NAG FL Interface
g02bbf (coeffs_pearson_miss_case)
1
Purpose
g02bbf computes means and standard deviations of variables, sums of squares and crossproducts of deviations from means, and Pearson productmoment correlation coefficients for a set of data omitting completely any cases with a missing observation for any variable.
2
Specification
Fortran Interface
Subroutine g02bbf ( 
n, m, x, ldx, miss, xmiss, xbar, std, ssp, ldssp, r, ldr, ncases, ifail) 
Integer, Intent (In) 
:: 
n, m, ldx, ldssp, ldr 
Integer, Intent (Inout) 
:: 
miss(m), ifail 
Integer, Intent (Out) 
:: 
ncases 
Real (Kind=nag_wp), Intent (In) 
:: 
x(ldx,m) 
Real (Kind=nag_wp), Intent (Inout) 
:: 
xmiss(m), ssp(ldssp,m), r(ldr,m) 
Real (Kind=nag_wp), Intent (Out) 
:: 
xbar(m), std(m) 

C Header Interface
#include <nag.h>
void 
g02bbf_ (const Integer *n, const Integer *m, const double x[], const Integer *ldx, Integer miss[], double xmiss[], double xbar[], double std[], double ssp[], const Integer *ldssp, double r[], const Integer *ldr, Integer *ncases, Integer *ifail) 

C++ Header Interface
#include <nag.h> extern "C" {
void 
g02bbf_ (const Integer &n, const Integer &m, const double x[], const Integer &ldx, Integer miss[], double xmiss[], double xbar[], double std[], double ssp[], const Integer &ldssp, double r[], const Integer &ldr, Integer &ncases, Integer &ifail) 
}

The routine may be called by the names g02bbf or nagf_correg_coeffs_pearson_miss_case.
3
Description
The input data consist of
$n$ observations for each of
$m$ variables, given as an array
where
${x}_{ij}$ is the
$i$th observation on the
$j$th variable. In addition, each of the
$m$ variables may optionally have associated with it a value which is to be considered as representing a missing observation for that variable; the missing value for the
$j$th variable is denoted by
$x{m}_{j}$. Missing values need not be specified for all variables.
Let
${w}_{i}=0$ if observation
$i$ contains a missing value for any of those variables for which missing values have been declared, i.e., if
${x}_{ij}=x{m}_{j}$ for any
$j$ for which an
$x{m}_{j}$ has been assigned (see also
Section 7); and
${w}_{i}=1$ otherwise, for
$\mathit{i}=1,2,\dots ,n$.
The quantities calculated are:

(a)Means:

(b)Standard deviations:

(c)Sums of squares and crossproducts of deviations from means:

(d)Pearson productmoment correlation coefficients:
If ${S}_{jj}$ or ${S}_{kk}$ is zero, ${R}_{jk}$ is set to zero.
4
References
None.
5
Arguments

1:
$\mathbf{n}$ – Integer
Input

On entry: $n$, the number of observations or cases.
Constraint:
${\mathbf{n}}\ge 2$.

2:
$\mathbf{m}$ – Integer
Input

On entry: $m$, the number of variables.
Constraint:
${\mathbf{m}}\ge 2$.

3:
$\mathbf{x}\left({\mathbf{ldx}},{\mathbf{m}}\right)$ – Real (Kind=nag_wp) array
Input

On entry: ${\mathbf{x}}\left(\mathit{i},\mathit{j}\right)$ must be set to ${x}_{\mathit{i}\mathit{j}}$, the value of the $\mathit{i}$th observation on the $\mathit{j}$th variable, for $\mathit{i}=1,2,\dots ,n$ and $\mathit{j}=1,2,\dots ,m$.

4:
$\mathbf{ldx}$ – Integer
Input

On entry: the first dimension of the array
x as declared in the (sub)program from which
g02bbf is called.
Constraint:
${\mathbf{ldx}}\ge {\mathbf{n}}$.

5:
$\mathbf{miss}\left({\mathbf{m}}\right)$ – Integer array
Input/Output

On entry:
${\mathbf{miss}}\left(j\right)$ must be set equal to
$1$ if a missing value,
$x{m}_{j}$, is to be specified for the
$j$th variable in the array
x, or set equal to
$0$ otherwise. Values of
miss must be given for all
$m$ variables in the array
x.
On exit: the array
miss is overwritten by the routine, and the information it contained on entry is lost.

6:
$\mathbf{xmiss}\left({\mathbf{m}}\right)$ – Real (Kind=nag_wp) array
Input/Output

On entry:
${\mathbf{xmiss}}\left(j\right)$ must be set to the missing value,
$x{m}_{j}$, to be associated with the
$j$th variable in the array
x, for those variables for which missing values are specified by means of the array
miss (see
Section 7).
On exit: the array
xmiss is overwritten by the routine, and the information it contained on entry is lost.

7:
$\mathbf{xbar}\left({\mathbf{m}}\right)$ – Real (Kind=nag_wp) array
Output

On exit: the mean value,
${\overline{x}}_{\mathit{j}}$, of the $\mathit{j}$th variable, for $\mathit{j}=1,2,\dots ,m$.

8:
$\mathbf{std}\left({\mathbf{m}}\right)$ – Real (Kind=nag_wp) array
Output

On exit: the standard deviation,
${s}_{\mathit{j}}$, of the $\mathit{j}$th variable, for $\mathit{j}=1,2,\dots ,m$.

9:
$\mathbf{ssp}\left({\mathbf{ldssp}},{\mathbf{m}}\right)$ – Real (Kind=nag_wp) array
Output

On exit: ${\mathbf{ssp}}\left(\mathit{j},\mathit{k}\right)$ is the crossproduct of deviations ${S}_{\mathit{j}\mathit{k}}$, for $\mathit{j}=1,2,\dots ,m$ and $\mathit{k}=1,2,\dots ,m$.

10:
$\mathbf{ldssp}$ – Integer
Input

On entry: the first dimension of the array
ssp as declared in the (sub)program from which
g02bbf is called.
Constraint:
${\mathbf{ldssp}}\ge {\mathbf{m}}$.

11:
$\mathbf{r}\left({\mathbf{ldr}},{\mathbf{m}}\right)$ – Real (Kind=nag_wp) array
Output

On exit: ${\mathbf{r}}\left(\mathit{j},\mathit{k}\right)$ is the productmoment correlation coefficient ${R}_{\mathit{j}\mathit{k}}$ between the $\mathit{j}$th and $\mathit{k}$th variables, for $\mathit{j}=1,2,\dots ,m$ and $\mathit{k}=1,2,\dots ,m$.

12:
$\mathbf{ldr}$ – Integer
Input

On entry: the first dimension of the array
r as declared in the (sub)program from which
g02bbf is called.
Constraint:
${\mathbf{ldr}}\ge {\mathbf{m}}$.

13:
$\mathbf{ncases}$ – Integer
Output

On exit: the number of cases actually used in the calculations (when cases involving missing values have been eliminated).

14:
$\mathbf{ifail}$ – 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
$0$ is recommended.
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).
6
Error 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:
 ${\mathbf{ifail}}=1$

On entry, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{n}}\ge 2$.
 ${\mathbf{ifail}}=2$

On entry, ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{m}}\ge 2$.
 ${\mathbf{ifail}}=3$

On entry, ${\mathbf{ldr}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{ldr}}\ge {\mathbf{m}}$.
On entry, ${\mathbf{ldssp}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{ldssp}}\ge {\mathbf{m}}$.
On entry, ${\mathbf{ldx}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{ldx}}\ge {\mathbf{n}}$.
 ${\mathbf{ifail}}=4$

After observations with missing values were omitted, no cases remained.
 ${\mathbf{ifail}}=5$

After observations with missing values were omitted, only one case remained.
 ${\mathbf{ifail}}=99$
An unexpected error has been triggered by this routine. Please
contact
NAG.
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.
7
Accuracy
g02bbf does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large $n$.
You are warned of the need to exercise extreme care in your selection of missing values.
g02bbf treats all values in the inclusive range
$\left(1\pm {0.1}^{\left({\mathbf{x02bef}}2\right)}\right)\times {xm}_{j}$, where
${\mathit{xm}}_{j}$ is the missing value for variable
$j$ specified in
xmiss.
You must therefore ensure that the missing value chosen for each variable is sufficiently different from all valid values for that variable so that none of the valid values fall within the range indicated above.
8
Parallelism and Performance
g02bbf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
g02bbf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementationspecific information.
The time taken by g02bbf depends on $n$ and $m$, and the occurrence of missing values.
The routine uses a twopass algorithm.
9.1
Internal Changes
Internal changes have been made to this routine as follows:
 At Mark 27: The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multithreaded system.
For details of all known issues which have been reported for the NAG Library please refer to the
Known Issues.
10
Example
This example reads in a set of data consisting of five observations on each of three variables. Missing values of $0.0$ are declared for the first and third variables; no missing value is specified for the second variable. The means, standard deviations, sums of squares and crossproducts of deviations from means, and Pearson productmoment correlation coefficients for all three variables are then calculated and printed, omitting completely all cases containing missing values; cases $3$ and $4$ are therefore eliminated, leaving only three cases in the calculations.
10.1
Program Text
10.2
Program Data
10.3
Program Results