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NAG Toolbox: nag_correg_linregm_service_select (g02ce)
Purpose
nag_correg_linregm_service_select (g02ce) takes selected elements from two vectors (typically vectors of means and standard deviations) to form two smaller vectors, and selected rows and columns from two matrices (typically either matrices of sums of squares and cross-products of deviations from means and Pearson product-moment correlation coefficients, or matrices of sums of squares and cross-products about zero and correlation-like coefficients) to form two smaller matrices, allowing reordering of elements in the process.
Syntax
[
xbar2,
std2,
ssp2,
r2,
ifail] = g02ce(
xbar,
std,
ssp,
r,
korder, 'n',
n, 'm',
m)
[
xbar2,
std2,
ssp2,
r2,
ifail] = nag_correg_linregm_service_select(
xbar,
std,
ssp,
r,
korder, 'n',
n, 'm',
m)
Description
Input to the function consists of:
(a) |
A vector of means:
where is the number of input variables. |
(b) |
A vector of standard deviations:
|
(c) |
A matrix of sums of squares and cross-products of deviations from means:
|
(d) |
A matrix of correlation coefficients:
|
(e) |
The number of variables, , in the required subset, and their row/column numbers in the input data, ,
|
New vectors and matrices are output containing the following information:
(i) |
A vector of means:
|
(ii) |
A vector of standard deviations:
|
(iii) |
A matrix of sums of squares and cross-products of deviations from means:
|
(iv) |
A matrix of correlation coefficients:
|
Note: for sums of squares of cross-products of deviations about zero and correlation-like coefficients
and
should be replaced by
and
in the description of the input and output above.
References
None.
Parameters
Compulsory Input Parameters
- 1:
– double array
-
must be set to , the mean of variable , for .
- 2:
– double array
-
must be set to , the standard deviation of variable , for .
- 3:
– double array
-
ldssp, the first dimension of the array, must satisfy the constraint
.
must be set to the sum of cross-products of deviations from means (or about zero, ) for variables and , for and .
- 4:
– double array
-
ldr, the first dimension of the array, must satisfy the constraint
.
must be set to the Pearson product-moment correlation coefficient (or the correlation-like coefficient, ) for variables and , for and .
- 5:
– int64int32nag_int array
-
must be set to the number of the original variable which is to be the th variable in the output vectors and matrices, for .
Constraint:
, for .
Optional Input Parameters
- 1:
– int64int32nag_int scalar
-
Default:
the dimension of the arrays
xbar,
std and the first dimension of the arrays
ssp,
r and the second dimension of the arrays
ssp,
r. (An error is raised if these dimensions are not equal.)
, the number of variables in the input data.
Constraint:
.
- 2:
– int64int32nag_int scalar
-
Default:
the dimension of the array
korder.
The number of variables , required in the reduced vectors and matrices.
Constraint:
.
Output Parameters
- 1:
– double array
-
The mean of variable
,
, where
, for
. (The array
xbar2 must differ from
xbar and
std.)
- 2:
– double array
-
The standard deviation of variable
,
, where
, for
. (The array
std2 must differ from both
xbar and
std.)
- 3:
– double array
-
contains the value of
, where
and
, for
and
. (The array
ssp2 must differ from both
ssp and
r.)
That is to say: on exit, contains the sum of cross-products of deviations from means (or about zero, ).
- 4:
– double array
-
contains the value of
, where
and
, for
and
. (The array
r2 must differ from both
ssp and
r.)
That is to say: on exit, contains the Pearson product-moment coefficient (or the correlation-like coefficient, ).
- 5:
– int64int32nag_int scalar
unless the function detects an error (see
Error Indicators and Warnings).
Error Indicators and Warnings
Errors or warnings detected by the function:
-
-
-
-
-
-
On entry, | , |
or | , |
or | , |
or | . |
-
-
On entry, | , |
or | for some . |
-
An unexpected error has been triggered by this routine. Please
contact
NAG.
-
Your licence key may have expired or may not have been installed correctly.
-
Dynamic memory allocation failed.
Accuracy
Not applicable.
Further Comments
The time taken by nag_correg_linregm_service_select (g02ce) depends on and .
The function is intended primarily for use when a subset of variables from a larger set of variables is to be used in a regression, and is described accordingly. There is however no reason why the function should not also be used to select specific rows and columns from vectors and arrays which contain any other non-statistical information; the matrices need not be symmetric.
The function may be used either with sums of squares and cross-products of deviations from means and Pearson product-moment correlation coefficients in connection with a regression involving a constant, or with sums of squares and cross-products about zero and correlation-like coefficients in connection with a regression with no constant.
Example
This example reads in the means, standard deviations, sums of squares and cross-products, and correlation coefficients for four variables. New vectors and matrices are created containing the means, standard deviations, sums of squares and cross-products, and correlation coefficients for the fourth, first and second variables (in that order). Finally these new vectors and matrices are printed.
Open in the MATLAB editor:
g02ce_example
function g02ce_example
fprintf('g02ce example results\n\n');
xbar = [ 5.8; 2.8; 1.8; 5.4 ];
std = [ 5.0695; 1.924; 2.5884; 4.98 ];
ssp = [102.8, -29.2, -14.2, -57.6;
-29.2, 14.8, -6.2, 6.4;
-14.2, -6.2, 28.6, 42.4;
-57.6, 6.4, 42.4, 99.2 ];
r = [ 1, -0.7486, -0.2619, -0.5704;
-0.7486, 1, -0.3014, 0.167;
-0.2619, -0.3014, 1, 0.796;
-0.5704, 0.167, 0.796, 1 ];
korder = [int64(4); 1; 2];
fprintf('Original vector xbar : ');
fprintf(' %10.4f', xbar);
fprintf('\n\nOriginal vector std : ');
fprintf(' %10.4f', std);
fprintf('\n\n');
disp('Original matrix SSP :');
disp(ssp);
disp('Original matrix R :');
disp(r);
[xbar2, std2, ssp2, r2, ifail] = ...
g02ce( ...
xbar, std, ssp, r, korder);
fprintf('New vector xbar2 : ');
fprintf(' %10.4f', xbar2);
fprintf('\n\nNew vector std2 : ');
fprintf(' %10.4f', std2);
fprintf('\n\n');
disp('New matrix ssp2 :');
disp(ssp2);
disp('New matrix r2 :');
disp(r2);
g02ce example results
Original vector xbar : 5.8000 2.8000 1.8000 5.4000
Original vector std : 5.0695 1.9240 2.5884 4.9800
Original matrix SSP :
102.8000 -29.2000 -14.2000 -57.6000
-29.2000 14.8000 -6.2000 6.4000
-14.2000 -6.2000 28.6000 42.4000
-57.6000 6.4000 42.4000 99.2000
Original matrix R :
1.0000 -0.7486 -0.2619 -0.5704
-0.7486 1.0000 -0.3014 0.1670
-0.2619 -0.3014 1.0000 0.7960
-0.5704 0.1670 0.7960 1.0000
New vector xbar2 : 5.4000 5.8000 2.8000
New vector std2 : 4.9800 5.0695 1.9240
New matrix ssp2 :
99.2000 -57.6000 6.4000
-57.6000 102.8000 -29.2000
6.4000 -29.2000 14.8000
New matrix r2 :
1.0000 -0.5704 0.1670
-0.5704 1.0000 -0.7486
0.1670 -0.7486 1.0000
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