# How to use linspec

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Ann Little on 4 Dec 2019
Answered: Walter Roberson on 4 Dec 2019
given the question: Determine z = 2x^3 + 3y^2 + 5, when x and y vary from -4 to 4 with a spacing of 1.
solution: x = linspace(-4,4,9);
y = linspace(-4,4,9);
z = 2*x^3+3*y^2+5
Question: why is the "n" value for the linspace of x and y = 9 and not 1?

Walter Roberson on 4 Dec 2019
The parameters of linspace are
1. starting value
2. ending value
3. total number of values to use. In the below discussion I will refer to this as n
The output values are constructed so that the starting value and ending value are used exactly, and the (n-2) intermediate values are spaced approximately (ending - starting)/(n-1) apart .
So with -4, -4, 9, the (9-2)=7 intermediate values are spaced (4-(-4))/(9-1) = 8/8 = 1 apart, so -4 (used exactly), then -4+1*1 = -3, -4+1*2 = -2, -4+1*3 = -1, -4+1*4 = 0, -4+1*5 = +1, -4+1*6 = +2, -4+1*7 = +3, then +4 (used exactly).
This is not exactly the code that is used; the exact code has some subtle differences in the last few bits due to floating point round-off in how it is really calculated.

galaxy on 4 Dec 2019
n = 9 when user want to generate integer cases of x in [-4, 4]
if n = 1, so x alway = 4, it is no meaning