Sample Problems > Usage > Functions > floor

{ FLOOR_CEILING.PDE

This script demonstrates the FLOOR and CEILING functions.

This are provided as alternatives to the MIN and MAX functions that have continuous derivatives.

}

TITLE "FLOOR and CEILING Functions"

{ No variables, no equations }

DEFINITIONS

! floor

fmax = max(x, 0)

floor1 = floor(x, 0, 0.1)

floor2 = floor(x, 0, 0.2)

! ceiling

cmin = min(x, 0)

ceil1 = ceiling(x, 0, 0.1)

ceil2 = ceiling(x, 0, 0.2)

{ We need a plot domain even if no system variables : }

BOUNDARIES

region 1

start(-1,-0.1) line to (1,-0.1) to (1,0.1) to (-1,0.1) to close

PLOTS

elevation(fmax, floor1, floor2) from(-0.5, 0) to (0.5, 0) as "Floor compared to Max"

elevation(dx(fmax), dx(floor1), dx(floor2)) from(-0.5, 0) to (0.5, 0) as "dx(Floor) compared to dx(Max)"

elevation(cmin, ceil1, ceil2) from(-0.5, 0) to (0.5, 0) as "Ceiling compared to Min"

elevation(dx(cmin), dx(ceil1), dx(ceil2)) from(-0.5, 0) to (0.5,0) as "dx(Ceiling) compared to dx(Min)"

END

floor_ceiling