Sine example
This is a simple DACE example using the sine function, which demonstrates:
- How to load DACE.jl
- How to initialise the DACE library
- How to create a
DAobject - How to compute the sine of a
DAobject - How to print a
DAobject to screen - How to evaluate a
DAobject
Install dependencies
Make sure the required packages are installed
using Pkg
Pkg.add("DACE")Using DACE
Write
using DACEto load DACE functions and objects into our script.
Initialise DACE for 20th-order computations in 1 variable
DACE.init(20, 1)Initialise x as a DA object
x = DACE.DA(1, 1) I COEFFICIENT ORDER EXPONENTS
1 1.0000000000000000e+00 1 1
------------------------------------------------
Initialise y as the Taylor expansion of sin(x)
y = sin(x) I COEFFICIENT ORDER EXPONENTS
1 1.0000000000000000e+00 1 1
2 -1.6666666666666666e-01 3 3
3 8.3333333333333332e-03 5 5
4 -1.9841269841269841e-04 7 7
5 2.7557319223985893e-06 9 9
6 -2.5052108385441720e-08 11 11
7 1.6059043836821616e-10 13 13
8 -7.6471637318198174e-13 15 15
9 2.8114572543455210e-15 17 17
10 -8.2206352466243310e-18 19 19
------------------------------------------------
Print x and y to screen
println("x")
print(x)
println("y = sin(x)")
print(y)x
I COEFFICIENT ORDER EXPONENTS
1 1.0000000000000000e+00 1 1
------------------------------------------------
y = sin(x)
I COEFFICIENT ORDER EXPONENTS
1 1.0000000000000000e+00 1 1
2 -1.6666666666666666e-01 3 3
3 8.3333333333333332e-03 5 5
4 -1.9841269841269841e-04 7 7
5 2.7557319223985893e-06 9 9
6 -2.5052108385441720e-08 11 11
7 1.6059043836821616e-10 13 13
8 -7.6471637318198174e-13 15 15
9 2.8114572543455210e-15 17 17
10 -8.2206352466243310e-18 19 19
------------------------------------------------
Evaluate y at 1.0 and compare with the builtin sin function.
println(" y(1.0) = $(DACE.evalScalar(y, 1.0))")
println("sin(1.0) = $(sin(1.0))") y(1.0) = 0.8414709848078965
sin(1.0) = 0.8414709848078965
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