Documentation ¶
Overview ¶
Package stat provides generalized statistical functions.
Index ¶
 func Bhattacharyya(p, q []float64) float64
 func BivariateMoment(r, s float64, x, y, weights []float64) float64
 func CDF(q float64, c CumulantKind, x, weights []float64) float64
 func ChiSquare(obs, exp []float64) float64
 func CircularMean(x, weights []float64) float64
 func Correlation(x, y, weights []float64) float64
 func CorrelationMatrix(dst *mat.SymDense, x mat.Matrix, weights []float64)
 func Covariance(x, y, weights []float64) float64
 func CovarianceMatrix(dst *mat.SymDense, x mat.Matrix, weights []float64)
 func CrossEntropy(p, q []float64) float64
 func Entropy(p []float64) float64
 func ExKurtosis(x, weights []float64) float64
 func GeometricMean(x, weights []float64) float64
 func HarmonicMean(x, weights []float64) float64
 func Hellinger(p, q []float64) float64
 func Histogram(count, dividers, x, weights []float64) []float64
 func JensenShannon(p, q []float64) float64
 func Kendall(x, y, weights []float64) float64
 func KolmogorovSmirnov(x, xWeights, y, yWeights []float64) float64
 func KullbackLeibler(p, q []float64) float64
 func LinearRegression(x, y, weights []float64, origin bool) (alpha, beta float64)
 func Mahalanobis(x, y mat.Vector, chol *mat.Cholesky) float64
 func Mean(x, weights []float64) float64
 func MeanStdDev(x, weights []float64) (mean, std float64)
 func MeanVariance(x, weights []float64) (mean, variance float64)
 func Mode(x, weights []float64) (val float64, count float64)
 func Moment(moment float64, x, weights []float64) float64
 func MomentAbout(moment float64, x []float64, mean float64, weights []float64) float64
 func PopMeanStdDev(x, weights []float64) (mean, std float64)
 func PopMeanVariance(x, weights []float64) (mean, variance float64)
 func PopStdDev(x, weights []float64) float64
 func PopVariance(x, weights []float64) float64
 func Quantile(p float64, c CumulantKind, x, weights []float64) float64
 func RNoughtSquared(x, y, weights []float64, beta float64) float64
 func ROC(cutoffs, y []float64, classes []bool, weights []float64) (tpr, fpr, thresh []float64)
 func RSquared(x, y, weights []float64, alpha, beta float64) float64
 func RSquaredFrom(estimates, values, weights []float64) float64
 func Skew(x, weights []float64) float64
 func SortWeighted(x, weights []float64)
 func SortWeightedLabeled(x []float64, labels []bool, weights []float64)
 func StdDev(x, weights []float64) float64
 func StdErr(std, sampleSize float64) float64
 func StdScore(x, mean, std float64) float64
 func Variance(x, weights []float64) float64
 type CC
 type CumulantKind
 type PC
Examples ¶
 CC
 CircularMean
 Correlation
 Covariance
 Entropy
 ExKurtosis
 GeometricMean
 HarmonicMean
 Histogram
 Kendall
 KullbackLeibler
 LinearRegression
 Mean
 PC
 PopStdDev
 PopVariance
 ROC (AUC)
 ROC (EquallySpacedCutoffs)
 ROC (KnownCutoffs)
 ROC (Threshold)
 ROC (Unsorted)
 ROC (Unweighted)
 ROC (Weighted)
 StdDev
 StdErr
 Variance
Constants ¶
Variables ¶
Functions ¶
func Bhattacharyya ¶
Bhattacharyya computes the distance between the probability distributions p and q given by:
\ln ( \sum_i \sqrt{p_i q_i} )
The lengths of p and q must be equal. It is assumed that p and q sum to 1.
func BivariateMoment ¶
BivariateMoment computes the weighted mixed moment between the samples x and y.
E[(x  μ_x)^r*(y  μ_y)^s]
No degrees of freedom correction is done. The lengths of x and y must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
func CDF ¶
func CDF(q float64, c CumulantKind, x, weights []float64) float64
CDF returns the empirical cumulative distribution function value of x, that is the fraction of the samples less than or equal to q. The exact behavior is determined by the CumulantKind. CDF is theoretically the inverse of the Quantile function, though it may not be the actual inverse for all values q and CumulantKinds.
The x data must be sorted in increasing order. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
CumulantKind behaviors:
 Empirical: Returns the lowest fraction for which q is greater than or equal to that fraction of samples
func ChiSquare ¶
ChiSquare computes the chisquare distance between the observed frequencies 'obs' and expected frequencies 'exp' given by:
\sum_i (obs_iexp_i)^2 / exp_i
The lengths of obs and exp must be equal.
func CircularMean ¶
CircularMean returns the circular mean of the dataset.
atan2(\sum_i w_i * sin(alpha_i), \sum_i w_i * cos(alpha_i))
If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: The circular mean is 1.37037.
func Correlation ¶
Correlation returns the weighted correlation between the samples of x and y with the given means.
sum_i {w_i (x_i  meanX) * (y_i  meanY)} / (stdX * stdY)
The lengths of x and y must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: Correlation computes the degree to which two datasets move together about their mean. For example, x and y above move similarly. Correlation is 0.59915
func CorrelationMatrix ¶
CorrelationMatrix returns the correlation matrix calculated from a matrix of data, x, using a twopass algorithm. The result is stored in dst.
If weights is not nil the weighted correlation of x is calculated. weights must have length equal to the number of rows in input data matrix and must not contain negative elements. The dst matrix must either be empty or have the same number of columns as the input data matrix.
func Covariance ¶
Covariance returns the weighted covariance between the samples of x and y.
sum_i {w_i (x_i  meanX) * (y_i  meanY)} / (sum_j {w_j}  1)
The lengths of x and y must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: Covariance computes the degree to which datasets move together about their mean. Cov = 13.8000 If datasets move perfectly together, the variance equals the covariance Cov2 is 37.7000, VarX is 37.7000
func CovarianceMatrix ¶
CovarianceMatrix calculates the covariance matrix (also known as the variancecovariance matrix) calculated from a matrix of data, x, using a twopass algorithm. The result is stored in dst.
If weights is not nil the weighted covariance of x is calculated. weights must have length equal to the number of rows in input data matrix and must not contain negative elements. The dst matrix must either be empty or have the same number of columns as the input data matrix.
func CrossEntropy ¶
CrossEntropy computes the crossentropy between the two distributions specified in p and q.
func Entropy ¶
Entropy computes the Shannon entropy of a distribution or the distance between two distributions. The natural logarithm is used.
 sum_i (p_i * log_e(p_i))
Example ¶
Output: Entropy is a measure of the amount of uncertainty in a distribution The second bin of p is very likely to occur. It's entropy is 0.6247 The distribution of q is more spread out. It's entropy is 1.3195 Adding buckets with zero probability does not change the entropy. The entropy of r is: 1.2206 A distribution with no uncertainty has entropy 0.0000
func ExKurtosis ¶
ExKurtosis returns the population excess kurtosis of the sample. The kurtosis is defined by the 4th moment of the mean divided by the squared variance. The excess kurtosis subtracts 3.0 so that the excess kurtosis of the normal distribution is zero. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: Kurtosis is a measure of the 'peakedness' of a distribution, and the excess kurtosis is the kurtosis above or below that of the standard normal distribution ExKurtosis = 5.41200 Weighted ExKurtosis is 0.6779
func GeometricMean ¶
GeometricMean returns the weighted geometric mean of the dataset
\prod_i {x_i ^ w_i}
This only applies with positive x and positive weights. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: The arithmetic mean is 10.1667, but the geometric mean is 8.7637. The exponential of the mean of the logs is 8.7637
func HarmonicMean ¶
HarmonicMean returns the weighted harmonic mean of the dataset
\sum_i {w_i} / ( sum_i {w_i / x_i} )
This only applies with positive x and positive weights. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: The arithmetic mean is 10.16667, but the harmonic mean is 6.8354.
func Hellinger ¶
Hellinger computes the distance between the probability distributions p and q given by:
\sqrt{ 1  \sum_i \sqrt{p_i q_i} }
The lengths of p and q must be equal. It is assumed that p and q sum to 1.
func Histogram ¶
Histogram sums up the weighted number of data points in each bin. The weight of data point x[i] will be placed into count[j] if dividers[j] <= x < dividers[j+1]. The "span" function in the floats package can assist with bin creation.
The following conditions on the inputs apply:
 The count variable must either be nil or have length of one less than dividers.  The values in dividers must be sorted (use the sort package).  The x values must be sorted.  If weights is nil then all of the weights are 1.  If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: Histogram counts the amount of data in the bins specified by the dividers. In this data set, there are 7 data points less than 7 (between dividers[0] and dividers[1]), 12 data points between 7 and 20 (dividers[1] and dividers[2]), and 0 data points above 1000. Since dividers has length 5, there will be 4 bins. Hist = [7 12 72 10] For ease, the floats Span function can be used to set the dividers Hist = [11 10 10 10 10 10 10 10 10 10] Histogram also works with weighted data, and allows reusing of the count field in order to avoid extra garbage Weighted Hist = [66 165 265 365 465 565 665 765 865 965]
func JensenShannon ¶
JensenShannon computes the JensenShannon divergence between the distributions p and q. The JensenShannon divergence is defined as
m = 0.5 * (p + q) JS(p, q) = 0.5 ( KL(p, m) + KL(q, m) )
Unlike KullbackLiebler, the JensenShannon distance is symmetric. The value is between 0 and ln(2).
func Kendall ¶
Kendall returns the weighted Taua Kendall correlation between the samples of x and y. The Kendall correlation measures the quantity of concordant and discordant pairs of numbers. If weights are specified then each pair is weighted by weights[i] * weights[j] and the final sum is normalized to stay between 1 and 1. The lengths of x and y must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: Kendall correlation computes the number of ordered pairs between two datasets. Kendall correlation is 0.25000
func KolmogorovSmirnov ¶
KolmogorovSmirnov computes the largest distance between two empirical CDFs. Each dataset x and y consists of sample locations and counts, xWeights and yWeights, respectively.
x and y may have different lengths, though len(x) must equal len(xWeights), and len(y) must equal len(yWeights). Both x and y must be sorted.
Special cases are:
= 0 if len(x) == len(y) == 0 = 1 if len(x) == 0, len(y) != 0 or len(x) != 0 and len(y) == 0
func KullbackLeibler ¶
KullbackLeibler computes the KullbackLeibler distance between the distributions p and q. The natural logarithm is used.
sum_i(p_i * log(p_i / q_i))
Note that the KullbackLeibler distance is not symmetric; KullbackLeibler(p,q) != KullbackLeibler(q,p)
Example ¶
Output:
func LinearRegression ¶
LinearRegression computes the bestfit line
y = alpha + beta*x
to the data in x and y with the given weights. If origin is true, the regression is forced to pass through the origin.
Specifically, LinearRegression computes the values of alpha and beta such that the total residual
\sum_i w[i]*(y[i]  alpha  beta*x[i])^2
is minimized. If origin is true, then alpha is forced to be zero.
The lengths of x and y must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
func Mahalanobis ¶
Mahalanobis computes the Mahalanobis distance
D = sqrt((xy)ᵀ * Σ^1 * (xy))
between the column vectors x and y given the cholesky decomposition of Σ. Mahalanobis returns NaN if the linear solve fails.
See https://en.wikipedia.org/wiki/Mahalanobis_distance for more information.
func Mean ¶
Mean computes the weighted mean of the data set.
sum_i {w_i * x_i} / sum_i {w_i}
If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: The mean of the samples is 3.5500 The weighted mean of the samples is 1.9000 The mean of x2 is 1.9000 The weights act as if there were more samples of that number
func MeanStdDev ¶
MeanStdDev returns the sample mean and unbiased standard deviation When weights sum to 1 or less, a biased variance estimator should be used.
func MeanVariance ¶
MeanVariance computes the sample mean and unbiased variance, where the mean and variance are
\sum_i w_i * x_i / (sum_i w_i) \sum_i w_i (x_i  mean)^2 / (sum_i w_i  1)
respectively. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights). When weights sum to 1 or less, a biased variance estimator should be used.
func Mode ¶
Mode returns the most common value in the dataset specified by x and the given weights. Strict float64 equality is used when comparing values, so users should take caution. If several values are the mode, any of them may be returned.
func Moment ¶
Moment computes the weighted n^th moment of the samples,
E[(x  μ)^N]
No degrees of freedom correction is done. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
func MomentAbout ¶
MomentAbout computes the weighted n^th weighted moment of the samples about the given mean \mu,
E[(x  μ)^N]
No degrees of freedom correction is done. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
func PopMeanStdDev ¶
PopMeanStdDev returns the sample mean and biased standard deviation (also known as "population standard deviation").
func PopMeanVariance ¶
PopMeanVariance computes the sample mean and biased variance (also known as "population variance"), where the mean and variance are
\sum_i w_i * x_i / (sum_i w_i) \sum_i w_i (x_i  mean)^2 / (sum_i w_i)
respectively. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
func PopStdDev ¶
PopStdDev returns the population standard deviation, i.e., a square root of the biased variance estimate.
Example ¶
Output: The standard deviation of the population is 7.8740 The weighted standard deviation of the population is 10.2754
func PopVariance ¶
PopVariance computes the unbiased weighted sample variance:
\sum_i w_i (x_i  mean)^2 / (sum_i w_i)
If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
Example ¶
Output: The biased variance of the samples is 62.0000 The weighted biased variance of the samples is 105.5833
func Quantile ¶
func Quantile(p float64, c CumulantKind, x, weights []float64) float64
Quantile returns the sample of x such that x is greater than or equal to the fraction p of samples. The exact behavior is determined by the CumulantKind, and p should be a number between 0 and 1. Quantile is theoretically the inverse of the CDF function, though it may not be the actual inverse for all values p and CumulantKinds.
The x data must be sorted in increasing order. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
CumulantKind behaviors:
 Empirical: Returns the lowest value q for which q is greater than or equal to the fraction p of samples  LinInterp: Returns the linearly interpolated value
func RNoughtSquared ¶
RNoughtSquared returns the coefficient of determination defined as
R₀^2 = \sum_i w[i]*(beta*x[i])^2 / \sum_i w[i]*y[i]^2
for the line
y = beta*x
and the data in x and y with the given weights. RNoughtSquared should only be used for bestfit lines regressed through the origin.
The lengths of x and y must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
func ROC ¶
ROC returns paired false positive rate (FPR) and true positive rate (TPR) values corresponding to cutoff points on the receiver operator characteristic (ROC) curve obtained when y is treated as a binary classifier for classes with weights. The cutoff thresholds used to calculate the ROC are returned in thresh such that tpr[i] and fpr[i] are the true and false positive rates for y >= thresh[i].
The input y and cutoffs must be sorted, and values in y must correspond to values in classes and weights. SortWeightedLabeled can be used to sort y together with classes and weights.
For a given cutoff value, observations corresponding to entries in y greater than the cutoff value are classified as true, while those less than or equal to the cutoff value are classified as false. These assigned class labels are compared with the true values in the classes slice and used to calculate the FPR and TPR.
If weights is nil, all weights are treated as 1. If weights is not nil it must have the same length as y and classes, otherwise ROC will panic.
If cutoffs is nil or empty, all possible cutoffs are calculated, resulting in fpr and tpr having length one greater than the number of unique values in y. Otherwise fpr and tpr will be returned with the same length as cutoffs. floats.Span can be used to generate equally spaced cutoffs.
More details about ROC curves are available at https://en.wikipedia.org/wiki/Receiver_operating_characteristic
Example (AUC) ¶
Output: true positive rate: [0 0 0.5 0.5 1] false positive rate: [0 0.5 0.5 1 1] auc: 0.25
Example (EquallySpacedCutoffs) ¶
Output: true positive rate: [0.167 0.333 0.583 0.583 0.583 0.667 0.667 0.667 1] false positive rate: [0 0 0 1 1 1 1 1 1]
Example (Threshold) ¶
Output: true positive rate: [0 0.5 0.5 1 1] false positive rate: [0 0 0.5 0.5 1] cutoff thresholds: [+Inf 0.8 0.4 0.35 0.1]
Example (Unsorted) ¶
Output: true positive rate: [0 0.25 0.5 0.875 0.875 1 1] false positive rate: [0 0 0 0 0.6 0.6 1]
Example (Unweighted) ¶
Output: true positive rate: [0 0.25 0.5 0.75 0.75 1 1] false positive rate: [0 0 0 0 0.5 0.5 1]
Example (Weighted) ¶
Output: true positive rate: [0 0.25 0.5 0.875 0.875 1 1] false positive rate: [0 0 0 0 0.6 0.6 1]
func RSquared ¶
RSquared returns the coefficient of determination defined as
R^2 = 1  \sum_i w[i]*(y[i]  alpha  beta*x[i])^2 / \sum_i w[i]*(y[i]  mean(y))^2
for the line
y = alpha + beta*x
and the data in x and y with the given weights.
The lengths of x and y must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
func RSquaredFrom ¶
RSquaredFrom returns the coefficient of determination defined as
R^2 = 1  \sum_i w[i]*(estimate[i]  value[i])^2 / \sum_i w[i]*(value[i]  mean(values))^2
and the data in estimates and values with the given weights.
The lengths of estimates and values must be equal. If weights is nil then all of the weights are 1. If weights is not nil, then len(values) must equal len(weights).
func Skew ¶
Skew computes the skewness of the sample data. If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights). When weights sum to 1 or less, a biased variance estimator should be used.
func SortWeighted ¶
func SortWeighted(x, weights []float64)
SortWeighted rearranges the data in x along with their corresponding weights so that the x data are sorted. The data is sorted in place. Weights may be nil, but if weights is nonnil then it must have the same length as x.
func SortWeightedLabeled ¶
SortWeightedLabeled rearranges the data in x along with their corresponding weights and boolean labels so that the x data are sorted. The data is sorted in place. Weights and labels may be nil, if either is nonnil it must have the same length as x.
func StdDev ¶
StdDev returns the sample standard deviation.
Example ¶
Output: The standard deviation of the samples is 8.8034 The weighted standard deviation of the samples is 10.5733
func StdErr ¶
StdErr returns the standard error in the mean with the given values.
Example ¶
Output: The standard deviation is 10.5733 and there are 18 samples, so the mean is likely 4.1667 ± 2.4921.
func StdScore ¶
StdScore returns the standard score (a.k.a. zscore, zvalue) for the value x with the given mean and standard deviation, i.e.
(x  mean) / std
func Variance ¶
Variance computes the unbiased weighted sample variance:
\sum_i w_i (x_i  mean)^2 / (sum_i w_i  1)
If weights is nil then all of the weights are 1. If weights is not nil, then len(x) must equal len(weights). When weights sum to 1 or less, a biased variance estimator should be used.
Example ¶
Output: The variance of the samples is 77.5000 The weighted variance of the samples is 111.7941
Types ¶
type CC ¶
type CC struct {
// contains filtered or unexported fields
}
CC is a type for computing the canonical correlations of a pair of matrices. The results of the canonical correlation analysis are only valid if the call to CanonicalCorrelations was successful.
Example ¶
Output: corRaw = ⎡0.2192 0.3527 0.5828 0.3883⎤ ⎢0.3917 0.6448 0.7208 0.4837⎥ ⎢0.3022 0.7315 0.6680 0.4273⎥ ⎢ 0.2052 0.7479 0.5344 0.2499⎥ ⎢0.2098 0.4560 0.9102 0.3816⎥ ⎢0.3555 0.2615 0.4609 0.5078⎥ ⎣ 0.1281 0.2735 0.4418 0.3335⎦ corSph = ⎡ 0.0118 0.0525 0.2300 0.1363⎤ ⎢0.1810 0.3213 0.3814 0.1412⎥ ⎢ 0.0166 0.2241 0.0104 0.2235⎥ ⎢ 0.0346 0.5481 0.0034 0.1994⎥ ⎢ 0.0303 0.0956 0.7152 0.2039⎥ ⎢0.0298 0.0022 0.0739 0.3703⎥ ⎣0.1226 0.0746 0.3899 0.1541⎦ ccors = [0.9451 0.6787 0.5714 0.2010] pVecs = ⎡0.2574 0.0158 0.2122 0.0946⎤ ⎢0.4837 0.3837 0.1474 0.6597⎥ ⎢0.0801 0.3494 0.3287 0.2862⎥ ⎢ 0.1278 0.7337 0.4851 0.2248⎥ ⎢0.6969 0.4342 0.3603 0.0291⎥ ⎢0.0991 0.0503 0.6384 0.1022⎥ ⎣ 0.4260 0.0323 0.2290 0.6419⎦ qVecs = ⎡ 0.0182 0.1583 0.0067 0.9872⎤ ⎢0.2348 0.9483 0.1462 0.1554⎥ ⎢0.9701 0.2406 0.0252 0.0209⎥ ⎣ 0.0593 0.1330 0.9889 0.0291⎦ phiVs = ⎡0.0027 0.0093 0.0490 0.0155⎤ ⎢0.0429 0.0242 0.0361 0.1839⎥ ⎢1.2248 5.6031 5.8094 4.7927⎥ ⎢0.0044 0.3424 0.4470 0.1150⎥ ⎢0.0742 0.1193 0.1116 0.0022⎥ ⎢0.0233 0.1046 0.3853 0.0161⎥ ⎣ 0.0001 0.0005 0.0030 0.0082⎦ psiVs = ⎡ 0.0302 0.3002 0.0878 1.9583⎤ ⎢0.0065 0.0392 0.0118 0.0061⎥ ⎢0.0052 0.0046 0.0023 0.0008⎥ ⎣ 0.0020 0.0037 0.1293 0.1038⎦
func (*CC) CanonicalCorrelations ¶
CanonicalCorrelations performs a canonical correlation analysis of the input data x and y, columns of which should be interpretable as two sets of measurements on the same observations (rows). These observations are optionally weighted by weights. The result of the analysis is stored in the receiver if the analysis is successful.
Canonical correlation analysis finds associations between two sets of variables on the same observations by finding linear combinations of the two sphered datasets that maximize the correlation between them.
Some notation: let Xc and Yc denote the centered input data matrices x and y (column means subtracted from each column), let Sx and Sy denote the sample covariance matrices within x and y respectively, and let Sxy denote the covariance matrix between x and y. The sphered data can then be expressed as Xc * Sx^{1/2} and Yc * Sy^{1/2} respectively, and the correlation matrix between the sphered data is called the canonical correlation matrix, Sx^{1/2} * Sxy * Sy^{1/2}. In cases where S^{1/2} is ambiguous for some covariance matrix S, S^{1/2} is taken to be E * D^{1/2} * Eᵀ where S can be eigendecomposed as S = E * D * Eᵀ.
The canonical correlations are the correlations between the corresponding pairs of canonical variables and can be obtained with c.Corrs(). Canonical variables can be obtained by projecting the sphered data into the left and right eigenvectors of the canonical correlation matrix, and these eigenvectors can be obtained with c.Left(m, true) and c.Right(m, true) respectively. The canonical variables can also be obtained directly from the centered raw data by using the backtransformed eigenvectors which can be obtained with c.Left(m, false) and c.Right(m, false) respectively.
The first pair of left and right eigenvectors of the canonical correlation matrix can be interpreted as directions into which the respective sphered data can be projected such that the correlation between the two projections is maximized. The second pair and onwards solve the same optimization but under the constraint that they are uncorrelated (orthogonal in sphered space) to previous projections.
CanonicalCorrelations will panic if the inputs x and y do not have the same number of rows.
The slice weights is used to weight the observations. If weights is nil, each weight is considered to have a value of one, otherwise the length of weights must match the number of observations (rows of both x and y) or CanonicalCorrelations will panic.
More details can be found at https://en.wikipedia.org/wiki/Canonical_correlation or in Chapter 3 of Koch, Inge. Analysis of multivariate and highdimensional data. Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
func (*CC) CorrsTo ¶
CorrsTo returns the canonical correlations, using dst if it is not nil. If dst is not nil and len(dst) does not match the number of columns in the y input matrix, Corrs will panic.
func (*CC) LeftTo ¶
LeftTo returns the left eigenvectors of the canonical correlation matrix if spheredSpace is true. If spheredSpace is false it returns these eigenvectors backtransformed to the original data space.
If dst is empty, LeftTo will resize dst to be xd×yd. When dst is nonempty, LeftTo will panic if dst is not xd×yd. LeftTo will also panic if the receiver does not contain a successful CC.
func (*CC) RightTo ¶
RightTo returns the right eigenvectors of the canonical correlation matrix if spheredSpace is true. If spheredSpace is false it returns these eigenvectors backtransformed to the original data space.
If dst is empty, RightTo will resize dst to be yd×yd. When dst is nonempty, RightTo will panic if dst is not yd×yd. RightTo will also panic if the receiver does not contain a successful CC.
type CumulantKind ¶
type CumulantKind int
CumulantKind specifies the behavior for calculating the empirical CDF or Quantile
const ( // Empirical treats the distribution as the actual empirical distribution. Empirical CumulantKind = 1 // LinInterp linearly interpolates the empirical distribution between sample values, with a flat extrapolation. LinInterp CumulantKind = 4 )
List of supported CumulantKind values for the Quantile function. Constant values should match the R nomenclature. See https://en.wikipedia.org/wiki/Quantile#Estimating_the_quantiles_of_a_population
type PC ¶
type PC struct {
// contains filtered or unexported fields
}
PC is a type for computing and extracting the principal components of a matrix. The results of the principal components analysis are only valid if the call to PrincipalComponents was successful.
Example ¶
Output: variances = [0.1666 0.0207 0.0079 0.0019] proj = ⎡6.1686 1.4659⎤ ⎢5.6767 1.6459⎥ ⎢5.6699 1.3642⎥ ⎢5.5643 1.3816⎥ ⎢6.1734 1.3309⎥ ⎢6.7278 1.4021⎥ ⎢5.7743 1.1498⎥ ⎢6.0466 1.4714⎥ ⎢5.2709 1.3570⎥ ⎣5.7533 1.6207⎦
func (*PC) PrincipalComponents ¶
PrincipalComponents performs a weighted principal components analysis on the matrix of the input data which is represented as an n×d matrix a where each row is an observation and each column is a variable.
PrincipalComponents centers the variables but does not scale the variance.
The weights slice is used to weight the observations. If weights is nil, each weight is considered to have a value of one, otherwise the length of weights must match the number of observations or PrincipalComponents will panic.
PrincipalComponents returns whether the analysis was successful.
func (*PC) VarsTo ¶
VarsTo returns the column variances of the principal component scores, b * vecs, where b is a matrix with centered columns. Variances are returned in descending order. If dst is not nil it is used to store the variances and returned. Vars will panic if the receiver has not successfully performed a principal components analysis or dst is not nil and the length of dst is not min(n, d).
func (*PC) VectorsTo ¶
VectorsTo returns the component direction vectors of a principal components analysis. The vectors are returned in the columns of a d×min(n, d) matrix.
If dst is empty, VectorsTo will resize dst to be d×min(n, d). When dst is nonempty, VectorsTo will panic if dst is not d×min(n, d). VectorsTo will also panic if the receiver does not contain a successful PC.
Directories ¶
Path  Synopsis 

Package card provides cardinality estimation functions.

Package card provides cardinality estimation functions. 
Package combin implements routines involving combinatorics (permutations, combinations, etc.).

Package combin implements routines involving combinatorics (permutations, combinations, etc.). 
Package distmat provides probability distributions over matrices.

Package distmat provides probability distributions over matrices. 
Package distmv provides multivariate random distribution types.

Package distmv provides multivariate random distribution types. 
Package distuv provides univariate random distribution types.

Package distuv provides univariate random distribution types. 
Package mds provides multidimensional scaling functions.

Package mds provides multidimensional scaling functions. 
Package samplemv implements advanced sampling routines from explicit and implicit probability distributions.

Package samplemv implements advanced sampling routines from explicit and implicit probability distributions. 
Package sampleuv implements advanced sampling routines from explicit and implicit probability distributions.

Package sampleuv implements advanced sampling routines from explicit and implicit probability distributions. 
Package spatial provides spatial statistical functions.

Package spatial provides spatial statistical functions. 