Questions tagged [machine-precision]
For questions on the use of machine-precision real numbers (also known as floats), the numbers that can be directly manipulated through the underlying numerical capabilities of your computer system.
229
questions
3
votes
1
answer
98
views
problem in matching two sets of particles
I have been trying to simulate a simple system in which there are two set of particles. One kind of particles are localized on the boundary of a circle (shown in purple below), whereas the second kind ...
- 12.2k
7
votes
4
answers
351
views
Definition of $MachineEpsilon
$MachineEpsilon
x = 0.0000000000000001
% + 1
% - 1
As expected the final result equals zero, since x < MachineEpsilon ($2.22045\times10^{-16}$).
However, if I ...
- 234k
2
votes
2
answers
978
views
Export numeric data with preset decimal places
I have a table of pairs of numbers, each with 300 decimal places, which are all important. If saved using Export["data.dat", data] and then imported back via Import["data.dat"] - then the 300 decimal ...
CommunityBot
- 1
6
votes
4
answers
3k
views
Making a calculation with high precision
I would like to make the following calculation:
1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1
Mathematica 8 returns 0. The result is obviously not 0, but my ...
- 2,618
4
votes
1
answer
75
views
A simple syntax does not work
The code below does not work. Can anyone tell me why? Thanks!
...
- 270k
6
votes
1
answer
290
views
ConvexHullMesh fails with small numbers
When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors:
...
- 270k
8
votes
1
answer
931
views
Machine-Precision and Arbitrary Precision [closed]
What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision?
- 22.9k
16
votes
4
answers
456
views
Does Mathematica have an equivalent of C's nextafter?
In C (and many other programming languages), there is a function
double nextafter(double x, double y)
which takes two (IEEE 754) floating-point numbers and ...
- 61.5k
5
votes
1
answer
444
views
MachinePrecision versus $MachinePrecision in NDSolve
I'd like to understand why one of these inputs gives me an error and the other doesn't:
...
CommunityBot
- 1
3
votes
1
answer
3k
views
10
votes
2
answers
927
views
Why is Mathematica destroying this graph?
Here I have a picture of a function I graphed:
reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]];
Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic]
And here is ...
- 234k
4
votes
2
answers
3k
views
How do I overcome an Overflow?
I'm trying to calculate entropies for an absolutely giant system by counting states, and this means I have to use some obscenely large numbers. I'm running
...
- 124k
3
votes
1
answer
645
views
Mathematica Precisions vs Doubles in C/C++
I'm having a bit of an issue regarding numerical precision and I'm not sure how to deal with it.
I have a certain randomly generated matrix, say $M$, that I wish to compute the eigenvalues. The ...
- 233k
4
votes
1
answer
460
views
How to calculate accurate answer in Mathematica?
I accidentally discovered for myself, that Mathematica outputs inaccurate answer. For instance, if I take $\sin(2 \cdot \pi \cdot 0.5) = 0 $, then in Mathematica it is:
But if I calculate it on site ...
- 107k
4
votes
1
answer
111
views
My NIntegrate expression returns a wildly inaccurate value
I am trying to integrate a function using NIntegrate:
...
- 65.8k
2
votes
1
answer
362
views
How to tell Mathematica to treat all numbers (including those in decimal form) as arbitrary precision numbers
I have code that is essentially numerical. It uses functions like NDSolve and NIntegrate. But in most interesting cases, the ...
CommunityBot
- 1
10
votes
2
answers
2k
views
DeleteDuplicates[] does not work as expected on floating point values
Here is my simple example, and in this case function DeleteDuplicates does not work as expected.
I want to FindRoot of my ...
CommunityBot
- 1
10
votes
1
answer
395
views
Plot of $\sin(x^x)$ is missing from $x=143$
When plotting the graph of $\sin(x^x)$ I noticed that there is no plot from about $x=143$. I don't suppose there is a purely mathematical explanation for this?
So, why is there no graph in ...
- 124k
4
votes
0
answers
244
views
Classification problem using SVM methods
I am running SVM on mathematica and I a used this code with classes:
...
- 1,976
1
vote
1
answer
104
views
Wrong Limit[...] for inexact expressions
I noticed that Limit can return nonsense when using inexact parameters. In the following code, a is my (exact/inexact) parameter,...
- 753
7
votes
1
answer
268
views
Bug in ListPlot?
I want to check if this is a bug before I email WR about it.
I can't get ListPlot[] to make scatter plots over a very small area:
...
- 20.5k
5
votes
1
answer
235
views
Compilation, square roots, and integers
After looking at this question, particularly this answer, I wrote my own performance test, using the two functions
...
CommunityBot
- 1
11
votes
1
answer
143
views
Abnormal behavior of RealDigits[x]
In the Details of the document of RealDigits writes the following line:
RealDigits[x] normally returns a list of digits of ...
- 36.2k
3
votes
2
answers
122
views
Make mathematica "forget" numbers beyond the precision goal
I need Mathematica to remember only things upto two decimal places.
I'm currently using the unwieldy Floor[x*100]/100 which works but is there a better way to ...
- 48.6k
1
vote
1
answer
569
views
How to increase the precision to get the correct roots at the boundaries?
I want to solve an equation and Plot a graph of $\delta(\tau)$, where $0<\tau,\delta<1$. In principal $\delta(0)=1,\delta(1)=0$. However, when I solve the equation, the points near $\tau=1$ can'...
- 234k
17
votes
2
answers
343
views
CompiledFunction returns machine numbers smaller than $MinMachineNumber
When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
CommunityBot
- 1
0
votes
1
answer
146
views
N, machine precision and expression evaluation [closed]
I should state that I am a Mathematica beginner but I checked the questions about machine vs arbitrary precision (such as: this one ) and I continue to have the following issue while trying to ...
CommunityBot
- 1
11
votes
1
answer
689
views
Compilation of Total with compensated summation
I sometimes obtain an unexpected error when trying to call a compiled version of Total with compensated summation turned on. More specifically I define
...
CommunityBot
- 1
1
vote
0
answers
102
views
Odd plotting/math issue (could be a precision problem) [closed]
I've got a pretty odd error on a project I'm working on and was hoping to enlist some advice to fix it. The goal of this notebook is to show that I can eliminate the non-normalizable (blowing up part) ...
- 65.8k
0
votes
2
answers
94
views
Varying results from the Round function
My problem is simple. Consider the following.
...
CommunityBot
- 1
11
votes
2
answers
833
views
Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic
The following is the program.
...
- 124k
3
votes
2
answers
332
views
WorkingPrecision causes issue in the NIntegrate
I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
CommunityBot
- 1
10
votes
1
answer
310
views
Can Someone Please Explain Internal`$SameQTolerance?
If I input
Internal`$SameQTolerance
(* output = 0.30103 *)
which is the approximation of Log[10,2], or ...
CommunityBot
- 1
2
votes
1
answer
232
views
Precision of LinearModelFit with Polynomials
I have a Problem regarding the fit of given points with a polynomial up to the fifth degree.
tableofvalues=Import["tableofvalues.csv"]
My polynomial is:
...
- 40.6k
5
votes
2
answers
905
views
How to make the computer consider two numbers equal up to a certain precision
My problem is that I have a matrix A and the computer says is not Hermitian (self-adjoint). Then I check which elements make A ...
CommunityBot
- 1
26
votes
2
answers
2k
views
Different floating-point numbers equal?
Let's define two different numbers.
x = 1.
y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *)
Let's make sure they're different with ...
CommunityBot
- 1
1
vote
1
answer
165
views
Why does it matter at what point I replace?
I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points.
I use (LK4 is defined below, but its shape should have nothing to do with my problem)...
- 234k
2
votes
1
answer
295
views
0
votes
1
answer
172
views
Floating point arithmetic bug caused by Table[]
I was doing something fairly ordinary and noticed something I can't, for the life of me, explain. For context, I wanted to take make a function that takes an array of data like the one below, then an ...
- 1,635
2
votes
0
answers
161
views
Enforcing WorkingPrecision in NIntegrate
I have a very complicated 2D integral that I need to calculate repeatedly, and I'm trying to speed it up a bit, since at the moment it's taking a couple of days to complete.
One thing I've noticed is ...
- 199
3
votes
2
answers
1k
views
NIntegrate 2D highly oscillatory function
I am trying to integrate a function, and the error I get is greater than the result.
So I need to calculate
...
- 234k
6
votes
1
answer
235
views
Machine precision infinity
Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
CommunityBot
- 1
6
votes
0
answers
168
views
Can I force Mathematica to use machine precision? [duplicate]
Some built-in functions (like Exp) give an arbitrary precision result, even when the argument is a machine precision number. Example:
...
- 36k
1
vote
0
answers
65
views
Which operations preserve digit precision?
Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
- 2,517
3
votes
1
answer
522
views
Reasonable choice of MachinePrecision, AccuracyGoal and PrecisionGoal for NDSolve
I am trying to use this model for later use in FindFit:
...
CommunityBot
- 1
2
votes
1
answer
1k
views
How to increase significant digits in Mathematica
How can I increase the number of significant digits in Mathematica?
When I import a matrix, an element like 112.5276 is rounded to 112.528. I would like to increase the number of significant digits ...
- 88.3k
1
vote
2
answers
119
views
Decimal output from a simple equation
Let
x= 0.0000000000000000036;
y = 1 - x
If i type this in Mathematica the answer of y is 1. I want the answer to be as it ...
- 152k
4
votes
1
answer
176
views
How to map HoldForm?
I'm trying to compare between Sqrt[3.] and Sqrt[3]. To display the result, I mapped HoldForm to display the expressions on the left hand column (code at end), but it seems like Sqrt[3.] had been ...
- 25.6k
9
votes
1
answer
167
views
Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?
Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
- 233k
0
votes
1
answer
90
views
Unexpected behavior of subtraction with approximate numbers [duplicate]
I'm using the Table command to generate a list of values:
FullForm /@ Table[10. - x, {x, 2.7, 2.8, .1}]
and I get the ...
- 1