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.
221
questions
1
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2
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50
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How to modify the given codes (NIntegrate of Boole) to get the most accurate result possible?
I have five conditions con1 to con5 over the two-dimensional domain $t,u\in[o,2\pi]$. I want to compute this area $(con1 \cap con2 )\cup(con3 \cap con4 \cap con5)$ numerically. I try the two codes ...
- 337
1
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1
answer
50
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How to modify NIntegrate code below so that it gives the most accurate/reliable numerical result?
Imagine that I have two conditions con1 and con2 over the two-dimensional domain $x,y\in[-2,2]$. I want to compute the area of the union of these two conditions i.e. the region $(con1 )\cup(con2)$. I ...
- 337
6
votes
1
answer
343
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Table does not give expected result with `30 but right with `40
I want Mathematica to generate a table, but I am very confused by its behaviour.
tab = Table[i, {i, 6.311, 6.312, 0.001}]
Now I get the desired result, namely {6....
7
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3
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426
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2
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0
answers
33
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0
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1
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93
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Is there any alternative for conditional plot that gives a more precise result in a shorter time?
I have the given function $Func$ and want to have a plot of those domains where $-3\leq Func\leq 3$ in precise details. I am using ...
- 361
1
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0
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68
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How to handle "too small to represent as a normalized machine number" when plotting a figure [duplicate]
I am trying to plot a figure by the following codes:
Plot[(27 2^((-2 + a)/(-1 + a)) 5^(a/(-1 + a)) 7^(1/(1 - a))
a^2)/((-1 + a) (4 + 9 a)), {a, 1.001, 3}]
...
- 123
1
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2
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246
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How to prevent Mathematica from rounding some PDF values to 0?
Dear Mathematica community,
I'm having a problem with the PDF function for the hypoexponential distribution. Specifically, Mathematica returns 0 as soon as the value is very small. Below is an example:...
- 21
0
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1
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69
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0
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1
answer
158
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Floating point precision and speed [closed]
I am attempting to understand how to speed up the evaluation of numerical expression.
Specifically, following the first point of this blog, Mathematica is much quicker dealing with floating-point ...
- 1,349
9
votes
1
answer
305
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IntegerPart - is this a known bug?
I'm working in Mathematica 13.0 and I type
a=0.00001;
IntegerPart[a/a]
and well, the output is 0.
Try with almost any other value of ...
4
votes
2
answers
152
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Adding numbers with defined precision produces incorrect result
I've tracked a bug in my code down to the problem of adding two numbers together, with the left argument having machine precision, e.g by 3` . The issue is, if ...
- 557
1
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0
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54
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Issue with some floating-point errors and not others
Not looking for a solution necessarily, but just trying to understand why this issue occurrs.
I have a 'Do' loop which iterates some algorithm over values of a parameter 'x' with range {x,0,1,0.1} and ...
- 185
3
votes
1
answer
152
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How to handle very numbers that are "too small to represent as a normalized machine number"?
I will preface this by saying that I am not very familiar with Mathematica whatsoever. That is why I am asking this here even though I have found a few forum posts that might provide the solution to ...
- 45
2
votes
2
answers
1k
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Error "is too small to represent as a normalized machine number; precision \ may be lost " for small values in Plot
I'm trying to plot two curves but I'm having issues with the lower end of the range:
...
- 1,304
0
votes
1
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122
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Spurious poles in a gain plot (due to machine precision or complex numbers?)
I have the following plot that I like to make. It details the gain of an amplifier.
...
- 373
4
votes
1
answer
347
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Real number equality (==) not working: what's the least-overcomplicated solution?
I'm running a program that evaluates equalities after I substitute all symbols for numbers. The equalities on floats are giving me trouble. My program is reaching a point where something like the ...
- 558
3
votes
1
answer
140
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FixedPoint not working, despite quick convergence of sequence [closed]
Trying the computation below, with Mathematica 13.0.0, I am not getting a result returned.
FixedPoint[Cos, 0.85]
This appears in the 3rd edition of "...
- 315
1
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1
answer
117
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0
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0
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51
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How to set up precision by default?
I have a table computing many numbers with large precision. Because of this, probably, Mathematica consumes a lot of RAM. Is it possible to restrict the precision in any calculations by default (...
- 4,866
1
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2
answers
45
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`KernelMixtureDistribution` error message about precision
I want to use KernelMixtureDistribution to deal with a large amount of data points. For example, the following codes shows how I use it:
...
- 503
0
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0
answers
42
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Why is the `N` function giving me the wrong result when using WolframScript? [duplicate]
I am using wolframscript.exe to learn mathematica and I would expect the following code to return 0.7071:
...
- 185
1
vote
0
answers
50
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plot and limit are not in agreement [closed]
I am plotting the following function $\frac{\sqrt{t \text{$\omega_c $}}-\sqrt{\pi } e^{\frac{1}{t \text{$\omega_c $}}} \text{erfc}\left(\frac{1}{\sqrt{t \text{$\omega_c$}}}\right)}{(t \text{$\omega_c$}...
- 573
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1
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41
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0
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0
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62
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Mathematica accuracy errors when creating data
I created training data for a neural network and below are two errors I got
The only code that uses "FindRoot" command is the following
...
- 295
1
vote
1
answer
152
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General:munfl error problem
I have the following function, that is the result of The integration between x and some upper limit of a positive function, thus should be positive
$f(x,vE) = \frac{e^{-1140.09 x} \left(e^{67945.5 \...
- 349
1
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0
answers
57
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How does WorkingPrecision in NDSolve handle MachinePrecision?
I'm wondering why the following code
NDSolve[{y''[t] + y[t] == 0, y[0] == 1., y'[0] == 0}, y, {t, 0, 10},
WorkingPrecision -> 6]
throws the error/warning, that ...
- 851
1
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0
answers
43
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ContourPlot3D with small domain produces glitchy mess
I'm able to plot some graphs over small domains, but not others.
For example, this works just fine:
...
- 61
3
votes
2
answers
171
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Simplify for precision
I have an a set of equations to solve — details irrelevant — the result of which will be converted into PostScript, a 1980s printer-control language the only floating precision of which is single. ...
- 499
0
votes
0
answers
39
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General::munfl - Precision lost in LinearModelFit
I am new to mathematica so I am confused regarding the loss of precision in LinearModelFit. In building a linear model with uora (1 or 2) and encodeSeverity (1,2 or 3)
...
3
votes
0
answers
220
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How to deal with too small numbers
When dealing with a code that produces too small numbers (in a complicated way) like
0.33691 4.015757066049965*10^-330
I get the following warning
General::munfl: ...
- 317
0
votes
0
answers
50
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Solving a determinant to get non-zero roots in a heat transfer problem
I am trying to solve a mathematical model of a heat transfer problem.
As an intermediate step there is a characteristic equation in the form of a determinant, which needs to be solved for variable <...
- 297
0
votes
0
answers
87
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How to change Machine Precision digits to meet the tolerances
I am trying to solve for Tcm and Mag by solving nonlinear equations using FindRoot command using following code:
...
- 51
1
vote
0
answers
46
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Are pixels machine numbers? [closed]
Mathematica allows one to work with the information that is behind a photo. For example, the command ImageData generates a list containing the “pixels” (which will it be a number from $0$ to $1$ if no ...
- 141
0
votes
0
answers
67
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Problem with the Rank of a matrix after a FindRoot
I am solving a boundary problem defined by a set of four-component vectorial functions. Without going into many details, I have two functions on the left and two on the right of an interface. The ...
- 101
1
vote
2
answers
85
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How to increase the value of MinMachineNumber to avoid overflow error?
I have a complicated function called f2[re]
...
- 1,238
0
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0
answers
83
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How to copy and paste numbers with "`" mark and use them in calculations, without using N or setting precision every time
Suppose we have run a calculation and get a number like
2.758952615889003`
If we then copy-paste this number and do a calculation like
...
- 779
2
votes
0
answers
106
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Generalizing technique to handle General::munfl error?
In contrast to earlier versions of Mathematica, in versions 11.3 and later Mathematica no longer switches to arbitrary precision when it detects a MachineNumber underflow. While this behavior is ...
- 550
3
votes
1
answer
87
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Too small to represent and Chop in inaccessible algorithm
Overview
I want to apply a specified Chop function to every step in an function call in Mathematica (in my case LegendreP), ...
- 33
0
votes
0
answers
27
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Different sensitivies from LinearSolve and Eigenvalues. How to conciliate them?
I use the following functions to receive a matrix, and make it symmetric positive definite:
...
- 2,517
2
votes
0
answers
1k
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General:: Exp[-717.401] is too small to represent as a normalized machine number; precision may be lost
I am solving pde.
For the post processing bvp, there is solution given in output which is the solution from mathematica version 10.0.1.
Output from above in mathematica 10.0.1 is,
But when the similar ...
- 87
3
votes
1
answer
55
views
Avoid MachinePrecision numbers in Message
Can I change the output of Message to not show MachinePrecision numbers? E.g.
...
- 19.1k
1
vote
4
answers
198
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Can I change the default behavior so that "0.1" is interpreted as "1/10" automatically?
Consider the function
f[a_] := NIntegrate[Sqrt[a + Log[x]], {x, 1, 10}, WorkingPrecision -> 30].
With this definition, I cannot call ...
- 844
1
vote
1
answer
108
views
Machine-precision numbers cause loss of precision
I am trying to use the Mod function as follows.
Table[
Nest[Mod[2 #, 1] &, FractionalPart[Pi], n],
{n, 100}] // N
...
- 183
3
votes
3
answers
679
views
How can I compute Erf of large numbers to more precision?
I would like to compute Erf[80/3] to enough precision to know the order of magnitude of 1 - Erf[80/3]
How can I do that?
I ...
- 457
3
votes
1
answer
153
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Why does precision decrease after increasing PrecisionGoal and WorkingPrecision on this integral?
I am trying to calculate a messy double-integral to many digits of precision. As shown below, the precision seems to increase reliably as WorkingPrecision goes from ...
- 844
0
votes
1
answer
227
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How to improve working precision?
I'm trying to fit the array data as follow:
NonlinearModelFit[
data,
s*t^r + (A/(w*(Pi/2)^0.5))*Exp[-2*((t - u)/w)^2],
{s, r, A, w, u},
t];
But when ...
1
vote
1
answer
68
views
How to get the output for the following code involving differentiation and integration?
I need to evaluate the following Mathematica code to get a numerical value as my output. But during compilation I get the error message
NumericalMath`FixedPrecisionEvaluate::precbd: Requested ...
- 343
0
votes
0
answers
84
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Understanding Working Precision - two example equations
I am trying to understand how WorkingPrecision works, and in general how very small/large numbers are to be handled.
Let me preface I probably do not have ...
- 745
0
votes
0
answers
20
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Conflicting output provided by `N[...]`
I am trying to evaluate an expression :
(-((I (k2 - k1) (-1 + E^(2 I (k2 - k1) \[Pi])))/(-1 + (k2 -
k1)^2))) /. {k1 -> 2, k2 -> 7}
This gives ...
- 431