Common way to inverse a double value - dart

I need to create an inverse function that would flip double values: x/y = y/x
inverseDouble(1.2) // 0.83
inverseDouble(0.2) // 5
inverseDouble(6.0) // 0.17
I didn't find any solutions (maybe because I'm not an English speaker and don't know how to google this). By the way, are there any easy solutions to do this? I'm using Dart. Solutions using any programming language would be acceptable. I'd also appreciate even any tips or ideas about where and what to look for. Thank you.

This is about a mathematcal solution. The inverse of a number is always one divided by that number.
Look this execution in python:
>>> 1/1.2
0.8333333333333334
>>> 1/5.0
0.2
>>> 1/6.0
0.16666666666666666
In dart you can implement this function that way:
void main() {
print(inverseDouble(1.2));
print(inverseDouble(0.2));
print(inverseDouble(6.0));
}
double inverseDouble(double number)=>1/number;
And the result is:
0.8333333333333334
5
0.16666666666666666

I'm not a pro in math, but isn't an inverse of a fraction 1/fraction?
So the function would look something like that :
double inverseDouble(double nb){
return 1/nb;
}

If you want to use dart:math for that, note that 1/x is x⁻¹, or pow(x, -1):
import 'dart:math' show pow;
void main() {
print(pow(1.2, -1)); // 0.8333333333333334
print(pow(0.2, -1)); // 5
print(pow(6.0, -1)); // 0.16666666666666666
}
Why make it simple when we can make it complicated 😂

Related

toStringAsFixed() returns a round-up value of a given number in Dart

I want to get one decimal place of a double in Dart. I use the toStringAsFixed() method to get it, but it returns a round-up value.
double d1 = 1.151;
double d2 = 1.150;
print('$d1 is ${d1.toStringAsFixed(1)}');
print('$d2 is ${d2.toStringAsFixed(1)}');
Console output:
1.151 is 1.2
1.15 is 1.1
How can I get it without a round-up value? Like 1.1 for 1.151 too. Thanks in advance.
Not rounding seems highly questionable to me1, but if you really want to truncate the string representation without rounding, then I'd take the string representation, find the decimal point, and create the appropriate substring.
There are a few potential pitfalls:
The value might be so large that its normal string representation is in exponential form. Note that double.toStringAsFixed just returns the exponential form anyway for such large numbers, so maybe do the same thing.
The value might be so small that its normal string representation is in exponential form. double.toStringAsFixed already handles this, so instead of using double.toString, use double.toStringAsFixed with the maximum number of fractional digits.
The value might not have a decimal point at all (e.g. NaN, +infinity, -infinity). Just return those values as they are.
extension on double {
// Like [toStringAsFixed] but truncates (toward zero) to the specified
// number of fractional digits instead of rounding.
String toStringAsTruncated(int fractionDigits) {
// Require same limits as [toStringAsFixed].
assert(fractionDigits >= 0);
assert(fractionDigits <= 20);
if (fractionDigits == 0) {
return truncateToDouble().toString();
}
// [toString] will represent very small numbers in exponential form.
// Instead use [toStringAsFixed] with the maximum number of fractional
// digits.
var s = toStringAsFixed(20);
// [toStringAsFixed] will still represent very large numbers in
// exponential form.
if (s.contains('e')) {
// Ignore values in exponential form.
return s;
}
// Ignore unrecognized values (e.g. NaN, +infinity, -infinity).
var i = s.indexOf('.');
if (i == -1) {
return s;
}
return s.substring(0, i + fractionDigits + 1);
}
}
void main() {
var values = [
1.151,
1.15,
1.1999,
-1.1999,
1.0,
1e21,
1e-20,
double.nan,
double.infinity,
double.negativeInfinity,
];
for (var v in values) {
print(v.toStringAsTruncated(1));
}
}
Another approach one might consider is to multiply by pow(10, fractionalDigits), use double.truncateToDouble, divide by the power-of-10 used earlier, and then use .toStringAsFixed(fractionalDigits). That could work for human-scaled values, but it could generate unexpected results for very large values due to precision loss from floating-point arithmetic. (This approach would work if you used package:decimal instead of double, though.)
1 Not rounding seems especially bad given that using doubles to represent fractional base-10 numbers is inherently imprecise. For example, since the closest IEEE-754 double-precision floating number to 0.7 is 0.6999999999999999555910790149937383830547332763671875, do you really want 0.7.toStringAsTruncated(1) to return '0.6' instead of '0.7'?

Enhanced for each loop optimization

I have tried multiple things but is there a way i can optimize this code to work within 2 seconds for p and q of size greater than 50000 in Java 7. p and q are 2 array lists of different sizes.
for(Integer x:q){
for(Integer y: p){
counter++;
if(x<= y){
ls.add(count);
}
}
//some code logic here based on ls
ls.clear();
counter=0;
}
Thanks in advance!

16 bit logic/computer simulation in Swift

I’m trying to make a basic simulation of a 16 bit computer with Swift. The computer will feature
An ALU
2 registers
That’s all. I have enough knowledge to create these parts visually and understand how they work, but it has become increasingly difficult to make larger components with more inputs while using my current approach.
My current approach has been to wrap each component in a struct. This worked early on, but is becoming increasingly difficult to manage multiple inputs while staying true to the principles of computer science.
The primary issue is that the components aren’t updating with the clock signal. I have the output of the component updating when get is called on the output variable, c. This, however, neglects the idea of a clock signal and will likely cause further problems later on.
It’s also difficult to make getters and setters for each variable without getting errors about mutability. Although I have worked through these errors, they are annoying and slow down the development process.
The last big issue is updating the output. The output doesn’t update when the inputs change; it updates when told to do so. This isn’t accurate to the qualities of real computers and is a fundamental error.
This is an example. It is the ALU I mentioned earlier. It takes two 16 bit inputs and outputs 16 bits. It has two unary ALUs, which can make a 16 bit number zero, negate it, or both. Lastly, it either adds or does a bit wise and comparison based on the f flag and inverts the output if the no flag is selected.
struct ALU {
//Operations are done in the order listed. For example, if zx and nx are 1, it first makes input 1 zero and then inverts it.
var x : [Int] //Input 1
var y : [Int] //Input 2
var zx : Int //Make input 1 zero
var zy : Int //Make input 2 zero
var nx : Int //Invert input 1
var ny : Int //Invert input 2
var f : Int //If 0, do a bitwise AND operation. If 1, add the inputs
var no : Int //Invert the output
public var c : [Int] { //Output
get {
//Numbers first go through unary ALUs. These can negate the input (and output the value), return 0, or return the inverse of 0. They then undergo the operation specified by f, either addition or a bitwise and operation, and are negated if n is 1.
var ux = UnaryALU(z: zx, n: nx, x: x).c //Unary ALU. See comments for more
var uy = UnaryALU(z: zy, n: ny, x: y).c
var fd = select16(s: f, d1: Add16(a: ux, b: uy).c, d0: and16(a: ux, b: uy).c).c //Adds a 16 bit number or does a bitwise and operation. For more on select16, see the line below.
var out = select16(s: no, d1: not16(a: fd).c, d0: fd).c //Selects a number. If s is 1, it returns d1. If s is 0, it returns d0. d0 is the value returned by fd, while d1 is the inverse.
return out
}
}
public init(x:[Int],y:[Int],zx:Int,zy:Int,nx:Int,ny:Int,f:Int,no:Int) {
self.x = x
self.y = y
self.zx = zx
self.zy = zy
self.nx = nx
self.ny = ny
self.f = f
self.no = no
}
}
I use c for the output variable, store values with multiple bits in Int arrays, and store single bits in Int values.
I’m doing this on Swift Playgrounds 3.0 with Swift 5.0 on a 6th generation iPad. I’m storing each component or set of components in a separate file in a module, which is why some variables and all structs are marked public. I would greatly appreciate any help. Thanks in advance.
So, I’ve completely redone my approach and have found a way to bypass the issues I was facing. What I’ve done is make what I call “tracker variables” for each input. When get is called for each variable, it returns that value of the tracker assigned to it. When set is called it calls an update() function that updates the output of the circuit. It also updates the value of the tracker. This essentially creates a ‘copy’ of each variable. I did this to prevent any infinite loops.
Trackers are unfortunately necessary here. I’ll demonstrate why
var variable : Type {
get {
return variable //Calls the getter again, resulting in an infinite loop
}
set {
//Do something
}
}
In order to make a setter, Swift requires a getter to be made as well. In this example, calling variable simply calls get again, resulting in a never-ending cascade of calls to get. Tracker variables are a workaround that use minimal extra code.
Using an update method makes sure the output responds to a change in any input. This also works with a clock signal, due to the architecture of the components themselves. Although it appears to act as the clock, it does not.
For example, in data flip-flops, the clock signal is passed into gates. All a clock signal does is deactivate a component when the signal is off. So, I can implement that within update() while remaining faithful to reality.
Here’s an example of a half adder. Note that the tracker variables I mentioned are marked by an underscore in front of their name. It has two inputs, x and y, which are 1 bit each. It also has two outputs, high and low, also known as carry and sum. The outputs are also one bit.
struct halfAdder {
private var _x : Bool //Tracker for x
public var x: Bool { //Input 1
get {
return _x //Return the tracker’s value
}
set {
_x = x //Set the tracker to x
update() //Update the output
}
}
private var _y : Bool //Tracker for y
public var y: Bool { //Input 2
get {
return _y
}
set {
_y = y
update()
}
}
public var high : Bool //High output, or ‘carry’
public var low : Bool //Low output, or ‘sum’
internal mutating func update(){ //Updates the output
high = x && y //AND gate, sets the high output
low = (x || y) && !(x && y) //XOR gate, sets the low output
}
public init(x:Bool, y:Bool){ //Initializer
self.high = false //This will change when the variables are set, ensuring a correct output.
self.low = false //See above
self._x = x //Setting trackers and variables
self._y = y
self.x = x
self.y = y
}
}
This is a very clean way, save for the trackers, do accomplish this task. It can trivially be expanded to fit any number of bits by using arrays of Bool instead of a single value. It respects the clock signal, updates the output when the inputs change, and is very similar to real computers.

Anybody know where this code to normalize spherical harmonics coefficients come from?

I found this code on the internet and would like to know the theory behind it, can anybody point me in the right direction?
Here is the code:
float4 SHCNormalize(in float4 res)
{
// extract direction
float l = dot(res.gba, res.gba);
res.gba /= max(0.05f, sqrt(l));
res.r = 1.0;
return res;
}
To give you a little context, this code gets passed in 4 zonal harmonics coefficients representing a clamped cosine lobe in SH space.
Thanks!
the max in the function is to avoid devision by 0.0. the res.r = 1.0f is an implementation detail that only applies to the code was looking at and has no theoretical basis.

L-BFGS from RISO not working

I am testing the implementation of RISO's L-BFGS library for function minimization for logistic regression in Java. Here is the link to the class that I am using.
To test the library, I am trying to minimize the function:
f(x) = 2*(x1^2) + 4*x2 + 5
The library needs the objective and the gradient functions which I implemented as below:
/**
The value of the objective function, given variable assignments
x. This is specific to your problem, so you must override it.
Remember that LBFGS only minimizes, so lower is better.
**/
public double objectiveFunction(double[] x) throws Exception {
return (2*x[0]*x[0] + 3*x[1] + 1);
}
/**
The gradient of the objective function, given variable assignments
x. This is specific to your problem, so you must override it.
**/
public double[] evaluateGradient(double[] x) throws Exception {
double[] result = new double[x.length];
result[0] = 4 * x[0];
result[1] = 3;
return result;
}
Running the code with this implementation of the objective function and gradient gives me the following exception:
Exception in thread "main" Line search failed. See documentation of routine mcsrch.
Error return of line search: info = 3 Possible causes:
function or gradient are incorrect, or incorrect tolerances. (iflag == -1)
I haven't changed the tolerances from the default values. What am I doing wrong?
I don't think your cost function has a minimum since x2 can reach -Inf, and gradient algorithm won't find it.
It is a quadratic function for x1, but not for x2. I suspect the exception is thrown out because the gradient algorithm cannot find out the optimal solution, and it 'thinks' the problem is the tolerance coefficient is not correctly set, or the gradient function is wrong
Do you mean f(x) = 2*(x^2) + 3*x + 1 in your object function?

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