naginterfaces.library.correg.linregm_​service_​reorder

naginterfaces.library.correg.linregm_service_reorder(korder, xbar, std, ssp, r)

linregm_service_reorder reorders the elements in two vectors (typically vectors of means and standard deviations), and the rows and columns in two matrices (typically either matrices of sums of squares and cross-products of deviations from means and Pearson product-moment correlation coefficients, or matrices of sums of squares and cross-products about zero and correlation-like coefficients).

For full information please refer to the NAG Library document for g02cf

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g02/g02cff.html

Parameters

korderint, array-like, shape $\left(n\right)$

$korder[\text{i}-1]$ must be set to the number of the original variable which is to be the $\text{i}$th variable in the re-arranged data, for $\text{i}=1,2,\dots ,n$.

xbarfloat, array-like, shape $\left(n\right)$

$xbar[\text{i}-1]$ must be set to the mean of variable $\text{i}$, for $\text{i}=1,2,\dots ,n$.

stdfloat, array-like, shape $\left(n\right)$

$std[\text{i}-1]$ must be set to the standard deviation of variable $\text{i}$, for $\text{i}=1,2,\dots ,n$.

sspfloat, array-like, shape $(n,n)$

$ssp[\text{i}-1,\text{j}-1]$ must be set to the sum of cross-products of deviations from means $S_{\text{i}\text{j}}$ (or about zero ${\tilde{S}}_{\text{i}\text{j}}$) for variables $\text{i}$ and $\text{j}$, for $\text{j}=1,2,\dots ,n$, for $\text{i}=1,2,\dots ,n$.

rfloat, array-like, shape $(n,n)$

$r[\text{i}-1,\text{j}-1]$ must be set to the Pearson product-moment correlation coefficient $R_{\text{i}\text{j}}$ (or the correlation-like coefficient ${\tilde{R}}_{\text{i}\text{j}}$) for variables $\text{i}$ and $\text{j}$, for $\text{j}=1,2,\dots ,n$, for $\text{i}=1,2,\dots ,n$.

Returns

xbarfloat, ndarray, shape $\left(n\right)$

$xbar[\text{i}-1]$ contains the mean of variable $k$ where $k=korder[\text{i}-1]$, for $\text{i}=1,2,\dots ,n$.

stdfloat, ndarray, shape $\left(n\right)$

$std[\text{i}-1]$ contains the standard deviation of variable $k$ where $k=korder[\text{i}-1]$, for $\text{i}=1,2,\dots ,n$.

sspfloat, ndarray, shape $(n,n)$

$ssp[i-1,j-1]$ contains the sum of cross-products of deviations from means $S_{kl}$ (or about zero ${\tilde{S}}_{kl}$) for variables $k$ and $l$, where $k=korder[i-1]$, and $l=korder[j-1]$, $i,j=1,2,\dots ,n$.

rfloat, ndarray, shape $(n,n)$

$r[\text{i}-1,\text{j}-1]$ contains the Pearson product-moment correlation coefficient $R_{kl}$ (or the correlation-like coefficient ${\tilde{R}}_{kl}$) for variables $k$ and $l$, where $k=korder[\text{i}-1]$ and $l=korder[\text{j}-1]$, for $\text{j}=1,2,\dots ,n$, for $\text{i}=1,2,\dots ,n$.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 2$.

(errno $3$)

On entry, $korder[⟨value⟩]=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $1\le korder[i-1]\le n$, for $i=1,2,\dots ,m$.

(errno $4$)

On entry, there is not a one-to-one correspondence between the old variables and the new variables; at least one of the original variables is not included in the new set, and consequently at least one other variable has been included more than once.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

Input to the function consists of:

1. A list of the order in which the $n$ variables are to be arranged on exit:

   $$i_1,i_2,i_3,\dots ,i_n\text{.}$$

2. A vector of means:

   $$({\overline{x}}_1,{\overline{x}}_2,{\overline{x}}_3,\dots ,{\overline{x}}_n)\text{.}$$

3. A vector of standard deviations:

   $$(s_1,s_2,s_3,\dots ,s_n)\text{.}$$

4. A matrix of sums of squares and cross-products of deviations from means:

   $$\begin{array}{c}\left(\begin{array}{ccccccc}{S}_{11}& S_{12}& S_{13}& .& .& .& S_{1n}\\ S_{21}& S_{22}& & & & & .\\ S_{31}& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ S_{n1}& S_{n2}& .& .& .& .& S_{nn}\end{array}\right)\text{.}\end{array}$$

5. A matrix of correlation coefficients:

   $$\begin{array}{c}\left(\begin{array}{ccccccc}{R}_{11}& R_{12}& R_{13}& .& .& .& R_{1n}\\ R_{21}& R_{22}& & & & & .\\ R_{31}& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ R_{n1}& R_{n2}& .& .& .& .& R_{nn}\end{array}\right)\text{.}\end{array}$$

On exit from the function, these same vectors and matrices are reordered, in the manner specified, and contain the following information:

1. The vector of means:

   $$({\overline{x}}_{i_1},{\overline{x}}_{i_2},{\overline{x}}_{i_3},\dots ,{\overline{x}}_{i_n})\text{.}$$

2. The vector of standard deviations:

   $$(s_{i_1},s_{i_2},s_{i_3},\dots s_{i_n})\text{.}$$

3. The matrix of sums of squares and cross-products of deviations from means:

   $$\begin{array}{c}\left(\begin{array}{ccccccc}{S}_{i_1{i}_1}& S_{i_1{i}_2}& S_{i_1{i}_3}& .& .& .& S_{i_1{i}_n}\\ S_{i_2{i}_1}& S_{i_2{i}_2}& & & & & .\\ S_{i_3{i}_1}& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ S_{i_n{i}_1}& S_{i_n{i}_2}& .& .& .& .& S_{i_n{i}_n}\end{array}\right)\text{.}\end{array}$$

4. The matrix of correlation coefficients:

   $$\begin{array}{c}\left(\begin{array}{ccccccc}{R}_{i_1{i}_1}& R_{i_1{i}_2}& R_{i_1{i}_3}& .& .& .& R_{i_1{i}_n}\\ R_{i_2{i}_1}& R_{i_2{i}_2}& & & & & .\\ R_{i_3{i}_1}& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ .& & & & & & .\\ R_{i_n{i}_1}& R_{i_n{i}_2}& .& .& .& .& R_{i_n{i}_n}\end{array}\right)\text{.}\end{array}$$

Note: for sums of squares of cross-products of deviations about zero and correlation-like coefficients $S_{ij}$ and $R_{ij}$ should be replaced by ${\tilde{S}}_{ij}$ and ${\tilde{R}}_{ij}$ in the description of the input and output above.