What is the fastest way to lookup the index of a value in sorted vector in MATLAB?
That is, is there a fast find(vector == myNumber, 1, 'first') for when vector is sorted?
I have a large matrix (200,000 x 4) of locations each with a unique integer ID recorded in the first column. I want to find the right the location of a known ID but thousands of searches can take me a little bit to find.
If you use ismembc2, the loc output should give you what you need. See this for more details:
http://www.mathworks.com/support/solutions/en/data/1-9NIE1N/index.html?product=ML&solution=1-9NIE1N
There are a number of submissions for this on FEX: http://www.mathworks.com/matlabcentral/fileexchange/?term=binary+search+vector
I do not know if it is faster but you may want to try
result=vector(vector(:,1)==myNumber,:)
result will contain the 4 elements row for which vector first column == myNumber
Related
If I want to find the minimum value in each column of a NumPy array, I can use the numpy.amin() function. However, is there a way to find the two minimum values in each column, that is faster than sorting each column?
You can simply use np.partition along the columns to get smallest N numbers -
N = 2
np.partition(a,kth=N-1,axis=0)[:N]
This doesn't actually sort the entire data, simply partitions into two sections such that smallest N numbers are in the first section, also called as partial-sort.
Bonus (Getting top N elements) : Similarly, to get the top N numbers per col, simply use negative kth value -
np.partition(a,kth=-N,axis=0)[-N:]
Along other axes and higher dim arrays
To use it along other axes, change the axis value. So, along rows, it would be axis=1 for a 2D array and extend the same way for higher dimension ndarrays.
Use the min() method, and specify the axis you want to average over:
a = np.random.rand(10,3)
a.min(axis=0)
gives:
array([0.04435587, 0.00163139, 0.06327353])
a.min(axis=1)
gives
array([0.01354386, 0.08996586, 0.19332211, 0.00163139, 0.55650945,
0.08409907, 0.23015718, 0.31463493, 0.49117553, 0.53646868])
Help with homework problem: "Let us define the "data science experience" of a given person as the person's largest score among Regression, Classification, and Clustering. Compute the average data science experience among all MSIS students."
Beginner to coding. I am trying to figure out how to check amongst columns and compare those columns to each other for the largest value. And then take the average of those found values.
I greatly appreciate your help in advance!
Picture of the sample data set: 1: https://i.stack.imgur.com/9OSjz.png
Provided Code:
import pandas as pd
df = pd.read_csv("cleaned_survey.csv", index_col=0)
df.drop(['ProgSkills','Languages','Expert'],axis=1,inplace=True)
Sample Data:
What I have tried so far:
df[data_science_experience]=df[["Regression","Classification","Clustering"]].values.max()
df['z']=df[['Regression','Classification','Clustering']].apply(np.max,axis=1)
df[data_science_experience]=df[["Regression","Classification","Clustering"]].apply(np.max,axis=1)
If you want to get the highest score of column 'hw1' you can get it with:
pd['hw1'].max(). this gives you a series of all the values in that column and max returns the maximum. for average use mean:
pd['hw1'].mean()
if you want to find the maximum of multiple columns, you can use:
maximum_list = list()
for col in pd.columns:
maximum_list.append(pd[col].max)
max = maximum_list.max()
avg = maximum_list.mean()
hope this helps.
First, you want to get only the rows with MSIS in the Program column. That can be done in the following way:
df[df['Program'] == 'MSIS']
Next, you want to get only the Regression, Classification and Clustering columns. The previous query filtered only rows; we can add to that, like this:
df.loc[df['Program'] == 'MSIS', ['Regression', 'Classification', 'Clustering']]
Now, for each row remaining, we want to take the maximum. That can be done by appending .max(axis=1) to the previous line (axis=1 because we want the maximum of each row, not each column).
At this point, we should have a DataFrame where each row represents the highest score of the three categories for each student. Now, all that's left to do is take the mean, which can be done with .mean(). The full code should therefore look like this:
df.loc[df['Program'] == 'MSIS', ['Regression', 'Classification', 'Clustering']].max(axis=1).mean()
I would like to use an array rows for indexing rows of another array x. Initially, rows contains indices of all rows of x (and is therefor sorted). Throughout the program, some indices exclude are chosen to be removed from rows. Similar to rows itself, exclude is a sorted array.
What is the best way of finding the set difference of rows and exclude?
I have thought of a few different options, but I think their complexities are more than O(n + m), where n is the length of rows and m is the length of exclude.
new_rows = [r for r in rows if r not in exclude]
This solutions requires looking up exclude every time and therefore, O(mn) complexity.
new_rows = setdiff1d(rows, exclude, assume_unique=True)
This will probably take O(nlogm), but I'm not sure.
Convert exclude to a dict and run 1. The problem with this approach is that it requires extra memory, but it meets the complexity requirement.
Here are outlines of two O(n+m) options:
1) heapq.merge will combine two sorted sequences in linear time. As the combined sequence is sorted, shared indices will sit next to each other.
2) as rows as you describe it is a "thinned out range" I assume that the the max value of rows is not excessively large. You can therfore allocate an array E of that size (O(1) if we don't initialize it, i.e. use np.empty). Then you use rows and exclude to index into the empty array. For example, you write E[rows] = 1 E[exclude] = 0 and then check back E[rows] and remove all elements of rows at which E has changed from 1 to 0.
Option 2 also works if the two sets are not sorted.
I currently have a 3 dimensional array full of different values. I would like to find the indices corresponding to the "nth" smallest values in the array. For example... If the 3 smallest values were 0.1, 0.2 and 0.3 I would like to see, in order, the indices for these values. Any help would be greatly appreciated.
A possible way to approach this would be adding an original index dimension into your 3rd array, then sorting, by the current values to find out the smallest item and returning the original index. Take a look into this: VBA array sort function?
I basically need the answer to this SO question that provides a power-law distribution, translated to T-SQL for me.
I want to pull a last name, one at a time, from a census provided table of names. I want to get roughly the same distribution as occurs in the population. The table has 88,799 names ranked by frequency. "Smith" is rank 1 with 1.006% frequency, "Alderink" is rank 88,799 with frequency of 1.7 x 10^-6. "Sanders" is rank 75 with a frequency of 0.100%.
The curve doesn't have to fit precisely at all. Just give me about 1% "Smith" and about 1 in a million "Alderink"
Here's what I have so far.
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank] = ROUND(88799 * RAND(), 0)
But this of course yields a uniform distribution.
I promise I'll still be trying to figure this out myself by the time a smarter person responds.
Why settle for the power-law distribution when you can draw from the actual distribution ?
I suggest you alter the LastNames table to include a numeric column which would contain a numeric value representing the actual number of indivuduals with a name that is more common. You'll probably want a number on a smaller but proportional scale, say, maybe 10,000 for each percent of representation.
The list would then look something like:
(other than the 3 names mentioned in the question, I'm guessing about White, Johnson et al)
Smith 0
White 10,060
Johnson 19,123
Williams 28,456
...
Sanders 200,987
..
Alderink 999,997
And the name selection would be
SELECT TOP 1 [LastName]
FROM [LastNames] as LN
WHERE LN.[number_described_above] < ROUND(100000 * RAND(), 0)
ORDER BY [number_described_above] DESC
That's picking the first name which number does not exceed the [uniform distribution] random number. Note how the query, uses less than and ordering in desc-ending order; this will guaranty that the very first entry (Smith) gets picked. The alternative would be to start the series with Smith at 10,060 rather than zero and to discard the random draws smaller than this value.
Aside from the matter of boundary management (starting at zero rather than 10,060) mentioned above, this solution, along with the two other responses so far, are the same as the one suggested in dmckee's answer to the question referenced in this question. Essentially the idea is to use the CDF (Cumulative Distribution function).
Edit:
If you insist on using a mathematical function rather than the actual distribution, the following should provide a power law function which would somehow convey the "long tail" shape of the real distribution. You may wan to tweak the #PwrCoef value (which BTW needn't be a integer), essentially the bigger the coeficient, the more skewed to the beginning of the list the function is.
DECLARE #PwrCoef INT
SET #PwrCoef = 2
SELECT 88799 - ROUND(POWER(POWER(88799.0, #PwrCoef) * RAND(), 1.0/#PwrCoef), 0)
Notes:
- the extra ".0" in the function above are important to force SQL to perform float operations rather than integer operations.
- the reason why we subtract the power calculation from 88799 is that the calculation's distribution is such that the closer a number is closer to the end of our scale, the more likely it is to be drawn. The List of family names being sorted in the reverse order (most likely names first), we need this substraction.
Assuming a power of, say, 3 the query would then look something like
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank]
= 88799 - ROUND(POWER(POWER(88799.0, 3) * RAND(), 1.0/3), 0)
Which is the query from the question except for the last line.
Re-Edit:
In looking at the actual distribution, as apparent in the Census data, the curve is extremely steep and would require a very big power coefficient, which in turn would cause overflows and/or extreme rounding errors in the naive formula shown above.
A more sensible approach may be to operate in several tiers i.e. to perform an equal number of draws in each of the, say, three thirds (or four quarters or...) of the cumulative distribution; within each of these parts list, we would draw using a power law function, possibly with the same coeficient, but with different ranges.
For example
Assuming thirds, the list divides as follow:
First third = 425 names, from Smith to Alvarado
Second third = 6,277 names, from to Gainer
Last third = 82,097 names, from Frisby to the end
If we were to need, say, 1,000 names, we'd draw 334 from the top third of the list, 333 from the second third and 333 from the last third.
For each of the thirds we'd use a similar formula, maybe with a bigger power coeficient for the first third (were were are really interested in favoring the earlier names in the list, and also where the relative frequencies are more statistically relevant). The three selection queries could look like the following:
-- Random Drawing of a single Name in top third
-- Power Coef = 12
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank]
= 425 - ROUND(POWER(POWER(425.0, 12) * RAND(), 1.0/12), 0)
-- Second third; Power Coef = 7
...
WHERE LN.[Rank]
= (425 + 6277) - ROUND(POWER(POWER(6277.0, 7) * RAND(), 1.0/7), 0)
-- Bottom third; Power Coef = 4
...
WHERE LN.[Rank]
= (425 + 6277 + 82097) - ROUND(POWER(POWER(82097.0, 4) * RAND(), 1.0/4), 0)
Instead of storing the pdf as rank, store the CDF (the sum of all frequencies until that name, starting from Aldekirk).
Then modify your select to retrieve the first LN with rank greater than your formula result.
I read the question as "I need to get a stream of names which will mirror the frequency of last names from the 1990 US Census"
I might have read the question a bit differently than the other suggestions and although an answer has been accepted, and a very through answer it is, I will contribute my experience with the Census last names.
I had downloaded the same data from the 1990 census. My goal was to produce a large number of names to be submitted for search testing during performance testing of a medical record app. I inserted the last names and the percentage of frequency into a table. I added a column and filled it with a integer which was the product of the "total names required * frequency". The frequency data from the census did not add up to exactly 100% so my total number of names was also a bit short of the requirement. I was able to correct the number by selecting random names from the list and increasing their count until I had exactly the required number, the randomly added count never ammounted to more than .05% of the total of 10 million.
I generated 10 million random numbers in the range of 1 to 88799. With each random number I would pick that name from the list and decrement the counter for that name. My approach was to simulate dealing a deck of cards except my deck had many more distinct cards and a varing number of each card.
Do you store the actual frequencies with the ranks?
Converting the algebra from that accepted answer to MySQL is no bother, if you know what values to use for n. y would be what you currently have ROUND(88799 * RAND(), 0) and x0,x1 = 1,88799 I think, though I might misunderstand it. The only non-standard maths operator involved from a T-SQL perspective is ^ which is just POWER(x,y) == x^y.