The routine may be called by the names g02bdf or nagf_correg_coeffs_zero.
The input data consists of observations for each of variables, given as an array
where is the th observation on the th variable.
The quantities calculated are:
(c)Sums of squares and cross-products about zero:
If or is zero, is set to zero.
1: – IntegerInput
On entry: , the number of observations or cases.
2: – IntegerInput
On entry: , the number of variables.
3: – Real (Kind=nag_wp) arrayInput
On entry: must be set to the value of , the th observation on the th variable, for and .
4: – IntegerInput
On entry: the first dimension of the array x as declared in the (sub)program from which g02bdf is called.
5: – Real (Kind=nag_wp) arrayOutput
On exit: contains the mean value, , of the th variable, for .
6: – Real (Kind=nag_wp) arrayOutput
On exit: the standard deviation,
, of the th variable, for .
7: – Real (Kind=nag_wp) arrayOutput
On exit: is the cross-product about zero, , for and .
8: – IntegerInput
On entry: the first dimension of the array sspz as declared in the (sub)program from which g02bdf is called.
9: – Real (Kind=nag_wp) arrayOutput
On exit: is the correlation-like coefficient, , between the th and th variables, for and .
10: – IntegerInput
On entry: the first dimension of the array rz as declared in the (sub)program from which g02bdf is called.
11: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, .
On entry, .
On entry, and .
On entry, and .
On entry, and .
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
g02bdf does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large .
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
g02bdf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
g02bdf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The time taken by g02bdf depends on and .
The routine uses a two-pass algorithm.
Internal changes have been made to this routine as follows:
At Mark 27: The algorithm underlying this routine was altered to improve efficiency for large problem sizes on a multi-threaded system.
For details of all known issues which have been reported for the NAG Library please refer to the Known Issues.
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.