find similar numbers within a matrix

Hi. I need to identify the position of a triplet of numbers (P) inside an array (M).

P = [-3.4970900e+01	  -2.0289890e+02	  -1.7948105e+02];

I am using the 'find' function but the numbers in P is very close to the respective numbers in M.

This does not determine the line of interest for me.

[r,c] = find(M(:,1) == P(1,1) & M(:,2) == P(1,2) & M(:,3) == P(1,3));

That is:

• P(1,1) is equal to or similar to M(?,1);
• P(1,2) is equal to or similar to M(?,2);
• P(1,3) is equal to or similar to M(?,3);

Instead, I determine the line of interest in this way:

[r,c] = find(M(:,1) == P(1,1));

p.s. The variation is only present after the decimal point.

Is there a way to identify within M the (very similar) values present in P? For example by considering a variation of +-0.01 in the numbers in M?

Answer 1

[Dyuman Joshi]

isequal or eq, == are not the best choices when comparing floating point numbers.

arr = load('M.mat')

arr = struct with fields:
    M: [61×3 double]

M = arr.M;

P = [-3.4970900e+01	  -2.0289890e+02	  -1.7948105e+02];

tol = 0.01;

%Rows that satisfy the condition for all column elements
idx = all(abs(M-P)<tol, 2)

idx = 61×1 logical array
   0
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%Get the output using the row indices
out = M(idx, :)

out = 1×3

-34.9709 -202.8989 -179.4810

Answer 2

[John D'Errico]

Lots of good answers posted. I did not see this one.

load M.mat
size(M)

ans = 1×2

61 3

The array M has 61 rows.

P = [-3.4970900e+01	  -2.0289890e+02	  -1.7948105e+02];

And we want to find an element in M that is close to P.

help knnsearch

 KNNSEARCH Find K nearest neighbors.
    IDX = KNNSEARCH(X,Y) finds the nearest neighbor in X for each point in
    Y. X is an MX-by-N matrix and Y is an MY-by-N matrix. Rows of X and Y
    correspond to observations and columns correspond to variables. IDX is
    a column vector with MY rows. Each row in IDX contains the index of
    the nearest neighbor in X for the corresponding row in Y.
 
    [IDX, D] = KNNSEARCH(X,Y) returns a MY-by-1 vector D containing the
    distances between each row of Y and its closest point in X.
 
    [IDX, D]= KNNSEARCH(X,Y,'NAME1',VALUE1,...,'NAMEN',VALUEN) specifies
    optional argument name/value pairs:
 
      Name          Value
      'K'           A positive integer, K, specifying the number of nearest
                    neighbors in X to find for each point in Y. Default is
                    1. IDX and D are MY-by-K matrices. D sorts the
                    distances in each row in ascending order. Each row in
                    IDX contains the indices of K closest neighbors in X
                    corresponding to the K smallest distances in D.
 
      'NSMethod'    Nearest neighbors search method. Value is either:
                    'kdtree'    - Creates and uses a kd-tree to find
                                  nearest neighbors. 'kdtree' is only valid
                                  when the distance metric is one of the
                                  following metrics:
                                    - 'euclidean'
                                    - 'cityblock'
                                    - 'minkowski'
                                    - 'chebychev'
                    'exhaustive' - Uses the exhaustive search algorithm.
                                   The distance values from all the points
                                   in X to each point in Y are computed to
                                   find nearest neighbors.
                    Default is 'kdtree' when the number of columns of X is
                    not greater than 10, X is not sparse, and the distance
                    metric is one of the above 4 metrics; otherwise,
                    default is 'exhaustive'.
 
     'IncludeTies'  A logical value indicating whether KNNSEARCH will
                    include all the neighbors whose distance values are
                    equal to the Kth smallest distance. Default is false.
                    If the value is true, KNNSEARCH includes all these
                    neighbors. In this case, IDX and D are MY-by-1 cell
                    arrays. Each row in IDX and D contains a vector with at
                    least K numeric numbers. D sorts the distances in each
                    vector in ascending order. Each row in IDX contains the
                    indices of the closest neighbors corresponding to these
                    smallest distances in D.
 
     'Distance'     A string or a function handle specifying the distance
                    metric. The value can be one of the following:
                    'euclidean'   - Euclidean distance (default).
                    'seuclidean'  - Standardized Euclidean distance. Each
                                    coordinate difference between X and a
                                    query point is scaled by dividing by a
                                    scale value S. The default value of S
                                    is the standard deviation computed from
                                    X, S=NANSTD(X). To specify another
                                    value for S, use the 'Scale' argument.
                    'fasteuclidean'    
                                  - Euclidean distance computed by using an
                                    alternative algorithm that saves time. 
                                    This faster algorithm can, in some 
                                    cases, reduce accuracy.
                    'fastseuclidean'   
                                  - Standardized Euclidean distance computed 
                                    by using an alternative algorithm that 
                                    saves time. This faster algorithm can, 
                                    in some cases, reduce accuracy.
                    'cityblock'   - City Block distance.
                    'chebychev'   - Chebychev distance (maximum coordinate
                                    difference).
                    'minkowski'   - Minkowski distance. The default
                                    exponent is 2. To specify a different
                                    exponent, use the 'P' argument.
                    'mahalanobis' - Mahalanobis distance, computed using a
                                    positive definite covariance matrix C.
                                    The default value of C is the sample
                                    covariance matrix of X, as computed by
                                    NANCOV(X). To specify another value for
                                    C, use the 'Cov' argument.
                    'cosine'      - One minus the cosine of the included
                                    angle between observations (treated as
                                    vectors).
                    'correlation' - One minus the sample linear
                                    correlation between observations
                                    (treated as sequences of values).
                    'spearman'    - One minus the sample Spearman's rank
                                    correlation between observations
                                   (treated as sequences of values).
                    'hamming'     - Hamming distance, percentage of
                                    coordinates that differ.
                    'jaccard'     - One minus the Jaccard coefficient, the
                                    percentage of nonzero coordinates that
                                    differ.
                    function      - A distance function specified using @
                                    (for example @DISTFUN). A distance
                                    function must be of the form
   
                                    function D2 = DISTFUN(ZI, ZJ),
   
                                    taking as arguments a 1-by-N vector ZI
                                    containing a single row of X or Y, an
                                    M2-by-N matrix ZJ containing multiple
                                    rows of X or Y, and returning an
                                    M2-by-1 vector of distances D2, whose
                                    Jth element is the distance between the
                                    observations ZI and ZJ(J,:).
 
     'P'            A positive scalar indicating the exponent of Minkowski
                    distance. This argument is only valid when 'Distance'
                    is 'minkowski'. Default is 2.
   
     'Cov'          A positive definite matrix indicating the covariance
                    matrix when computing the Mahalanobis distance. This
                    argument is only valid when 'Distance' is
                   'mahalanobis'. Default is NANCOV(X).
   
     'Scale'        A vector S containing non-negative values, with length
                    equal to the number of columns in X. Each coordinate
                    difference between X and a query point is scaled by the
                    corresponding element of S. This argument is only valid
                    when 'Distance' is 'seuclidean'. Default is NANSTD(X).
   
     'BucketSize'   The maximum number of data points in the leaf node of the
                    kd-tree (default is 50). This argument is only
                    meaningful when kd-tree is used for finding nearest
                    neighbors.
 
     'SortIndices'  A flag to indicate if output distances and the
                    corresponding indices should be sorted in the order of 
                    distances ranging from the smallest to the largest 
                    distance.  Default is true.
 
     'CacheSize'    A positive scalar or 'maximal'. The default is 1e3. 
                    This argument is only meaningful when the alternative
                    algorithm of computing Euclidean distance is used which
                    requires an intermediate matrix (when 'NSMethod' is
                    'exhaustive', and 'Distance' is one of
                    {'fasteuclidean','fastseuclidean'}).
                    If numeric, this argument specifies the cache size in 
                    megabytes (MB) to allocate for an intermediate matrix. 
                    If 'maximal', knnsearch attempts to allocate enough  
                    memory for an entire intermediate matrix whose size 
                    is MX-by-MY (MX is the number of rows of the input 
                    data X, and MY is the number of rows of the input
                    data Y).
                    'CacheSize' does not have to be large enough for an 
                    entire intermediate matrix, but must be at least large
                    enough to hold an MX-by-1 vector. Otherwise, the 
                    regular algorithm of computing Euclidean distance will
                    be used instead. If the specified cache size exceeds
                    the available memory, MATLAB issues an out-of-memory
                    error.
  
    Example:
       % Find 2 nearest neighbors in X and the corresponding values to each
       % point in Y using the distance metric 'cityblock'
       X = randn(100,5);
       Y = randn(25, 5);
       [idx, dist] = knnsearch(X,Y,'dist','cityblock','k',2);
 
    See also CREATENS, ExhaustiveSearcher, KDTreeSearcher, RANGESEARCH.

    Documentation for knnsearch
       doc knnsearch

    Other uses of knnsearch

       ExhaustiveSearcher/knnsearch    tall/knnsearch
       gpuArray/knnsearch              textanalytics/knnsearch
       KDTreeSearcher/knnsearch

[idx,D] = knnsearch(M,P)

idx = 16

D = 2.8422e-14

It tells us that row 16 of M is the closest one to P, and the distance between the two vectors is not exactly zero, but is very close.

format long g
M(idx,:)

ans = 1×3

-34.9709 -202.8989 -179.48105

P - M(idx,:)

ans = 1×3

1.0e+00 * 0 0 -2.8421709430404e-14

So it misses only in the third element. If the distance is too arge to be acceptable, then D will tell you that. For example...

[idx,D] = knnsearch(M,[-100 -200 -300])

idx = 
     1

D = 
          131.959875743576

So that was a miss by a mile.

M(idx,:)

ans = 1×3

-28.1429 -199.4923 -189.3216

Answer 3

[VINAYAK LUHA]

Hi Alberto,

Try this

[r, ~] = find(abs(M(:,1) - P(1,1)) <= 0.01 & abs(M(:,2) - P(1,2)) <= 0.01 & abs(M(:,3) - P(1,3)) <= 0.01);

Answer 4

[Hassaan]

% Define the matrix M and the vector P
loadedArray = load('M.mat');

M = loadedArray.M;
P = [-3.49799e+01, -2.02899e+02, -1.794815e+02]; % example vector P

% Define the tolerance for similarity
tolerance = 0.01; % For example, 0.01 means we're allowing a difference of up to ±0.01

% Preallocate a logical array for row matches
row_matches = true(size(M, 1), 1);

% Loop through each element in P and update the row_matches array
for i = 1:length(P)
    row_matches = row_matches & (abs(M(:, i) - P(i)) < tolerance);
end

% Find the row indices where all elements match P within the tolerance
matching_rows = find(row_matches);

% Display the matching row indices
disp('Matching row indices:');
disp(matching_rows);

---------------------------------------------------------------------------------------------------------------------------------------------------

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Answer 5

[Steven Lord]

If you want to find a row of numbers that's close to (but perhaps not exactly equal to, due to roundoff error) another row of numbers, I would use the ismembertol function with the 'ByRows' option.

[Dyuman Joshi]

@Steven Lord, I don't know the inner workings of ismembertol so I'll just ask you instead -

How similar is it to the code I've written? And if there is a significant difference, which code is better?

On the surface, it looks very similar -

arr = load('M.mat');
M = arr.M;
P = [-3.4970900e+01	  -2.0289890e+02	  -1.7948105e+02];
tol = 0.01;

idx = all(abs(M-P)<tol, 2)

idx = 61×1 logical array
   0
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out = M(idx, :)

out = 1×3

-34.9709 -202.8989 -179.4810

IDX = ismembertol(M, P, tol, 'ByRows', 1)

IDX = 61×1 logical array
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OUT = M(IDX,:)

OUT = 1×3

-34.9709 -202.8989 -179.4810