design_matrix Function

public pure function design_matrix(order, intercept, x) result(c)

Computes the design matrix $X$ for the linear least-squares regression problem of $X \beta = y$, where $X$ is the matrix computed here, $\beta$ is the vector of coefficients to be determined, and $y$ is the vector of measured dependent variables.

See Also

• Wikipedia - Linear Regression
• Wikipedia - Vandermonde Matrix
• Wikipedia - Design Matrix

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int32),	intent(in)			::	order	The order of the equation to fit. This value must be at least one (linear equation), but can be higher as desired.
logical,	intent(in)			::	intercept	Set to true if the intercept is being computed as part of the regression; else, false.
real(kind=real64),	intent(in)			::	x(:)	An N-element array containing the independent variable measurement points.

Return Value real(kind=real64), allocatable, (:,:)

An N-by-K matrix where the results will be written. K must equal order + 1 in the event intercept is true; however, if intercept is false, K must equal order.