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
139
views
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 ...
- 18.7k
3
votes
1
answer
141
views
Numerical precision problem
I have this simple code:
ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000))
ep // N
-8.27404*10^-8
...
- 793
3
votes
1
answer
136
views
Copy-paste with annoying trailing 0s
When one copies an output containing machine-precision numbers to a input, many trailing 0s appears.
For example :
Evaluate the following expression :
...
- 17.8k
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
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
...
- 33
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 ...
- 31
3
votes
1
answer
162
views
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 ...
- 854
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
3
votes
1
answer
136
views
Floor inconsistent with Less for machine-precision approximate numbers
For machine-precision numbers, Mathematica uses a tolerance for comparisons, so that 1.-$MachineEpsilon==1. However, Floor does ...
- 257
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:
...
- 325
3
votes
0
answers
258
views
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
3
votes
0
answers
2k
views
Set Global Maximum Precision
I'm sure this has been asked before, but I've looked around and can't figure it out:
How do I set a global maximum precision for a notebook (or in general, globally)?
I have a large notebook in ...
- 625
2
votes
2
answers
177
views
Long run time for older code that ran fast in older versions
The following code block is in Trott's Guidebook for Programming. The associated notebook says that this and a few other routines ran in a matter of seconds. I killed it after half an hour.
I am ...
- 23
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: ...
- 3,439
2
votes
2
answers
254
views
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:...
- 31
2
votes
1
answer
371
views
Why is arithmetic faster for inexact arithmetic?
I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...
- 463
2
votes
2
answers
2k
views
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
2
votes
1
answer
295
views
2
votes
2
answers
495
views
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 ...
- 4,553
2
votes
2
answers
431
views
What's the smallest positive real allowed in mathematica?
This question may be a bit strange, but in this question, one of the answers suggests substituting some negatives values in a matrix by the smallest positive real number allowed. So, I was wondering ...
- 2,517
2
votes
1
answer
526
views
How to use adaptive precision in matrix computations?
I wish to compute the pseudo inverse of rectangular (or square) matrices by the cubically method of Chebyshev given by $X_{k+1}=X_k(3I-AX_k(3I-AX_k))$ where $X_0=\frac{1}{\|A\|_F^2}A^*$. The procedure ...
- 1,817
2
votes
2
answers
1k
views
FindRoot errors
I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
- 6,818
2
votes
3
answers
104
views
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 ...
- 349
2
votes
1
answer
180
views
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 ...
- 17k
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 ...
- 755
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:
...
- 451
2
votes
2
answers
745
views
'eps' equivalent in Mathematica
In MATLAB, there is a function named eps.
eps Spacing of floating point numbers.
D = eps(X), is the positive distance from ABS(X) to the next larger in
...
- 407
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 ...
- 3,834
2
votes
1
answer
857
views
How to Chop correctly?
I want to count degeneracies in a list called spectrum. The list contains numbers of double (~ 15digits) precision. So it makes no sense if the noise below this ...
- 1,567
2
votes
1
answer
171
views
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.
...
- 2,921
2
votes
2
answers
2k
views
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
...
- 45
2
votes
1
answer
158
views
Working Precision warnings for ParametricPlot
I wish to plot a series of parametric curves for the following function called poly that has five parameters (Γ, ...
- 385
2
votes
1
answer
155
views
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
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 ...
- 19.5k
2
votes
1
answer
140
views
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 ...
- 8,900
2
votes
0
answers
33
views
2
votes
0
answers
115
views
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
2
votes
0
answers
1k
views
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
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
2
votes
0
answers
300
views
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
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
2
votes
1
answer
2k
views
Plot periodic function from Dirac delta function [duplicate]
Sorry for my bad english.
I need to plot periodic function from dirac delta:
δT(t)=∑δ(t–n*T), where T - is a constant, and n=-20..20
And after them, plot new function fd=f(t)*δT(t) - discrete signal ...
- 21
2
votes
0
answers
568
views
how to calculate with just double floating point precision [duplicate]
I want to calculate with simple double floating point precision.
...
- 21
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
...
1
vote
2
answers
154
views
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
1
vote
3
answers
136
views
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 ...
- 2,480
1
vote
1
answer
2k
views
Adding precision for the calculation of a function
I have some function $f(x)$ I wish to evaluate, which is yielding divide-by-zero errors for sufficiently large inputs. How do I increase the precision with which this function is evaluated in order ...
- 1,477
1
vote
4
answers
216
views
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 ...
- 854
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'...
- 1,725
1
vote
1
answer
66
views
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