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.

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1answer
153 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 ...
2
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0answers
147 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 ...
24
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2answers
1k 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 ...
3
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2answers
865 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 ...
6
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2answers
167 views

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 ...
6
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0answers
131 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: ...
3
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2answers
248 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 ...
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0answers
65 views

Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
2
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2answers
548 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 ...
3
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1answer
494 views

Reasonable choice of MachinePrecision, AccuracyGoal and PrecisionGoal for NDSolve

I am trying to use this model for later use in FindFit: ...
3
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4answers
234 views

Precision problem with numerical solution of a differential equation

I want solve $$ 2\sqrt{|\gamma|}x = \int_{1}^{t} dy \sqrt{\frac{1+2|\gamma_2|y}{y^2(1-y)}} $$ where $0<t\leq $1. I'm using a for cycle to evaluate t, calculate the integral and the assign the $x$. ...
2
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1answer
734 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 ...
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2answers
113 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 ...
4
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1answer
138 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 ...
9
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1answer
144 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. ...
9
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1answer
486 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
0
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1answer
79 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 ...
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1answer
1k views

How to get more accurate orthonormal eigenvectors?

I have a matrix M with real entries in MachinePrecision. I compute its eigenvectors and construct matrix ...
6
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1answer
157 views

Machine precision infinity

Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
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0answers
49 views

Number precision in a list [duplicate]

I have list with elements: ...
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2answers
200 views

The precision of the number

I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ...
4
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2answers
1k views

Floating point addition not associative

Can anybody explain the following behavior? x = 0.2 + (0.3 + 0.1); y = (0.2 + 0.3) + 0.1; x == y (* -> True *) But actually the variables do not exactly ...
2
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1answer
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 ...
3
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1answer
954 views

Error about limit MaxExtraPrecision

After my evaluations I have an error: N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ... ...
6
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1answer
133 views

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 ...
2
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0answers
523 views

how to calculate with just double floating point precision [duplicate]

I want to calculate with simple double floating point precision. ...
40
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1answer
1k views

Is there a difference between Divide[a,b] and a/b?

In this comment it was asserted that Divide[a,b] and a/b are different, though the documentation indicates that they are the ...
30
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8answers
1k views

Elegant high precision `log1p`?

Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
0
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1answer
254 views

How to improve the performance of this code

I have implemented a code in Mathematica 9 to simulate a scattering problem, and I got really disappointed about its performance when compared to Matlab. Since I am a newbie in Mathematica, would ...
17
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2answers
277 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 ...
2
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2answers
175 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 ...
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1answer
2k views

CompiledFunction::cfse: "Compiled expression X should be a machine-size integer

I am trying to use a compiled function in order to save time... LegrendeTransform = Compile[{y}, MaxValue[Sin[x] - x *y , x]] Now I want to to evaluate and ...
1
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1answer
59 views

Function that puts zero after a certain decimal in every element of the matrix

We know that in Mathematica there is some default precision, which you can also change. This means, that after a certain decimal(fixed by the precision), the computer puts pseudo random numbers. I am ...
5
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2answers
666 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 ...
2
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1answer
3k views

How to change machineprecision digits

I am trying to compute t0: ...
9
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3answers
1k views

Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
2
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1answer
437 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 ...
0
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1answer
296 views

Finite precision - how to get rid of “near zeros” [duplicate]

I am performing a finite-precision operation on a matrix A which I know precisely; call the result B. The operation is taking ...
6
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1answer
638 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 ...
4
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4answers
1k 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 ...
1
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1answer
324 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 ...
5
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6answers
2k views

Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?

The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration. ...
10
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2answers
1k 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 ...
1
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1answer
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 ...
8
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2answers
540 views

Precision differences

I run this sum and get the symbolic answer below : Sum[ (1/(k^2 - k) - 1/k^2), {k, 2, Infinity}] $2 - \frac{\pi^2}{6}$ I look up the sequence on OEIS and ...
1
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1answer
766 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 ...
3
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1answer
250 views

Why to do parentheses change the results of a calculation?

I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2 <...
2
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2answers
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 ...
2
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0answers
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 ...
4
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2answers
2k views

Precision of number not maintained when saved via Export

Assume that the output of my calculation is a and is a number such as: a = 100.1252135246354847; ...