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
5
votes
2
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585
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Why does N not upgrade precision? [duplicate]
Precision[N[1.0, 20]]
Precision[N[1, 20]]
MachinePrecision
20.
It would be so much more intuitive and less error prone, if <...
- 4,876
9
votes
1
answer
249
views
Plot3D discrepancy between MMA 10 and 11.3 - possible small numbers issue
I'm having some troubles with the following code I wrote in MMA 10 some time ago:
...
- 5,997
4
votes
1
answer
148
views
Machine Epsilon is not equal to $MachineEpsilon [duplicate]
I try to wrap my head around machine precision calculations in Mathematica (11.2, Linux). I do not understand the following behavior:
...
- 43
0
votes
2
answers
77
views
NIntegrate numerical accuracy and errors
I have the following 3x3 matrix
M = {{-I*ω + Γ/2, I*g1,
0}, {I*g1, -I*ω + κ1/2, I*g2}, {0,
I*g2, -I*ω + κ2/2}};
Finding the eigenvalues and eigenvectors
...
- 385
1
vote
1
answer
164
views
Performance Tuning - How can I make Mathematica to use less than certain digits number?
I would like to know if there is a way to make Mathematica to use at most certain digit number. For example, Suppose I want to calculate 2*Pi.
x=N[Pi]
y=2*x
...
0
votes
0
answers
104
views
Getting max precision limit overflow for a very simple calculation
I've never seen this error on such a simple calculation.
Does anybody know how to fix this annoying error?
user58873
5
votes
1
answer
78
views
Precision-related error in Audio
Bug introduced in 11.3 or earlier
CASE:4075745
I have been experimenting with using Audio and associated functions for data acquisition using an external sound ...
- 3,406
4
votes
1
answer
155
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The algorithm behind InputForm for machine numbers
There are several questions on this site about implementing fast CSV/TSV export for machine numbers without loss of precision. Recently I discovered that Export ...
- 61.5k
4
votes
0
answers
176
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Is it possible to get the original number from DecimalForm?
Bug introduced in 5.2 or earlier and persisting through 13.1.0
[CASE:4315787]
Wrong behavior of NumberForm (DecimalForm outputs ...
- 61.5k
21
votes
2
answers
3k
views
New General::munfl error and loss of precision
The latest version 11.3.0.0 of Mathematica returns Indeterminate when evaluating Log[Exp[-800.]]. I believe this was not ...
- 1,962
8
votes
1
answer
991
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What is wrong with importing Real32 or Real64?
Those who visit the chat might have seen the question of varkor. I'm posting it here in the hope that I have missed something.
Assume you have a real number
...
- 112k
1
vote
1
answer
66
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Precision Issue with Log
I have the following codes. Naturally, I expect to get zero. I thought it is due to some possible issues stated as "Machine-precision inputs can give numerically wrong answers on branch cuts:".
...
- 171
8
votes
2
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590
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how to get single, and quad Precision out of Mathematica which match Fortran result
by default, if a number has decimal . after it, then Mathematica will do computation using machine Precision, which on my PC (intel hardware) running windows 7 64 ...
- 137k
4
votes
1
answer
250
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Is Mathematica, while operating within $MachinePrecision IEEE 754 compliant?
I was looking in Mathematicas documentation and could not find to which point Mathematica includes the IEEE 754 standard?
It is mention it in its documentation MachinePrecision under Background & ...
- 447
30
votes
2
answers
4k
views
Why does Mathematica results differ from C++ results within machine precision?
I am trying to wrap my head around floating-point precision. Performing the following numeric operation:
275./6.*1.03692775514337
in Mathematica and C++ and ...
- 447
1
vote
0
answers
205
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Machine Learning Predict Precision
I have this code
p = Predict[{1 -> 123456789123456789, 3 -> 987654321987654321}]
values are big, more than 15 digits (standard machine precision).
when I ...
- 531
9
votes
1
answer
556
views
What explains the inaccuracies in machine-precision 'integers' with trigonometry or powers?
This Mathematica tutorial notes some strange behaviour with calculations such as Sin[10^50]:
...
- 607
6
votes
4
answers
497
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How do I convert an inexact number smaller than $MinMachineNumber to machine-precision?
I was trying to convert some arbitrary-precision numbers to machine-precision numbers using N[myNumber,MachinePrecision]. But, although my test number did lose some ...
- 7,122
3
votes
1
answer
91
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Precision improvement for solution of the simplest low-pass filter
I solved the most basic low-pass filter using NDSolve in Mathematica and LTSpice. The solution provided by Mathematica seems to lack precision. I tried to deal with WorkingPrecision but I didn't ...
- 548
1
vote
2
answers
154
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MemberQ[{0.01, 0.05}, (0.01*9*2)/9/2] returns False
Multiplying and dividing by the same stuff seems to alter the value. Quite curiously, if the value you start from is large enough (greater than 0.05 in my case) you do not see the problem. Any idea ...
- 1,410
0
votes
0
answers
64
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ListLinePlot gives the correct values but N doesn't
I have solved a set of 6 differential equations with DSolve. When I use the table command and produce the results of one of the equations given by DSolve, the ListLinePlot command gives me the correct ...
- 1,243
2
votes
0
answers
300
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Printing Precision of Machine Numbers
Is Mathematica making the print precision rounding judgment more stringent based on whether or not the number is above or below the rounding target? If so, why?
In my real case, I have many numbers ...
- 1,955
8
votes
1
answer
821
views
Really understanding precision
I've been reading the documentation in Mathematica about precision, namely:
Exact and Approximate Results
Arbitrary-Precision Numbers
Arbitrary-Precision Calculations
Machine-Precision Numbers
...
- 1,091
0
votes
2
answers
966
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How to use Working Precision to get good result and plot?
I have a function f(x) which I would like to see going up for very low values of x: from an asymptotic study, I expect it to go to Infinity for low x; however, I can see an elbow and many oscillations....
- 739
0
votes
0
answers
44
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Unpredictable behavior of numerical error
A comparison of float calculation and exact expression for
NumberForm[0.3^2 - (3/10)^2, 18]
gives an exact zero for $0.3$.
However,
...
- 1,567
3
votes
1
answer
266
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Precision of integers vs. Precision of floating numbers
It seems that Mathematica can handle very big integers accurately, but cannot do the same for floating numbers.
See the following code:
...
- 123
12
votes
1
answer
814
views
Why does 1 - Exp[-10.0^12] cause an out-of-memory error?
I would like to understand why evaluation of the expression
1 - Exp[-10.0^12]
causes an out-of-memory error and how can I prevent such errors when calculating ...
- 7,776
0
votes
1
answer
135
views
How to use a higher precision?
Below is my code. If I set W to $10^{55}$, it breaks down and the result is wrong. What do I need to do to use W as large as $10^{200}$?
...
- 123
1
vote
0
answers
292
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Treating a bad conditioned covariance matrix
I am trying to detect outliers in a big dataset using the Mahalanobys distance method. To calculate the Mahalanobys distance for a given vector $x$ from a mean vector $\mu$ you have to compute the ...
- 660
1
vote
0
answers
232
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Chop intermediate results of NDSolve after each step [closed]
Using NDSolve for a set of three ordinary differential equations, I ran into the problem that intermediate results quickly develop negligible imaginary parts. I get ...
- 1,281
8
votes
1
answer
121
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Unexpected behavior from CoordinateBoundingBoxArray with Into[1] and 0.41
I want to get the four corners of a Cuboid. This usually works:
CoordinateBoundingBoxArray[{-{1., 1.}, {1., 1.}}, Into@1]
gives
...
- 5,689
6
votes
1
answer
134
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Bug in floating-point number comparisons near $MachineEpsilon?
I stumbled over the following weird behavior when comparing floating-point numbers close to 1.0:
qq = 1.0 + 60.0 $MachineEpsilon;
and then
...
- 281
3
votes
1
answer
143
views
Why does this rounding happen at machine precision?
Clearly, dividing by two in a binary number shifts the decimal point like this:
BaseForm[InputForm[7], 2]
BaseForm[InputForm[7/2 // N], 2]
It gives: 2^^111 and 2^...
- 2,311
4
votes
1
answer
364
views
What happens at the end of MachinePrecision? Is the remainder discarded or rounded?
What happens at the end of MachinePrecision? Is the remainder discarded or rounded?
This code suggests it is discarded; is that conclusion correct? Why is it not rounded?
...
- 2,311
2
votes
1
answer
155
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Showing what happens with a number beyond machineprecision
I want to play around a bit in Mathematica to understand how floating-point precision, rounding and truncation actually works. I understand that Machineprecision is $2^{-52}$.
First of all I would ...
- 2,311
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 ...
- 8,900
7
votes
4
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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 ...
- 2,311
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:
...
- 1,067
4
votes
1
answer
75
views
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?
- 181
5
votes
1
answer
444
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MachinePrecision versus $MachinePrecision in NDSolve
I'd like to understand why one of these inputs gives me an error and the other doesn't:
...
- 1,040
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 ...
- 389
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
...
- 562
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 ...
- 147
4
votes
1
answer
460
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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 ...
- 218
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votes
1
answer
111
views
My NIntegrate expression returns a wildly inaccurate value
I am trying to integrate a function using NIntegrate:
...
- 41
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votes
1
answer
362
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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 ...
- 19.5k
10
votes
1
answer
395
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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 ...
- 2,311
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
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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