# NAG FL Interfaceg02bwf (ssqmat_​to_​corrmat)

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## 1Purpose

g02bwf calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products of deviations about the mean.

## 2Specification

Fortran Interface
 Subroutine g02bwf ( m, r,
 Integer, Intent (In) :: m Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (Inout) :: r((m*m+m)/2)
#include <nag.h>
 void g02bwf_ (const Integer *m, double r[], Integer *ifail)
The routine may be called by the names g02bwf or nagf_correg_ssqmat_to_corrmat.

## 3Description

g02bwf calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products about the mean for observations on $m$ variables which can be computed by a single call to g02buf or a series of calls to g02btf. The sums of squares and cross-products are stored in an array packed by column and are overwritten by the correlation coefficients.
Let ${c}_{jk}$ be the cross-product of deviations from the mean, for $\mathit{j}=1,2,\dots ,m$ and $\mathit{k}=j,\dots ,m$, then the product-moment correlation coefficient, ${r}_{jk}$ is given by
 $rjk=cjkcjjckk .$
None.

## 5Arguments

1: $\mathbf{m}$Integer Input
On entry: $m$, the number of variables.
Constraint: ${\mathbf{m}}\ge 1$.
2: $\mathbf{r}\left(\left({\mathbf{m}}×{\mathbf{m}}+{\mathbf{m}}\right)/2\right)$Real (Kind=nag_wp) array Input/Output
On entry: contains the upper triangular part of the sums of squares and cross-products matrix of deviations from the mean. These are stored packed by column, i.e., the cross-product between variable $j$ and $k$, $k\ge j$, is stored in ${\mathbf{r}}\left(\left(k×\left(k-1\right)/2+j\right)\right)$.
On exit: the Pearson product-moment correlation coefficients.
These are stored packed by column corresponding to the input cross-products.
3: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $-1$ is recommended since useful values can be provided in some output arguments even when ${\mathbf{ifail}}\ne {\mathbf{0}}$ on exit. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
Note: in some cases g02bwf may return useful information.
${\mathbf{ifail}}=1$
On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m}}\ge 1$.
${\mathbf{ifail}}=2$
A variable has a zero variance. All correlations involving the variable with zero variance will be returned as zero.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

## 7Accuracy

The accuracy of g02bwf is entirely dependent upon the accuracy of the elements of array r.

## 8Parallelism and Performance

g02bwf is not threaded in any implementation.

g02bwf may also be used to calculate the correlations between parameter estimates from the variance-covariance matrix of the parameter estimates as is given by several routines in this chapter.

## 10Example

A program to calculate the correlation matrix from raw data. The sum of squares and cross-products about the mean are calculated from the raw data by a call to g02buf. The correlation matrix is then calculated from these values.

### 10.1Program Text

Program Text (g02bwfe.f90)

### 10.2Program Data

Program Data (g02bwfe.d)

### 10.3Program Results

Program Results (g02bwfe.r)