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NAG Toolbox

NAG Toolbox: nag_correg_coeffs_zero_subset (g02bk)

Purpose

nag_correg_coeffs_zero_subset (g02bk) computes means and standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for selected variables.

Syntax

[xbar, std, sspz, rz, ifail] = g02bk(x, kvar, 'n', n, 'm', m, 'nvars', nvars)
[xbar, std, sspz, rz, ifail] = nag_correg_coeffs_zero_subset(x, kvar, 'n', n, 'm', m, 'nvars', nvars)
Note: the interface to this routine has changed since earlier releases of the toolbox:
Mark 22: n has been made optional
.

Description

The input data consists of nn observations for each of mm variables, given as an array
[xij],  i = 1,2,,n (n2),j = 1,2,,m (m2),
[xij],  i=1,2,,n (n2),j=1,2,,m (m2),
where xijxij is the iith observation on the jjth variable, together with the subset of these variables, v1,v2,,vpv1,v2,,vp, for which information is required.
The quantities calculated are:
(a) Means:
xj = (i = 1nxij)/n,  j = v1,v2,,vp.
x-j=i=1nxijn,  j=v1,v2,,vp.
(b) Standard deviations:
sj = sqrt(1/(n 1)i = 1n(xijxj)2),   j = v1,v2,,vp.
sj=1n- 1 i= 1n (xij-x-j) 2,   j=v1,v2,,vp.
(c) Sums of squares and cross-products about zero:
n
jk = xijxik,  j,k = v1,v2,,vp.
i = 1
S~jk=i=1nxijxik,  j,k=v1,v2,,vp.
(d) Correlation-like coefficients:
jk = (jk)/(sqrt(jjkk)),   j,k = v1,v2,,vp.
R~jk=S~jkS~jjS~kk ,   j,k=v1,v2,,vp.
If jjS~jj or kkS~kk is zero, jkR~jk is set to zero.

References

None.

Parameters

Compulsory Input Parameters

1:     x(ldx,m) – double array
ldx, the first dimension of the array, must satisfy the constraint ldxnldxn.
x(i,j)xij must be set to xijxij, the value of the iith observation on the jjth variable, for i = 1,2,,ni=1,2,,n and j = 1,2,,mj=1,2,,m.
2:     kvar(nvars) – int64int32nag_int array
nvars, the dimension of the array, must satisfy the constraint 2nvarsm2nvarsm.
kvar(j)kvarj must be set to the column number in x of the jjth variable for which information is required, for j = 1,2,,pj=1,2,,p.
Constraint: 1kvar(j)m1kvarjm, for j = 1,2,,pj=1,2,,p.

Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The first dimension of the array x.
nn, the number of observations or cases.
Constraint: n2n2.
2:     m – int64int32nag_int scalar
Default: The second dimension of the array x.
mm, the number of variables.
Constraint: m2m2.
3:     nvars – int64int32nag_int scalar
Default: The dimension of the array kvar.
pp, the number of variables for which information is required.
Constraint: 2nvarsm2nvarsm.

Input Parameters Omitted from the MATLAB Interface

ldx ldsspz ldrz

Output Parameters

1:     xbar(nvars) – double array
The mean value, xjx-j, of the variable specified in kvar(j)kvarj, for j = 1,2,,pj=1,2,,p.
2:     std(nvars) – double array
The standard deviation, sjsj, of the variable specified in kvar(j)kvarj, for j = 1,2,,pj=1,2,,p.
3:     sspz(ldsspz,nvars) – double array
ldsspznvarsldsspznvars.
sspz(j,k)sspzjk is the cross-product about zero, jkS~jk, for the variables specified in kvar(j)kvarj and kvar(k)kvark, for j = 1,2,,pj=1,2,,p and k = 1,2,,pk=1,2,,p.
4:     rz(ldrz,nvars) – double array
ldrznvarsldrznvars.
rz(j,k)rzjk is the correlation-like coefficient, jkR~jk, between the variables specified in kvar(j)kvarj and kvar(k)kvark, for j = 1,2,,pj=1,2,,p and k = 1,2,,pk=1,2,,p.
5:     ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry,n < 2n<2.
  ifail = 2ifail=2
On entry,nvars < 2nvars<2,
ornvars > mnvars>m.
  ifail = 3ifail=3
On entry,ldx < nldx<n,
orldsspz < nvarsldsspz<nvars,
orldrz < nvarsldrz<nvars.
  ifail = 4ifail=4
On entry,kvar(j) < 1kvarj<1,
orkvar(j) > mkvarj>m for some j = 1,2,,nvarsj=1,2,,nvars.

Accuracy

nag_correg_coeffs_zero_subset (g02bk) does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large nn.

Further Comments

The time taken by nag_correg_coeffs_zero_subset (g02bk) depends on nn and pp.
The function uses a two-pass algorithm.

Example

function nag_correg_coeffs_zero_subset_example
x = [3, 3, 1, 2;
     6, 4, -1, 4;
     9, 0, 5, 9;
     12, 2, 0, 0;
     -1, 5, 4, 12];
kvar = [int64(4);1;2];
[xbar, std, sspz, rz, ifail] = nag_correg_coeffs_zero_subset(x, kvar)
 

xbar =

    5.4000
    5.8000
    2.8000


std =

    4.9800
    5.0695
    1.9235


sspz =

   245    99    82
    99   271    52
    82    52    54


rz =

    1.0000    0.3842    0.7129
    0.3842    1.0000    0.4299
    0.7129    0.4299    1.0000


ifail =

                    0


function g02bk_example
x = [3, 3, 1, 2;
     6, 4, -1, 4;
     9, 0, 5, 9;
     12, 2, 0, 0;
     -1, 5, 4, 12];
kvar = [int64(4);1;2];
[xbar, std, sspz, rz, ifail] = g02bk(x, kvar)
 

xbar =

    5.4000
    5.8000
    2.8000


std =

    4.9800
    5.0695
    1.9235


sspz =

   245    99    82
    99   271    52
    82    52    54


rz =

    1.0000    0.3842    0.7129
    0.3842    1.0000    0.4299
    0.7129    0.4299    1.0000


ifail =

                    0



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Chapter Introduction
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