g02cff reorders the elements in two vectors (typically vectors of means and standard deviations), and the rows and columns in 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).

2 Specification

Fortran Interface

Subroutine g02cff (

n, korder, xbar, std, ssp, ldssp, r, ldr, kwork, ifail)

Integer, Intent (In)	::	n, korder(n), ldssp, ldr
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	kwork(n)
Real (Kind=nag_wp), Intent (Inout)	::	xbar(n), std(n), ssp(ldssp,n), r(ldr,n)

C Header Interface

#include <nag.h>

void	g02cff_ (const Integer n, const Integer korder[], double xbar[], double std[], double ssp[], const Integer ldssp, double r[], const Integer ldr, Integer kwork[], Integer ifail)

The routine may be called by the names g02cff or nagf_correg_linregm_service_reorder.

3 Description

Input to the routine consists of:

(a)A list of the order in which the $n$ variables are to be arranged on exit:

$i_{1}, i_{2}, i_{3}, \dots, i_{n} .$
(b)A vector of means:

$({\bar{x}}_{1}, {\bar{x}}_{2}, {\bar{x}}_{3}, \dots, {\bar{x}}_{n}) .$
(c)A vector of standard deviations:

$(s_{1}, s_{2}, s_{3}, \dots, s_{n}) .$

(d)A matrix of sums of squares and cross-products of deviations from means:

(\begin{array}{l} S_{11} & S_{12} & S_{13} & . & . & . & S_{1 n} \\ S_{21} & S_{22} & . \\ S_{31} & . \\ . & . \\ . & . \\ . & . \\ S_{n 1} & S_{n 2} & . & . & . & . & S_{n n} \end{array}) .

(e)A matrix of correlation coefficients:

(\begin{array}{l} R_{11} & R_{12} & R_{13} & . & . & . & R_{1 n} \\ R_{21} & R_{22} & . \\ R_{31} & . \\ . & . \\ . & . \\ . & . \\ R_{n 1} & R_{n 2} & . & . & . & . & R_{n n} \end{array}) .

On exit from the routine, these same vectors and matrices are reordered, in the manner specified, and contain the following information:

(i)The vector of means:

$({\bar{x}}_{i_{1}}, {\bar{x}}_{i_{2}}, {\bar{x}}_{i_{3}}, \dots, {\bar{x}}_{i_{n}}) .$
(ii)The vector of standard deviations:

$(s_{i_{1}}, s_{i_{2}}, s_{i_{3}}, \dots s_{i_{n}}) .$

(iii)The matrix of sums of squares and cross-products of deviations from means:

(\begin{array}{l} S_{i_{1} i_{1}} & S_{i_{1} i_{2}} & S_{i_{1} i_{3}} & . & . & . & S_{i_{1} i_{n}} \\ S_{i_{2} i_{1}} & S_{i_{2} i_{2}} & . \\ S_{i_{3} i_{1}} & . \\ . & . \\ . & . \\ . & . \\ S_{i_{n} i_{1}} & S_{i_{n} i_{2}} & . & . & . & . & S_{i_{n} i_{n}} \end{array}) .

(iv)The matrix of correlation coefficients:

(\begin{array}{l} R_{i_{1} i_{1}} & R_{i_{1} i_{2}} & R_{i_{1} i_{3}} & . & . & . & R_{i_{1} i_{n}} \\ R_{i_{2} i_{1}} & R_{i_{2} i_{2}} & . \\ R_{i_{3} i_{1}} & . \\ . & . \\ . & . \\ . & . \\ R_{i_{n} i_{1}} & R_{i_{n} i_{2}} & . & . & . & . & R_{i_{n} i_{n}} \end{array}) .

Note: for sums of squares of cross-products of deviations about zero and correlation-like coefficients

S_{i j}

and

R_{i j}

should be replaced by

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

and

{\tilde{R}}_{i j}

in the description of the input and output above.

4 References

None.

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of variables in the input data.

Constraint: $n \geq 2$ .
2: $korder (n)$ – Integer array Input: On entry: $korder (i)$ must be set to the number of the original variable which is to be the $i$ th variable in the re-arranged data, for $i = 1, 2, \dots, n$ .

Constraint: $1 \leq korder (i) \leq n$ , for $i = 1, 2, \dots, n$ .
3: $xbar (n)$ – Real (Kind=nag_wp) array Input/Output: On entry: $xbar (i)$ must be set to the mean of variable $i$ , for $i = 1, 2, \dots, n$ .

On exit: $xbar (i)$ contains the mean of variable $k$ where $k = korder (i)$ , for $i = 1, 2, \dots, n$ .
4: $std (n)$ – Real (Kind=nag_wp) array Input/Output: On entry: $std (i)$ must be set to the standard deviation of variable $i$ , for $i = 1, 2, \dots, n$ .

On exit: $std (i)$ contains the standard deviation of variable $k$ where $k = korder (i)$ , for $i = 1, 2, \dots, n$ .
5: $ssp (ldssp, n)$ – Real (Kind=nag_wp) array Input/Output: On entry: $ssp (i, j)$ must be set to the sum of cross-products of deviations from means $S_{i j}$ (or about zero ${\tilde{S}}_{i j}$ ) for variables $i$ and $j$ , for $i = 1, 2, \dots, n$ and $j = 1, 2, \dots, n$ .

On exit: $ssp (i, j)$ contains the sum of cross-products of deviations from means $S_{k l}$ (or about zero ${\tilde{S}}_{k l}$ ) for variables $k$ and $l$ , where $k = korder (i)$ , and $l = korder (j)$ , $i, j = 1, 2, \dots, n$ .
6: $ldssp$ – Integer Input: On entry: the first dimension of the array ssp as declared in the (sub)program from which g02cff is called.

Constraint: $ldssp \geq n$ .
7: $r (ldr, n)$ – Real (Kind=nag_wp) array Input/Output: On entry: $r (i, j)$ must be set to the Pearson product-moment correlation coefficient $R_{i j}$ (or the correlation-like coefficient ${\tilde{R}}_{i j}$ ) for variables $i$ and $j$ , for $i = 1, 2, \dots, n$ and $j = 1, 2, \dots, n$ .

On exit: $r (i, j)$ contains the Pearson product-moment correlation coefficient $R_{k l}$ (or the correlation-like coefficient ${\tilde{R}}_{k l}$ ) for variables $k$ and $l$ , where $k = korder (i)$ and $l = korder (j)$ , for $i = 1, 2, \dots, n$ and $j = 1, 2, \dots, n$ .
8: $ldr$ – Integer Input: On entry: the first dimension of the array r as declared in the (sub)program from which g02cff is called.

Constraint: $ldr \geq n$ .
9: $kwork (n)$ – Integer array Workspace
10: $ifail$ – 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 $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 2$ .

$ifail = 2$: On entry, $ldr = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $ldr \geq n$ .

On entry, $ldssp = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $ldssp \geq n$ .

$ifail = 3$: On entry, $korder (⟨ value ⟩) = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $1 \leq korder (i) \leq n$ , for $i = 1, 2, \dots, m$ .

$ifail = 4$: On entry, there is not a one-to-one correspondence between the old variables and the new variables; at least one of the original variables is not included in the new set, and consequently at least one other variable has been included more than once.

$ifail = - 99$: 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.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

g02cff is not threaded in any implementation.

9 Further Comments

The time taken by g02cff depends on

n

and the amount of re-arrangement involved.

The routine is intended primarily for use when a set of variables is to be reordered for use in a regression, and is described accordingly. There is however no reason why the routine should not also be used to reorder vectors and matrices which contain any other non-statistical information; the matrices need not be symmetric.

The routine 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.

10 Example

This example reads in the means, standard deviations, sums of squares and cross-products, and correlation coefficients for three variables. The vectors and matrices are reordered so that they contain the means, standard deviations, sums of squares and cross-products, and correlation coefficients for the first, third and second variables (in that order). Finally the reordered vectors and matrices are printed.

g02cf: FL CL CPP AD PY MB

NAG FL Interfaceg02cff (linregm_​service_​reorder)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g02cff (linregm_service_reorder)