MatrixCorr

MatrixCorr [/COV][/DEGC] waveA [, waveB ]

The MatrixCorr operation computes the correlation, covariance or degree of correlation matrix for the input 1D wave(s).

If we denote elements of waveA by {x_i } and elements of waveB by {y_i }, then the correlation matrix for these waves is the vector product of the form:

$$\displaystyle \left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \\ \vdots \\ x_{n} \end{array}\right]\left[\begin{array}{lllll} y_{1} & y_{2} & y_{3} & \ldots & y_{n} \end{array}\right]^{*}=\left[\begin{array}{ccccc} x_{1} y_{1}^{*} & x_{1} y_{2}^{*} & x_{1} y_{3}^{*} & \ldots & x_{1} y_{n}^{*} \\ x_{2} y_{1}^{*} & x_{2} y_{2}^{*} & x_{2} y_{3}^{*} & & x_{2} y_{n}^{*} \\ x_{3} y_{1}^{*} & x_{3} y_{2}^{*} & x_{3} y_{3}^{*} & & x_{3} y_{n}^{*} \\ \vdots & & & & \\ x_{n} y_{1}^{*} & x_{n} y_{2}^{*} & x_{n} y_{3}^{*} & \cdots & x_{n} y_{n}^{*} \end{array}\right]$$

where * denotes complex conjugation. If you use the optional waveB, then the matrix is the cross correlation matrix. waveB must have the same length of waveA, but it does not have to be the same number type.

Flags

The flags in this operation are mutually exclusive; only one matrix can be generated at a time.

/COV	Calculates the covariance matrix.
	The covariance matrix for the same input is formed in a similar way after subtracting from each vector its mean value, and then dividing the resulting matrix elements by (n -1), where n is the number of elements of waveA.
	Results are stored in the M_Corr or M_Covar waves in the current data folder or in destWave, if specified.
/DEGC	Calculates the complex degree of correlation. The degree of correlation is defined by:
	$\displaystyle \operatorname{degC} =\frac{M\_Covar}{\sqrt{{Var}({ waveA }) \cdot {Var}({ waveB })}},$
	here M_Covar is the covariance matrix and Var(w ) is the variance of the wave.
	The complex degree of correlation should satisfy:
	$\displaystyle 0 \leq\|\operatorname{deg} C\| \leq 1 .$
/DEST=destWave
	Specifies the output wave created by the operation.
	It is an error to specify the same wave as both destWave and waveA or waveB.
	When used in a function, this operation creates a real wave reference for the destination wave. See Automatic Creation of Wave References for details.
	/DEST flag was added in Igor Pro 10.00.
/FREE	Creates the wave destWave as a free wave.
	/FREE is allowed only in functions and only if destWave is a simple name or wave reference structure field.
	See Free Waves for more discussion.
	The /FREE flag was added in Igor Pro 10.00.

Examples

The covariance matrix calculation is equivalent to:

MatrixOP/O theCov=(subtractMean(waveA,0) x (subtractMean(waveB,0)^t))/(numpoints(waveA)-1)

References

Hayes, M.H., Statistical Digital Signal Processing And Modeling, 85 pp., John Wiley, 1996.

See Also

MatrixOP, variance