Is a scalar, it gives the spacing between points in the

y-direction. If HY is a vector, it must be of length SIZE(U,1) and

specifies the y-coordinates of the points.

L = DEL2(U,HX,HY,HZ,...), when U is N-D, uses the spacing given by

HX, HY, HZ, etc.

Class support for input U:

float: double, single

See also gradient, diff.

Overloaded methods:

cgnormfunction/del2

cglookuptwo/del2

Reference page in Help browser

doc del2

Correlation

<corrcoef> - Correlation coefficients.

CORRCOEF Correlation coefficients.

R=CORRCOEF(X) calculates a matrix R of correlation coefficients for

an array X, in which each row is an observation and each column is a

variable.

R=CORRCOEF(X,Y), where X and Y are column vectors, is the same as

R=CORRCOEF([X Y]). CORRCOEF converts X and Y to column vectors if they

are not, i.e., R=CORRCOEF(X,Y) is equivalent to R=CORRCOEF([X(:) Y(:)])

in that case.

If C is the covariance matrix, C = COV(X), then CORRCOEF(X) is

the matrix whose (i,j)'th element is

C(i,j)/SQRT(C(i,i)*C(j,j)).

[R,P]=CORRCOEF(...) also returns P, a matrix of p-values for testing

the hypothesis of no correlation. Each p-value is the probability

of getting a correlation as large as the observed value by random

chance, when the true correlation is zero. If P(i,j) is small, say

less than 0.05, then the correlation R(i,j) is significant.

[R,P,RLO,RUP]=CORRCOEF(...) also returns matrices RLO and RUP, of

the same size as R, containing lower and upper bounds for a 95%

confidence interval for each coefficient.

[...]=CORRCOEF(...,'PARAM1',VAL1,'PARAM2',VAL2,...) specifies additional

parameters and their values. Valid parameters are the following:

Parameter Value

'alpha' A number between 0 and 1 to specify a confidence

level of 100*(1-ALPHA)%. Default is 0.05 for 95%

confidence intervals.

'rows' Either 'all' (default) to use all rows, 'complete' to

use rows with no NaN values, or 'pairwise' to compute

R(i,j) using rows with no NaN values in column i or j.

The p-value is computed by transforming the correlation to create a t

statistic having N-2 degrees of freedom, where N is the number of rows

of X. The confidence bounds are based on an asymptotic normal

distribution of 0.5*log((1+R)/(1-R)), with an approximate variance equal

to 1/(N-3). These bounds are accurate for large samples when X has a

multivariate normal distribution. The 'pairwise' option can produce

an R matrix that is not positive definite.

Example: Generate random data having correlation between column 4

and the other columns.

x = randn(30,4); % uncorrelated data

x(:,4) = sum(x,2); % introduce correlation

[r,p] = corrcoef(x) % compute sample correlation and p-values

[i,j] = find(p<0.05); % find significant correlations

[i,j] % display their (row,col) indices

Class support for inputs X,Y:

float: double, single

See also cov, var, std.

Overloaded methods:

fints/corrcoef

Reference page in Help browser

doc corrcoef

<cov> - Covariance matrix.

COV Covariance matrix.

COV(X), if X is a vector, returns the variance. For matrices,

where each row is an observation, and each column a variable,

COV(X) is the covariance matrix. DIAG(COV(X)) is a vector of