned for each element of x. If x is another polynomial then the
composite polynomial p(x(t)) is returned.
:param p: (*array_like*) 1D array of polynomial coefficients (including coefficients equal to zero)
from highest degree to the constant term.
:param x: (*array_like*) A number, an array of numbers, or an instance of poly1d, at which to evaluate
p.
:returns: Polynomial value
"""
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
return MIArray(ArrayMath.polyVal(p, x.asarray()))
def __init__(self, x, y, kind='linear'):
if isinstance(x, list):
x = MIArray(ArrayUtil.array(x))
if isinstance(y, list):
y = MIArray(ArrayUtil.array(y))
self._func = InterpUtil.getInterpFunc(x.asarray(), y.asarray(), kind)
