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What's a good algorithm for checking if a given list of values alternates up and down?

Assuming the function takes in a list of double and an index to perform the check from, I need to check if the values alternates up and down consecutively.
For example, a list of [14.0,12.3,13.0,11.4] alternates consecutively but a list of [14.0,12.3,11.4,13.0] doesn't.
The algorithm doesn't have to be fast, but I'd like it to be compact to write (LINQ is totally fine). This is my current method, and it looks way too crude to my taste:
enum AlternatingDirection { Rise, Fall, None };
public bool CheckConsecutiveAlternation(List<double> dataList, int currDataIndex)
{
/*
* Result True : Fail
* Result False : Pass
*/
if (!_continuousRiseFallCheckBool)
return false;
if (dataList.Count < _continuousRiseFallValue)
return false;
if (currDataIndex + 1 < _continuousRiseFallValue)
return false;
AlternatingDirection direction = AlternatingDirection.None;
int startIndex = currDataIndex - _continuousRiseFallValue + 1;
double prevVal = 0;
for (int i = startIndex; i <= currDataIndex; i++)
{
if (i == startIndex)
{
prevVal = dataList[i];
continue;
}
if (prevVal > dataList[i])
{
prevVal = dataList[i];
switch (direction)
{
case AlternatingDirection.None:
direction = AlternatingDirection.Fall;
continue;
case AlternatingDirection.Rise:
direction = AlternatingDirection.Fall;
continue;
default:
//Two falls in a row. Not a signal.
return false;
}
}
if (prevVal < dataList[i])
{
prevVal = dataList[i];
switch (direction)
{
case AlternatingDirection.None:
direction = AlternatingDirection.Rise;
continue;
case AlternatingDirection.Fall:
direction = AlternatingDirection.Rise;
continue;
default:
//Two rise in a row. Not a signal.
return false;
}
}
return false;
}
//Alternated n times until here. Data is out of control.
return true;
}

Try this:
public static bool IsAlternating(double[] data)
{
var d = GetDerivative(data);
var signs = d.Select(val => Math.Sign(val));
bool isAlternating =
signs.Zip(signs.Skip(1), (a, b) => a != b).All(isAlt => isAlt);
return isAlternating;
}
private static IEnumerable<double> GetDerivative(double[] data)
{
var d = data.Zip(data.Skip(1), (a, b) => b - a);
return d;
}
Live demo
The idea is:
If the given list of values is alternating up and down, mathematically it means that it's derivative keeps changing its sign.
So this is exactly what this piece of code does:
Get the derivative.
Checks for sign fluctuations.
And the bonus is that it will not evaluate all of the derivative / signs arrays unless it is necessary.

I'd do it with a couple of consecutive zips, bundled in an extension method:
public static class AlternatingExtensions {
public static bool IsAlternating<T>(this IList<T> list) where T : IComparable<T>
{
var diffSigns = list.Zip(list.Skip(1), (a,b) => b.CompareTo(a));
var signChanges = diffSigns.Zip(diffSigns.Skip(1), (a,b) => a * b < 0);
return signChanges.All(s => s);
}
}
Edit: for completeness, here's how you'd use the feature:
var alternatingList = new List<double> { 14.0, 12.3, 13.0, 11.4 };
var nonAlternatingList = new List<double> { 14.0, 12.3, 11.4, 13.0 };
alternatingList.IsAlternating(); // true
nonAlternatingList.IsAlternating(); // false
I also changed the implementation to work on more types, making use of generics as much as possible.

Here is a small pseudo code. Assuming no repeated elements (can be handled easily though by few tweaks)
Idea is to have a sign variable which is alternating 1,-1,... that is multipled by the difference of two consecutive pairs, the difference multipled by this sign variable must always be positive. If it's not at some point, return false.
isUpAndDown(l):
if size(l) < 2: // empty,singleton list is always good.
return true
int sign = (l[0] < l[1] ? 1 : -1)
for i from 0 to n-1 (exclusive):
if sign * (l[i+1] - l[i]) < 0:
return false //not alternating
sign = sign * -1
end for
return true //all good

You may create kind of a signed array first:
double previous = 0;
var sign = myList.Select(x => {
int s = Math.Sign(x - previous);
previos = x;
return s;
});
This gives you a list similar to
{ -1, 1, -1, ... }
Now you can take a similar appraoch as the previos Select-statement to check if a -1 follows a 1:
var result = sign.All(x => {
bool b = x == -previous;
previous = x;
return b;
});
Now result is true if your list alternates, false otherwise.
EDIT: To ensure that the very first check within the second query also passes add previous = -sign[0]; before the second query.

Assuming that two equal values in a row are not acceptable (if they are, just skip over equal values):
if (dataList[0] == dataList[1])
return false;
bool nextMustRise = dataList[0] > dataList[1];
for (int i = 2; i < dataList.Count; i++) {
if (dataList[i - 1] == dataList[i] || (dataList[i - 1] < dataList[i]) != nextMustRise)
return false;
nextMustRise = !nextMustRise;
}
return true;

public double RatioOfAlternations(double[] dataList)
{
double Alternating = 0;
double Total = (dataList.Count()-2);
for (int (i) = 0; (i) < Total; (i)++)
{
if (((dataList[i+1]-dataList[i])*(dataList[i+2]-dataList[i+1]))<0)
// If previous change is opposite sign to current change, this will be negative
{
Alternating++;
}
else
{
}
}
return (Alternating/Total);
}

Split a collection of double by size of its contents

I have a collection of numbers (Collection) and it can be any size and contain negative and positive numbers. I am trying to split it up based on some criteria. starting at the first number in the collection I want to make a collection while that number is above -180 and below 180. Any numbers above 180 will go in a new collection or any numbers below -180 will go in an new collection. If the numbers become within the acceptable parameters again those will go in a new collection again. the problem is the collections need to stay in order.
For example.
Take a collection of 100:
the first 50 is between 180 and -180.
the next 20 are below -180
the next 20 are above 180
the last 10 are between 180 and -180
From the collection above I should now have 4 separate collection in the same order as the original 1 collection.
First collection numbers in original order between 180 and -180
second collection numbers in original order below -180
third collection numbers in original order above 180
fourth collection numbers in original order between 180 and -180
I have made an attempt, what I have doesn't work and is a nasty mess of if statements. I don't know linq very well but I think there may be a more elegant solution using that. Can anyone help me out here either with showing me how to create a linq statement or suggestions on how to get my if statements to work if that is the best way.
Collection<Tuple<Collection<double>, int>> collectionOfDataSets = new Collection<Tuple<Collection<double>, int>>();
Collection<double> newDataSet = new Collection<double>();
for (int i = 0; i < dataSet.Count; i++) {
if (dataSet[i] < 180 && dataSet[i] > -180) {
newDataSet.Add(dataSet[i]);
} else {
Tuple<Collection<double>, int> lastEntry = collectionOfDataSets.LastOrDefault(b => b.Item2 == i--);
if (lastEntry != null){
lastEntry.Item1.Add(dataSet[i]);
}
double lastInLastCollection = collectionOfDataSets.ElementAtOrDefault(collectionOfDataSets.Count).Item1.Last();
if (newDataSet.Count > 0 && lastInLastCollection!= dataSet[i]){
collectionOfDataSets.Add(new Tuple<Collection<double>, int>(newDataSet, i));
}
newDataSet = new Collection<double>();
}
}
Thank you in advance for any assistance.

Your example is complicated. I'll first state and solve a simpler problem, then use the same method to solve your original problem.
I want to split a list of numbers into contiguous groups of even and odd numbers. For example, given the list 2,2,4,3,6,2 I would split it into three groups [2,2,4], [3], [6,2]
This can be done concisely with a GroupAdjacentBy method
> var numbers = new List<int>{2,2,4,3,6,2};
> numbers.GroupAdjacentBy(x => x % 2)
[[2,2,4], [3], [6,2]]
To solve your problem, simply replace the even-odd classifying function above with your classification function:
> var points = new List<int>{-180,180};
> var f = new Func<int,int>(x => points.BinarySearch(x));
> var numbers = new List<int>{6,-50,100,190,200,20};
> numbers.GroupAdjacentBy(f)
[[6,-50,100], [190,200], [20]]

If you need the collections to be updated as soon as the values change why don;t you use properties? Something like
// your original collection
public IList<double> OriginalValues; //= new List<double> { -1000, 5, 7 1000 };
public IList<double> BelowMinus180
{
get { return OriginalValues.Where(x => x < -180).ToList().AsReadOnly(); }
}
public IList<double> BetweenMinus180And180
{
get { return OriginalValues.Where(x => x >= -180 && x <= 180).ToList().AsReadOnly(); }
}
public IList<double> Above180
{
get { return OriginalValues.Where(x => x > 180).ToList().AsReadOnly(); }
}

public static List<List<T>> PartitionBy<T>(this IEnumerable<T> seq, Func<T, bool> predicate)
{
bool lastPass = true;
return seq.Aggregate(new List<List<T>>(), (partitions, item) =>
{
bool inc = predicate(item);
if (inc == lastPass)
{
if (partitions.Count == 0)
{
partitions.Add(new List<T>());
}
partitions.Last().Add(item);
}
else
{
partitions.Add(new List<T> { item });
}
lastPass = inc;
return partitions;
});
}
You can then use:
List<List<double>> segments = newDataSet.PartitionBy(d => d > -180 && d < 180);

How about this possible solution using two passes. In the first pass we find the indices were a change occurs, and in the second pass we do the actual partitioning.
First an auxiliary method to determine the category:
protected int DetermineCategory(double number)
{
if (number < 180 && number > -180)
return 0;
else if (number < -180)
return 1;
else
return 2;
}
And then the actual algorithm:
List<int> indices = new List<int>();
int currentCategory = -1;
for (int i = 0; i < numbers.Count; i++)
{
int newCat = DetermineCategory(numbers[i]);
if (newCat != currentCategory)
{
indices.Add(i);
currentCategory = newCat;
}
}
List<List<double>> collections = new List<List<double>>(indices.Count);
for (int i = 1; i < indices.Count; ++i)
collections.Add(new List<double>(
numbers.Skip(indices[i - 1]).Take(indices[i] - indices[i - 1])));

Here is a new answer based on the new info you provided. I hope this time I will be closer to what you need
public IEnumerable<IList<double>> GetCollectionOfCollections(IList<double> values, IList<double> boundries)
{
var ordered = values.OrderBy(x => x).ToList();
for (int i = 0; i < boundries.Count; i++)
{
var collection = ordered.Where(x => x < boundries[i]).ToList();
if (collection.Count > 0)
{
ordered = ordered.Except(collection).ToList();
yield return collection.ToList();
}
}
if (ordered.Count() > 0)
{
yield return ordered;
}
}

One method with linq. Untested but should work
var firstSet = dataSet.TakeWhile(x=>x>-180&&x<180);
var totalCount = firstSet.Count();
var secondSet = dataSet.Skip(totalCount).TakeWhile(x=>x<-180);
totalCount+=secondSet.Count();
var thirdSet = dataSet.Skip(totalCount).TakeWhile(x=>x>180);
totalCount += thirdSet.Count();
var fourthSet = dataSet.Skip(totalCount);

finding closest value in an array

int[] array = new int[5]{5,7,8,15,20};
int TargetNumber = 13;
For a target number, I want to find the closest number in an array. For example, when the target number is 13, the closest number to it in the array above is 15. How would I accomplish that programmatically in C#?

EDIT: Have adjusted the queries below to convert to using long arithmetic, so that we avoid overflow issues.
I would probably use MoreLINQ's MinBy method:
var nearest = array.MinBy(x => Math.Abs((long) x - targetNumber));
Or you could just use:
var nearest = array.OrderBy(x => Math.Abs((long) x - targetNumber)).First();
... but that will sort the whole collection, which you really don't need. It won't make much difference for a small array, admittedly... but it just doesn't feel quite right, compared with describing what you're actually trying to do: find the element with the minimum value according to some function.
Note that both of these will fail if the array is empty, so you should check for that first.

If you're using .Net 3.5 or above LINQ can help you here:
var closest = array.OrderBy(v => Math.Abs((long)v - targetNumber)).First();
Alternatively, you could write your own extension method:
public static int ClosestTo(this IEnumerable<int> collection, int target)
{
// NB Method will return int.MaxValue for a sequence containing no elements.
// Apply any defensive coding here as necessary.
var closest = int.MaxValue;
var minDifference = int.MaxValue;
foreach (var element in collection)
{
var difference = Math.Abs((long)element - target);
if (minDifference > difference)
{
minDifference = (int)difference;
closest = element;
}
}
return closest;
}
Useable like so:
var closest = array.ClosestTo(targetNumber);

Both Jon and Rich gave great answers with MinBy and ClosestTo. But I would never recommend using OrderBy if your intent is to find a single element. It's far too inefficient for those kinds of tasks. It's simply the wrong tool for the job.
Here's a technique that performs marginally better than MinBy, is already included in the .NET framework, but less elegant than MinBy: Aggregate
var nearest = array.Aggregate((current, next) => Math.Abs((long)current - targetNumber) < Math.Abs((long)next - targetNumber) ? current : next);
As I said, not as elegant as Jon's method, but viable.
Performance on my computer:
For(each) Loops = fastest
Aggregate = 2.5x slower than loops
MinBy = 3.5x slower than loops
OrderBy = 12x slower than loops

I found this really sexy approach years ago in Math.NET Numerics https://numerics.mathdotnet.com/ which works with BinarySearch in the array. It was a good help in preparation for interpolations and works down to .Net 2.0:
public static int LeftSegmentIndex(double[] array, double t)
{
int index = Array.BinarySearch(array, t);
if (index < 0)
{
index = ~index - 1;
}
return Math.Min(Math.Max(index, 0), array.Length - 2);
}

If you need to find the closest value to the average
very open style
public static double Miidi(double[] list)
{
bool isEmpty = !list.Any();
if (isEmpty)
{
return 0;
}
else
{
double avg = list.Average();
double closest = 100;
double shortest = 100;
{
for ( int i = 0; i < list.Length; i++)
{
double lgth = list[i] - avg;
if (lgth < 0)
{
lgth = lgth - (2 * lgth);
}
else
lgth = list[i] - avg;
if (lgth < shortest)
{
shortest = lgth;
closest = list[i];
}
}
}
return closest;
}
}

Performance wise custom code will be more useful.
public static int FindNearest(int targetNumber, IEnumerable<int> collection) {
var results = collection.ToArray();
int nearestValue;
if (results.Any(ab => ab == targetNumber))
nearestValue = results.FirstOrDefault(i => i == targetNumber);
else{
int greaterThanTarget = 0;
int lessThanTarget = 0;
if (results.Any(ab => ab > targetNumber)) {
greaterThanTarget = results.Where(i => i > targetNumber).Min();
}
if (results.Any(ab => ab < targetNumber)) {
lessThanTarget = results.Where(i => i < targetNumber).Max();
}
if (lessThanTarget == 0) {
nearestValue = greaterThanTarget;
}
else if (greaterThanTarget == 0) {
nearestValue = lessThanTarget;
}
else if (targetNumber - lessThanTarget < greaterThanTarget - targetNumber) {
nearestValue = lessThanTarget;
}
else {
nearestValue = greaterThanTarget;
}
}
return nearestValue;
}

Good way to get the key of the highest value of a Dictionary in C#

I'm trying to get the key of the maximum value in the Dictionary<string, double> results.
This is what I have so far:
double max = results.Max(kvp => kvp.Value);
return results.Where(kvp => kvp.Value == max).Select(kvp => kvp.Key).First();
However, since this seems a little inefficient, I was wondering whether there was a better way to do this.

edit: .NET 6 introduced a new method
var max = results.MaxBy(kvp => kvp.Value).Key;
You should probably use that if you can.
I think this is the most readable O(n) answer using standard LINQ.
var max = results.Aggregate((l, r) => l.Value > r.Value ? l : r).Key;
edit: explanation for CoffeeAddict
Aggregate is the LINQ name for the commonly known functional concept Fold
It loops over each element of the set and applies whatever function you provide.
Here, the function I provide is a comparison function that returns the bigger value.
While looping, Aggregate remembers the return result from the last time it called my function. It feeds this into my comparison function as variable l. The variable r is the currently selected element.
So after aggregate has looped over the entire set, it returns the result from the very last time it called my comparison function. Then I read the .Key member from it because I know it's a dictionary entry
Here is a different way to look at it [I don't guarantee that this compiles ;) ]
var l = results[0];
for(int i=1; i<results.Count(); ++i)
{
var r = results[i];
if(r.Value > l.Value)
l = r;
}
var max = l.Key;

After reading various suggestions, I decided to benchmark them and share the results.
The code tested:
// TEST 1
for (int i = 0; i < 999999; i++)
{
KeyValuePair<GameMove, int> bestMove1 = possibleMoves.First();
foreach (KeyValuePair<GameMove, int> move in possibleMoves)
{
if (move.Value > bestMove1.Value) bestMove1 = move;
}
}
// TEST 2
for (int i = 0; i < 999999; i++)
{
KeyValuePair<GameMove, int> bestMove2 = possibleMoves.Aggregate((a, b) => a.Value > b.Value ? a : b);
}
// TEST 3
for (int i = 0; i < 999999; i++)
{
KeyValuePair<GameMove, int> bestMove3 = (from move in possibleMoves orderby move.Value descending select move).First();
}
// TEST 4
for (int i = 0; i < 999999; i++)
{
KeyValuePair<GameMove, int> bestMove4 = possibleMoves.OrderByDescending(entry => entry.Value).First();
}
The results:
Average Seconds Test 1 = 2.6
Average Seconds Test 2 = 4.4
Average Seconds Test 3 = 11.2
Average Seconds Test 4 = 11.2
This is just to give an idea of their relative performance.
If your optimizing 'foreach' is fastest, but LINQ is compact and flexible.

Maybe this isn't a good use for LINQ. I see 2 full scans of the dictionary using the LINQ solution (1 to get the max, then another to find the kvp to return the string.
You could do it in 1 pass with an "old fashioned" foreach:
KeyValuePair<string, double> max = new KeyValuePair<string, double>();
foreach (var kvp in results)
{
if (kvp.Value > max.Value)
max = kvp;
}
return max.Key;

You can sort dictionary by using OrderBy (for find min value) or OrderByDescending (for max value) then get first element. It also help when you need find second max/min element
Get dictionary key by max value:
double min = results.OrderByDescending(x => x.Value).First().Key;
Get dictionary key by min value:
double min = results.OrderBy(x => x.Value).First().Key;
Get dictionary key by second max value:
double min = results.OrderByDescending(x => x.Value).Skip(1).First().Key;
Get dictionary key by second min value:
double min = results.OrderBy(x => x.Value).Skip(1).First().Key;

This is a fast method. It is O(n), which is optimal. The only problem I see is that it iterates over the dictionary twice instead of just once.
You can do it iterating over the dictionary once by using MaxBy from morelinq.
results.MaxBy(kvp => kvp.Value).Key;

Little extension method:
public static KeyValuePair<K, V> GetMaxValuePair<K,V>(this Dictionary<K, V> source)
where V : IComparable
{
KeyValuePair<K, V> maxPair = source.First();
foreach (KeyValuePair<K, V> pair in source)
{
if (pair.Value.CompareTo(maxPair.Value) > 0)
maxPair = pair;
}
return maxPair;
}
Then:
int keyOfMax = myDictionary.GetMaxValuePair().Key;

Check These out:
result.Where(x=>x.Value==result.Values.Max()).Select(x=>x.Key).ToList()

My version based off the current Enumerable.Max implementation with an optional comparer:
public static TSource MaxValue<TSource, TConversionResult>(this IEnumerable<TSource> source, Func<TSource, TConversionResult> function, IComparer<TConversionResult> comparer = null)
{
comparer = comparer ?? Comparer<TConversionResult>.Default;
if (source == null) throw new ArgumentNullException(nameof(source));
TSource max = default;
TConversionResult maxFx = default;
if ( (object)maxFx == null) //nullable stuff
{
foreach (var x in source)
{
var fx = function(x);
if (fx == null || (maxFx != null && comparer.Compare(fx, maxFx) <= 0)) continue;
maxFx = fx;
max = x;
}
return max;
}
//valuetypes
var notFirst = false;
foreach (var x in source)
{
var fx = function(x);
if (notFirst)
{
if (comparer.Compare(fx, maxFx) <= 0) continue;
maxFx = fx;
max = x;
}
else
{
maxFx = fx;
max = x;
notFirst = true;
}
}
if (notFirst)
return max;
throw new InvalidOperationException("Sequence contains no elements");
}
Example usage:
class Wrapper
{
public int Value { get; set; }
}
[TestMethod]
public void TestMaxValue()
{
var dictionary = new Dictionary<string, Wrapper>();
for (var i = 0; i < 19; i++)
{
dictionary[$"s:{i}"] = new Wrapper{Value = (i % 10) * 10 } ;
}
var m = dictionary.Keys.MaxValue(x => dictionary[x].Value);
Assert.AreEqual(m, "s:9");
}

How about doing it in parallel using Interlocked.Exchange for thread safety :) Keep in mind that Interlocked.Exchange will only work with a reference type.(i.e. a struct or key value pair (unless wrapped in a class) will not work to hold the max value.
Here's an example from my own code:
//Parallel O(n) solution for finding max kvp in a dictionary...
ClassificationResult maxValue = new ClassificationResult(-1,-1,double.MinValue);
Parallel.ForEach(pTotals, pTotal =>
{
if(pTotal.Value > maxValue.score)
{
Interlocked.Exchange(ref maxValue, new
ClassificationResult(mhSet.sequenceId,pTotal.Key,pTotal.Value));
}
});
EDIT (Updated code to avoid possible race condition above):
Here's a more robust pattern which also shows selecting a min value in parallel. I think this addresses the concerns mentioned in the comments below regarding a possible race condition:
int minVal = int.MaxValue;
Parallel.ForEach(dictionary.Values, curVal =>
{
int oldVal = Volatile.Read(ref minVal);
//val can equal anything but the oldVal
int val = ~oldVal;
//Keep trying the atomic update until we are sure that either:
//1. CompareExchange successfully changed the value.
//2. Another thread has updated minVal with a smaller number than curVal.
// (in the case of #2, the update is no longer needed)
while (oldval > curVal && oldval != val)
{
val = oldval;
oldval = Interlocked.CompareExchange(ref minVal, curVal, oldval);
}
});

I think using the standard LINQ Libraries this is as fast as you can go.

How do I select every 6th element from a list (using Linq) [duplicate]

This question already has answers here:
How can I get every nth item from a List<T>?
(10 answers)
Closed 2 years ago.
I've got a list of 'double' values. I need to select every 6th record. It's a list of coordinates, where I need to get the minimum and maximum value of every 6th value.
List of coordinates (sample): [2.1, 4.3, 1.0, 7.1, 10.6, 39.23, 0.5, ... ]
with hundrets of coordinates.
Result should look like: [x_min, y_min, z_min, x_max, y_max, z_max]
with exactly 6 coordinates.
Following code works, but it takes to long to iterate over all coordinates. I'd like to use Linq instead (maybe faster?)
for (int i = 0; i < 6; i++)
{
List<double> coordinateRange = new List<double>();
for (int j = i; j < allCoordinates.Count(); j = j + 6)
coordinateRange.Add(allCoordinates[j]);
if (i < 3) boundingBox.Add(coordinateRange.Min());
else boundingBox.Add(coordinateRange.Max());
}
Any suggestions?
Many thanks! Greets!

coordinateRange.Where( ( coordinate, index ) => (index + 1) % 6 == 0 );
The answer from Webleeuw was posted prior to this one, but IMHO it's clearer to use the index as an argument instead of using the IndexOf method.

Something like this could help:
public static IEnumerable<T> Every<T>(this IEnumerable<T> source, int count)
{
int cnt = 0;
foreach(T item in source)
{
cnt++;
if (cnt == count)
{
cnt = 0;
yield return item;
}
}
}
You can use it like this:
int[] list = new []{1,2,3,4,5,6,7,8,9,10,11,12,13};
foreach(int i in list.Every(3))
{ Console.WriteLine(i); }
EDIT:
If you want to skip the first few entries, you can use the Skip() extension method:
foreach (int i in list.Skip(2).Every(6))
{ Console.WriteLine(i); }

There is an overload of the Where method with lets you use the index directly:
coordinateRange.Where((c,i) => (i + 1) % 6 == 0);

Any particular reason you want to use LINQ to do this?
Why not write a loop that steps with 6 increments each time and get access the value directly?

To find a faster solution start a profile!
Measure how long it takes for every step in your for loop and try to avoid the biggest bottleneck.
After making a second look at your code, it seems, your problem is that you run six times over your big list. So the time needed is always six times of the list size.
Instead you should run once over the whole list and put every item into the correct slot.
Just to make a performance test for yourself you should test these two approaches:
Sample class to hold data
public class Coordinates
{
public double x1 { get; set; }
public double x2 { get; set; }
public double y1 { get; set; }
public double y2 { get; set; }
public double z1 { get; set; }
public double z2 { get; set; }
}
Initializing of the value holder
Coordinates minCoordinates = new Coordinates();
//Cause we want to hold the minimum value, it will be initialized with
//value that is definitely greater or equal than the greatest in the list
minCoordinates.x1 = Double.MaxValue;
minCoordinates.x2 = Double.MaxValue;
minCoordinates.y1 = Double.MaxValue;
minCoordinates.y2 = Double.MaxValue;
minCoordinates.z1 = Double.MaxValue;
minCoordinates.z2 = Double.MaxValue;
Using a for loop if the index operator is O(1)
for (int i = 0; i < allCoordinates.Count; i++)
{
switch (i % 6)
{
case 0:
minCoordinates.x1 = Math.Min(minCoordinates.x1, allCoordinates[i]);
break;
case 1:
minCoordinates.x2 = Math.Min(minCoordinates.x2, allCoordinates[i]);
break;
case 2:
minCoordinates.y1 = Math.Min(minCoordinates.y1, allCoordinates[i]);
break;
case 3:
minCoordinates.y2 = Math.Min(minCoordinates.y2, allCoordinates[i]);
break;
case 4:
minCoordinates.z1 = Math.Min(minCoordinates.z1, allCoordinates[i]);
break;
case 5:
minCoordinates.z2 = Math.Min(minCoordinates.z2, allCoordinates[i]);
break;
}
}
Using foreach if IEnumerator is O(1)
int count = 0;
foreach (var item in allCoordinates)
{
switch (count % 6)
{
case 0:
minCoordinates.x1 = Math.Min(minCoordinates.x1, item);
break;
case 1:
minCoordinates.x2 = Math.Min(minCoordinates.x2, item);
break;
case 2:
minCoordinates.y1 = Math.Min(minCoordinates.y1, item);
break;
case 3:
minCoordinates.y2 = Math.Min(minCoordinates.y2, item);
break;
case 4:
minCoordinates.z1 = Math.Min(minCoordinates.z1, item);
break;
case 5:
minCoordinates.z2 = Math.Min(minCoordinates.z2, item);
break;
}
count++;
}

Well its not LINQ, but If you are worrying about performance, this might help.
public static class ListExtensions
{
public static IEnumerable<T> Every<T>(this IList<T> list, int stepSize, int startIndex)
{
if (stepSize <= 0)
throw new ArgumentException();
for (int i = startIndex; i < list.Count; i += stepSize)
yield return list[i];
}
}

Suggestion:
coordinateRange.Where(c => (coordinateRange.IndexOf(c) + 1) % 6 == 0);
I stand corrected, thanks for the comments.
As stated by codymanix, the correct answer is indeed:
coordinateRange.Where((c, i) => (i + 1) % 6 == 0);

The best way to do this would be refactoring the datastructure so that every dimension would be its own array. That way x1_max would be just x1.Max(). If you cannot change the input data structure, the next best way is to iterate over the array once and do all accesses locally. This helps with staying within the L1-cached memory:
var minValues = new double[] { Double.MaxValue, Double.MaxValue, Double.MaxValue };
var maxValues = new double[] { Double.MinValue, Double.MinValue, Double.MinValue };
for (int i = 0; i < allCoordinates.Length; i += 6)
{
for (int j = 0; i < 3; i++)
{
if (allCoordinates[i+j] < minValues[j])
minValues[j] = allCoordinates[i+j];
if (allCoordinates[i+j+3] > maxValues[j])
maxValues[j] = allCoordinates[i+j+3];
}
}

Use Skip and combintaion with Take.
coordinateRange.Skip(6).Take(1).First();
I recommend you move this to a extension method.