Discrete Gradient (Matlab Style)
Discrete numerical gradient.
gradient(F, h1 = 1, h2 = 1)
F |
vector of function values, or a matrix of values of a function of two variables. |
h1 |
x-coordinates of grid points, or one value for the difference between grid points in x-direction. |
h2 |
y-coordinates of grid points, or one value for the difference between grid points in y-direction. |
Returns the numerical gradient of a vector or matrix as a vector or matrix of discrete slopes in x- (i.e., the differences in horizontal direction) and slopes in y-direction (the differences in vertical direction).
A single spacing value, h, specifies the spacing between points in
every direction, where the points are assumed equally spaced.
If F is a vector, one gradient vector will be returned.
If F is a matrix, a list with two components will be returned:
X |
numerical gradient/slope in x-direction. |
Y |
numerical gradient/slope in x-direction. |
where each matrix is of the same size as F.
TODO: If h2 is missing, it will not automatically be adapted.
x <- seq(0, 1, by=0.2) y <- c(1, 2, 3) (M <- meshgrid(x, y)) gradient(M$X^2 + M$Y^2) gradient(M$X^2 + M$Y^2, x, y) ## Not run: # One-dimensional example x <- seq(0, 2*pi, length.out = 100) y <- sin(x) f <- gradient(y, x) max(f - cos(x)) #=> 0.00067086 plot(x, y, type = "l", col = "blue") lines(x, cos(x), col = "gray", lwd = 3) lines(x, f, col = "red") grid() # Two-dimensional example v <- seq(-2, 2, by=0.2) X <- meshgrid(v, v)$X Y <- meshgrid(v, v)$Y Z <- X * exp(-X^2 - Y^2) image(v, v, t(Z)) contour(v, v, t(Z), col="black", add = TRUE) grid(col="white") grX <- gradient(Z, v, v)$X grY <- gradient(Z, v, v)$Y quiver(X, Y, grX, grY, scale = 0.2, col="blue") ## End(Not run)
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