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

C#
public static void g02bd( int n, int m, double[,] x, double[] xbar, double[] std, double[,] sspz, double[,] rz, out int ifail )

Visual Basic
Public Shared Sub g02bd ( _ n As Integer, _ m As Integer, _ x As Double(,), _ xbar As Double(), _ std As Double(), _ sspz As Double(,), _ rz As Double(,), _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void g02bd( int n, int m, array<double,2>^ x, array<double>^ xbar, array<double>^ std, array<double,2>^ sspz, array<double,2>^ rz, [OutAttribute] int% ifail )

F#
static member g02bd : n : int * m : int * x : float[,] * xbar : float[] * std : float[] * sspz : float[,] * rz : float[,] * ifail : int byref -> unit

Parameters

n: Type: System..::..Int32
On entry: $n$ , the number of observations or cases.

Constraint: $n \geq 2$ .

m: Type: System..::..Int32
On entry: $m$ , the number of variables.

Constraint: $m \geq 2$ .

x: Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: $dim1 \geq n$
On entry: $x [i - 1, j - 1]$ must be set to the value of $x_{i j}$ , the $i$ th observation on the $j$ th variable, for $i = 1, 2, \dots, n$ and $j = 1, 2, \dots, m$ .

xbar: Type: array<System..::..Double>[]()[][]
An array of size [m]
On exit: $xbar [j - 1]$ contains the mean value, ${\bar{x}}_{j}$ , of the $j$ th variable, for $j = 1, 2, \dots, m$ .

std: Type: array<System..::..Double>[]()[][]
An array of size [m]
On exit: the standard deviation, $s_{j}$ , of the $j$ th variable, for $j = 1, 2, \dots, m$ .

sspz: Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: $dim1 \geq m$
On exit: $sspz [j - 1, k - 1]$ is the cross-product about zero, ${\tilde{S}}_{j k}$ , for $j = 1, 2, \dots, m$ and $k = 1, 2, \dots, m$ .

rz: Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: $dim1 \geq m$
On exit: $rz [j - 1, k - 1]$ is the correlation-like coefficient, ${\tilde{R}}_{j k}$ , between the $j$ th and $k$ th variables, for $j = 1, 2, \dots, m$ and $k = 1, 2, \dots, m$ .

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

The input data consists of

n

observations for each of

m

variables, given as an array

[x_{i j}], i = 1, 2, \dots, n (n \geq 2), j = 1, 2, \dots, m (m \geq 2),

where

x_{i j}

is the

i

th observation on the

j

th variable.

The quantities calculated are:

(a)

Means:

{\bar{x}}_{j} = \frac{1}{n} \sum_{i = 1}^{n} x_{i j}, j = 1, 2, \dots, m .

(b)

Standard deviations:

s_{j} = \sqrt{\frac{1}{n - 1} \sum_{i = 1}^{n} {(x_{i j} - {\bar{x}}_{j})}^{2}}, j = 1, 2, \dots, m .

(c)

Sums of squares and cross-products about zero:

{\tilde{S}}_{j k} = \sum_{i = 1}^{n} x_{i j} x_{i k}, j, k = 1, 2, \dots, m .

(d)

Correlation-like coefficients:

{\tilde{R}}_{j k} = \frac{{\tilde{S}}_{j k}}{\sqrt{{\tilde{S}}_{j j} {\tilde{S}}_{k k}}}, j, k = 1, 2, \dots, m .

{\tilde{S}}_{j j}

{\tilde{S}}_{k k}

is zero,

{\tilde{R}}_{j k}

is set to zero.

References

None.

Error Indicators and Warnings

Errors or warnings detected by the method:

Some error messages may refer to parameters that are dropped from this interface (LDX, LDSSPZ, LDRZ) In these cases, an error in another parameter has usually caused an incorrect value to be inferred.

$ifail = 1$

On entry,

n < 2

$ifail = 2$

On entry,

m < 2

$ifail = -9000$: An error occured, see message report.
$ifail = -6000$: Invalid Parameters $〈value〉$
$ifail = -4000$: Invalid dimension for array $〈value〉$
$ifail = -8000$: Negative dimension for array $〈value〉$
$ifail = -6000$: Invalid Parameters $〈value〉$

Accuracy

g02bd does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large

n

Parallelism and Performance

None.

Further Comments

The time taken by g02bd depends on

n

and

m

The method uses a two-pass algorithm.

Example

This example reads in a set of data consisting of five observations on each of three variables. The means, standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for all three variables are then calculated and printed.

Example program (C#): g02bde.cs

Example program data: g02bde.d

Example program results: g02bde.r