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NAG Toolbox

NAG Toolbox: nag_correg_coeffs_zero (g02bd)

Purpose

nag_correg_coeffs_zero (g02bd) computes means and standard deviations of variables, sums of squares and cross-products about zero, and correlation-like coefficients for a set of data.

Syntax

[xbar, std, sspz, rz, ifail] = g02bd(x, 'n', n, 'm', m)
[xbar, std, sspz, rz, ifail] = nag_correg_coeffs_zero(x, 'n', n, 'm', m)
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.
The quantities calculated are:
(a) Means:
n
xj = 1/nxij,  j = 1,2,,m.
i = 1
x-j=1ni=1nxij,  j=1,2,,m.
(b) Standard deviations:
sj = sqrt(1/(n 1)i = 1n(xijxj)2),   j = 1,2,,m.
sj=1n- 1 i= 1n (xij-x-j) 2,   j= 1,2,,m.
(c) Sums of squares and cross-products about zero:
n
jk = xijxik,  j,k = 1,2,,m.
i = 1
S~jk=i=1nxijxik,  j,k=1,2,,m.
(d) Correlation-like coefficients:
jk = (jk)/(sqrt(jjkk)),   j,k = 1,2,,m.
R~jk=S~jkS~jjS~kk ,   j,k= 1,2,,m.
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 the value of xijxij, the iith observation on the jjth variable, for i = 1,2,,ni=1,2,,n and j = 1,2,,mj=1,2,,m.

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.

Input Parameters Omitted from the MATLAB Interface

ldx ldsspz ldrz

Output Parameters

1:     xbar(m) – double array
xbar(j)xbarj contains the mean value, xjx-j, of the jjth variable, for j = 1,2,,mj=1,2,,m.
2:     std(m) – double array
The standard deviation, sjsj, of the jjth variable, for j = 1,2,,mj=1,2,,m.
3:     sspz(ldsspz,m) – double array
ldsspzmldsspzm.
sspz(j,k)sspzjk is the cross-product about zero, jkS~jk, for j = 1,2,,mj=1,2,,m and k = 1,2,,mk=1,2,,m.
4:     rz(ldrz,m) – double array
ldrzmldrzm.
rz(j,k)rzjk is the correlation-like coefficient, jkR~jk, between the jjth and kkth variables, for j = 1,2,,mj=1,2,,m and k = 1,2,,mk=1,2,,m.
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,m < 2m<2.
  ifail = 3ifail=3
On entry,ldx < nldx<n,
orldsspz < mldsspz<m,
orldrz < mldrz<m.

Accuracy

nag_correg_coeffs_zero (g02bd) 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 (g02bd) depends on nn and mm.
The function uses a two-pass algorithm.

Example

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

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 g02bd_example
x = [2, 3, 3;
     4, 6, 4;
     9, 9, 0;
     0, 12, 2;
     12, -1, 5];
[xbar, std, sspz, rz, ifail] = g02bd(x)
 

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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