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
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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
0
votes
0
answers
28
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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
3
votes
1
answer
57
views
Avoid MachinePrecision numbers in Message
Can I change the output of Message to not show MachinePrecision numbers? E.g.
...
- 234k
1
vote
4
answers
216
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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 ...
- 234k
1
vote
1
answer
110
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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
...
- 234k
3
votes
3
answers
763
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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 ...
- 65.8k
3
votes
1
answer
162
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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 ...
- 234k
0
votes
1
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252
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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 ...
- 40.6k
1
vote
1
answer
72
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 ...
- 65.8k
9
votes
1
answer
770
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Machine Epsilon
I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this:
...
- 124k
0
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0
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95
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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 ...
- 755
6
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1
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163
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Issues with $MachineEpsilon
I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ...
- 124k
0
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0
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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 ...
- 124k
0
votes
0
answers
352
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Dealing with General::munfl errors
Edit: So, while trying to figure out a minimal exmaple, I found out that my main problem was actually unrelated to this and it just happened to be that giant pile of warnings and error messages coming ...
- 21
1
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1
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702
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How can I suppress the warning "precision may be lost"?
When I import data from a .dat file, V11.3 emits the message: is too small to represent as a normalized machine number; precision may be lost.
How can I close the ...
- 124k
5
votes
1
answer
353
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Equality for floats
Suppose I have two floats (e.g. {x,y} = RandomReal[{0,1},2]). Might there be a situation where all three comparisons evaluate to ...
- 233k
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Numerical precision - simulating an unstable equilibrium
I was playing around with NDSolve and the following ODE
s = NDSolve[{y''[x] == -Sin[y[x]], y[0] == \[Pi], y'[0] == 0 },
y, {x, 0, 120}]
The equation and the ...
- 755
3
votes
1
answer
122
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DeleteCases with a case as float?
Might the DeleteCases have issues in matching when the list is of floats (machine precision numbers)? E.g. in this code it might fail to match correctly because ...
- 3,143
1
vote
1
answer
95
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Number definition and approximation
I run these lines:
a = 0.833
SetPrecision[a, 20]
and this is the output:
0.833
0.83299999999999996270
I expected to ...
CommunityBot
- 1
2
votes
0
answers
54
views
Set Underflow precision in Mathematica 12 same as version 11.x [duplicate]
It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ...
- 601
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0
answers
68
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FindRoot giving error in Mathematica version 12
I was using the same code in previous version of Mathematica but unfortunately I had to update Mathematica to version 12 because I upgraded MacOS to Catalina. Now when I run my code, I get this error
...
- 601
4
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0
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130
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How does Mathematica evaluate N[π, 30] == π?
I want to know how N[π, 30] == π works. The result is True. I wonder whether the exact number ...
- 107k
9
votes
2
answers
442
views
How to detect underflow/overflow (post 11.3)?
This old trick used to work before 11.3:
SetSystemOptions["CheckMachineUnderflow" -> True]
But no longer... so how can we explicitly check for this in v12+??
...
- 25.5k
1
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0
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59
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Changing machine precision notebook-wide leads to peculiarities
For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting.
The idea is to dynamically create a ...
- 234k
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1
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88
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Allow Mathematica to solve the differential equations with larger than 16 digits parameters
Consider the system of differential equations
...
- 4,652
3
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2
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926
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Why is Mathematica's default precision only 16 digits? [closed]
I was performing some basic computations when I noticed that
NumberForm[N[Zeta[3]], {100, 100}]
yields
...
- 124k
7
votes
2
answers
958
views
Accurately evaluating the hypergeometric function
As part of another problem, I am working to evaluate hypergeometric functions such as
Hypergeometric2F1[1, 1, n, -1]
for large $n$. I am hoping to obtain at ...
- 101
1
vote
1
answer
64
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why some parts of my curve are removed or wiped
When I try to draw the next code I get a curve with missing parts, as shown in the picture. I do not know if it is an precision problem in the Mathematica program or is some data not calculated. Or is ...
- 22.9k
0
votes
1
answer
141
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Preventing Mathematica from considering small values to be equal to zero [duplicate]
In my calculations I have a variable (say z) which can be an argument of Log, say, z Log[z]. ...
- 107k
0
votes
1
answer
99
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Why this very simple problem turns to "Indeterminate"?
Why the following calculation gives Indeterminate value?
...
- 17.8k
0
votes
0
answers
72
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How to resolve underflow occurrences?
I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve.
...
- 181
3
votes
1
answer
240
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Setting precision and machine underflow
As is well known, Mathematica changed how it handles numbers smaller than $MinMachineNumber in recent versions.
I'm running Mathematica 12 on a Mac, and I cannot figure out why it's treating these ...
- 104k
19
votes
5
answers
4k
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Numerical underflow for a scaled error function
I calculate a scaled error function defined as
f[x_] := Erfc[x]*Exp[x^2]
but it can not calculate f[30000.]. ...
- 584
2
votes
1
answer
453
views
Why would Evaluate[] in Plot give me warning about precision?
I have a code:-
Plot[Evaluate@PDF[NormalDistribution[1.6, 0.2], x], {x, -6, 6}]
And then I got the warning: ...
- 130k
5
votes
2
answers
867
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Underflow error General::munfl from E^x instead of Exp[x]
In contrast to earlier versions, Mathematica 11.3 and 12.0 generate lots of underflow errors from my code, e.g.
...
- 130k
2
votes
1
answer
171
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Correct syntax for working precision in functions version 12
I just recently updated from version 11.2 -> 12...there apparently are quite a few changes since 11.2. $\unicode{952}\unicode{960}$
One being how version >11.3 deal with numbers that approach zero.
...
- 130k
8
votes
2
answers
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 ...
- 234k
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3
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When should one write integer numbers with a decimal?
I often see different solutions where users have taken advantage of how Mathematica handles numbers differently. I.e. when is it appropriate to use a decimal point in a calculation?
Can someone ...
- 13.7k
1
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1
answer
96
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Drawing from InverseWishartMatrixDistribution. A machine precision error?
I'm drawing from the Inverse-Wishart Distribution, but I got the following error message:
...
- 24.3k
4
votes
1
answer
233
views
Inexact numbers as keys in Association?
Can someone explain me how Mathematica's Associations behave with inexact numbers as keys:
<| 0.22499999999999964` -> a |> [0.22499999999999965`]
and
<...
- 124k
2
votes
1
answer
180
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Efficient Round edition with different rounding direction
As pointed out in this post, Mathematica has a special version of Round that
Round rounds numbers of the form x.5 toward the nearest even integer.
A comment by ...
- 16.2k
2
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1
answer
140
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How to prevent Mathematica from giving inexact answers
Upon doing a simple subtraction 13.725 - 13.5 both Mathematica 11.3 and 12.0 beta version are giving me 0.22499999999999964 ...
- 65.8k
3
votes
1
answer
139
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Forcing divisions to be a machine-precision floating point divisions instead of multiplication by inverse
I want to imitate machine-precision, de facto IEEE division on Mathematica. On my quick trials I find this surprisingly hard to accomplish, since Mma rewrites a / b ...
- 130k
0
votes
1
answer
77
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ContourPlot showing breaks in contours
I'm trying find graphically the solutions of the intersection of the following functions.
...
- 2,096
6
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1
answer
159
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Extracting binary digits of machine precision numbers
Currently, I am developing an octree data structure. And I need it to be fast. To this end, I would like to have a fast way to extract the $m$ binary digits "after the dot" of each entry in a matrix ...
- 61.5k
6
votes
2
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178
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How can I make 1+$MachineEpsilon not look like 1?
I undarstand that 1+$MachineEpsilon is actually not equal 1. However, it persists to look like it was equal ...
- 46.2k
2
votes
2
answers
495
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Why is 0 vs 0.0 causing a precision problem?
I wasn't sure what to title this Question.
I tried calculating different forms of a continued fraction, and I found that I get a correct result when I set d to 0 but a wrong result (in the final two ...
- 46.6k
5
votes
0
answers
97
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Small positive machine number calculation in Mathematica 11.3
In Mathematica version < 11.3, any positive Machine‐Precision Numbers exceeding the range [$MinMachineNumber,$MaxMachineNumber...
- 51
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2
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Truncate a number in mathematica
I want to truncate a simple number to n decimal digits. For example, 2/3. I used
f[x_, n_] := N[IntegerPart[x 10^n]/10^n]
but I get
...
- 6,637
0
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1
answer
62
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How to get the correct result in a simple operation in Mathematica
I have the following values for x[[i]], y[[i]] and A[[i,j]]:
...
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