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# Operations on Arrays

.. highlight:: cpp

## abs

Calculates an absolute value of each matrix element.

.. ocv:function:: MatExpr abs( const Mat& m ) .. ocv:function:: MatExpr abs( const MatExpr& e )

:param m: matrix.
:param e: matrix expression.


abs is a meta-function that is expanded to one of :ocv:func:absdiff or :ocv:func:convertScaleAbs forms:

* C = abs(A-B)     is equivalent to absdiff(A, B, C)

* C = abs(A)     is equivalent to absdiff(A, Scalar::all(0), C)

* C = Mat_<Vec<uchar,n> >(abs(A*alpha + beta))     is equivalent to  convertScaleAbs(A, C, alpha, beta)


The output matrix has the same size and the same type as the input one except for the last case, where C is depth=CV_8U .

.. seealso:: :ref:MatrixExpressions, :ocv:func:absdiff, :ocv:func:convertScaleAbs


## absdiff

Calculates the per-element absolute difference between two arrays or between an array and a scalar.

.. ocv:function:: void absdiff(InputArray src1, InputArray src2, OutputArray dst)

.. ocv:pyfunction:: cv2.absdiff(src1, src2[, dst]) -> dst

.. ocv:cfunction:: void cvAbsDiff(const CvArr src1, const CvArr src2, CvArr dst) .. ocv:cfunction:: void cvAbsDiffS(const CvArr src, CvArr* dst, CvScalar value) .. ocv:pyoldfunction:: cv.AbsDiff(src1, src2, dst)-> None .. ocv:pyoldfunction:: cv.AbsDiffS(src, dst, value)-> None

:param src1: first input array or a scalar.

:param src2: second input array or a scalar.

:param src: single input array.

:param value: scalar value.

:param dst: output array that has the same size and type as input arrays.


The function absdiff calculates:

* Absolute difference between two arrays when they have the same size and type:

.. math::

\texttt{dst}(I) =  \texttt{saturate} (| \texttt{src1}(I) -  \texttt{src2}(I)|)


* Absolute difference between an array and a scalar when the second array is constructed from Scalar or has as many elements as the number of channels in src1:

.. math::

\texttt{dst}(I) =  \texttt{saturate} (| \texttt{src1}(I) -  \texttt{src2} |)


* Absolute difference between a scalar and an array when the first array is constructed from Scalar or has as many elements as the number of channels in src2:

.. math::

\texttt{dst}(I) =  \texttt{saturate} (| \texttt{src1} -  \texttt{src2}(I) |)

where  I is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.


.. note:: Saturation is not applied when the arrays have the depth CV_32S. You may even get a negative value in the case of overflow.

.. seealso:: :ocv:func:abs

Calculates the per-element sum of two arrays or an array and a scalar.

.. ocv:function:: void add(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)

:param src1: first input array or a scalar.

:param src2: second input array or a scalar.

:param src: single input array.

:param value: scalar value.

:param dst: output array that has the same size and number of channels as the input array(s); the depth is defined by dtype or src1/src2.

:param mask: optional operation mask - 8-bit single channel array, that specifies elements of the output array to be changed.

:param dtype: optional depth of the output array (see the discussion below).


The function add calculates:

* Sum of two arrays when both input arrays have the same size and the same number of channels:

.. math::



* Sum of an array and a scalar when src2 is constructed from Scalar or has the same number of elements as src1.channels():

.. math::

\texttt{dst}(I) =  \texttt{saturate} ( \texttt{src1}(I) +  \texttt{src2} ) \quad \texttt{if mask}(I) \ne0


* Sum of a scalar and an array when src1 is constructed from Scalar or has the same number of elements as src2.channels():

.. math::

\texttt{dst}(I) =  \texttt{saturate} ( \texttt{src1} +  \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0

where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.


The first function in the list above can be replaced with matrix expressions: ::

dst = src1 + src2;
dst += src1; // equivalent to add(dst, src1, dst);


The input arrays and the output array can all have the same or different depths. For example, you can add a 16-bit unsigned array to a 8-bit signed array and store the sum as a 32-bit floating-point array. Depth of the output array is determined by the dtype parameter. In the second and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this case, the output array will have the same depth as the input array, be it src1, src2 or both.

.. note:: Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

.. seealso::

:ocv:func:subtract,
:ocv:func:addWeighted,
:ocv:func:scaleAdd,
:ocv:func:Mat::convertTo,
:ref:MatrixExpressions


Calculates the weighted sum of two arrays.

.. ocv:function:: void addWeighted(InputArray src1, double alpha, InputArray src2, double beta, double gamma, OutputArray dst, int dtype=-1)

.. ocv:pyfunction:: cv2.addWeighted(src1, alpha, src2, beta, gamma[, dst[, dtype]]) -> dst

.. ocv:cfunction:: void cvAddWeighted(const CvArr src1, double alpha, const CvArr src2, double beta, double gamma, CvArr* dst) .. ocv:pyoldfunction:: cv.AddWeighted(src1, alpha, src2, beta, gamma, dst)-> None

:param src1: first input array.

:param alpha: weight of the first array elements.

:param src2: second input array of the same size and channel number as  src1.

:param beta: weight of the second array elements.

:param dst: output array that has the same size and number of channels as the input arrays.

:param gamma: scalar added to each sum.

:param dtype: optional depth of the output array; when both input arrays have the same depth, dtype can be set to -1, which will be equivalent to src1.depth().


The function addWeighted calculates the weighted sum of two arrays as follows:

.. math::

\texttt{dst} (I)= \texttt{saturate} ( \texttt{src1} (I)* \texttt{alpha} +  \texttt{src2} (I)* \texttt{beta} +  \texttt{gamma} )


where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.

The function can be replaced with a matrix expression: ::

dst = src1*alpha + src2*beta + gamma;


.. note:: Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

.. seealso::

:ocv:func:add,
:ocv:func:subtract,
:ocv:func:scaleAdd,
:ocv:func:Mat::convertTo,
:ref:MatrixExpressions


## bitwise_and

Calculates the per-element bit-wise conjunction of two arrays or an array and a scalar.

.. ocv:function:: void bitwise_and(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())

.. ocv:pyfunction:: cv2.bitwise_and(src1, src2[, dst[, mask]]) -> dst

.. ocv:cfunction:: void cvAnd(const CvArr src1, const CvArr src2, CvArr dst, const CvArr mask=NULL) .. ocv:cfunction:: void cvAndS(const CvArr src, CvScalar value, CvArr dst, const CvArr* mask=NULL) .. ocv:pyoldfunction:: cv.And(src1, src2, dst, mask=None)-> None .. ocv:pyoldfunction:: cv.AndS(src, value, dst, mask=None)-> None

:param src1: first input array or a scalar.

:param src2: second input array or a scalar.

:param src: single input array.

:param value: scalar value.

:param dst: output array that has the same size and type as the input arrays.

:param mask: optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.


The function calculates the per-element bit-wise logical conjunction for:

* Two arrays when src1 and src2 have the same size:

.. math::

\texttt{dst} (I) =  \texttt{src1} (I)  \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0


* An array and a scalar when src2 is constructed from Scalar or has the same number of elements as src1.channels():

.. math::

\texttt{dst} (I) =  \texttt{src1} (I)  \wedge \texttt{src2} \quad \texttt{if mask} (I) \ne0


* A scalar and an array when src1 is constructed from Scalar or has the same number of elements as src2.channels():

.. math::

\texttt{dst} (I) =  \texttt{src1}  \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0


In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the second and third cases above, the scalar is first converted to the array type.

## bitwise_not

Inverts every bit of an array.

.. ocv:function:: void bitwise_not(InputArray src, OutputArray dst, InputArray mask=noArray())

.. ocv:pyfunction:: cv2.bitwise_not(src[, dst[, mask]]) -> dst

.. ocv:cfunction:: void cvNot(const CvArr src, CvArr dst) .. ocv:pyoldfunction:: cv.Not(src, dst)-> None

:param src: input array.

:param dst: output array that has the same size and type as the input array.

:param mask: optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.


The function calculates per-element bit-wise inversion of the input array:

.. math::

\texttt{dst} (I) =  \neg \texttt{src} (I)


In case of a floating-point input array, its machine-specific bit representation (usually IEEE754-compliant) is used for the operation. In case of multi-channel arrays, each channel is processed independently.

## bitwise_or

Calculates the per-element bit-wise disjunction of two arrays or an array and a scalar.

.. ocv:function:: void bitwise_or(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())

.. ocv:pyfunction:: cv2.bitwise_or(src1, src2[, dst[, mask]]) -> dst

.. ocv:cfunction:: void cvOr(const CvArr src1, const CvArr src2, CvArr dst, const CvArr mask=NULL) .. ocv:cfunction:: void cvOrS(const CvArr src, CvScalar value, CvArr dst, const CvArr* mask=NULL) .. ocv:pyoldfunction:: cv.Or(src1, src2, dst, mask=None)-> None .. ocv:pyoldfunction:: cv.OrS(src, value, dst, mask=None)-> None

:param src1: first input array or a scalar.

:param src2: second input array or a scalar.

:param src: single input array.

:param value: scalar value.

:param dst: output array that has the same size and type as the input arrays.

:param mask: optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.


The function calculates the per-element bit-wise logical disjunction for:

* Two arrays when src1 and src2 have the same size:

    .. math::

\texttt{dst} (I) =  \texttt{src1} (I)  \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0


* An array and a scalar when src2 is constructed from Scalar or has the same number of elements as src1.channels():

    .. math::

\texttt{dst} (I) =  \texttt{src1} (I)  \vee \texttt{src2} \quad \texttt{if mask} (I) \ne0


* A scalar and an array when src1 is constructed from Scalar or has the same number of elements as src2.channels():

    .. math::

\texttt{dst} (I) =  \texttt{src1}  \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0


In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the second and third cases above, the scalar is first converted to the array type.

## bitwise_xor

Calculates the per-element bit-wise “exclusive or” operation on two arrays or an array and a scalar.

.. ocv:function:: void bitwise_xor(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())

.. ocv:pyfunction:: cv2.bitwise_xor(src1, src2[, dst[, mask]]) -> dst

.. ocv:cfunction:: void cvXor(const CvArr src1, const CvArr src2, CvArr dst, const CvArr mask=NULL) .. ocv:cfunction:: void cvXorS(const CvArr src, CvScalar value, CvArr dst, const CvArr* mask=NULL) .. ocv:pyoldfunction:: cv.Xor(src1, src2, dst, mask=None)-> None .. ocv:pyoldfunction:: cv.XorS(src, value, dst, mask=None)-> None

:param src1: first input array or a scalar.

:param src2: second input array or a scalar.

:param src: single input array.

:param value: scalar value.

:param dst: output array that has the same size and type as the input arrays.

:param mask: optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.


The function calculates the per-element bit-wise logical “exclusive-or” operation for:

* Two arrays when src1 and src2 have the same size:

    .. math::

\texttt{dst} (I) =  \texttt{src1} (I)  \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0


* An array and a scalar when src2 is constructed from Scalar or has the same number of elements as src1.channels():

    .. math::

\texttt{dst} (I) =  \texttt{src1} (I)  \oplus \texttt{src2} \quad \texttt{if mask} (I) \ne0


* A scalar and an array when src1 is constructed from Scalar or has the same number of elements as src2.channels():

    .. math::

\texttt{dst} (I) =  \texttt{src1}  \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0


In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the 2nd and 3rd cases above, the scalar is first converted to the array type.

## calcCovarMatrix

Calculates the covariance matrix of a set of vectors.

.. ocv:function:: void calcCovarMatrix( const Mat* samples, int nsamples, Mat& covar, Mat& mean, int flags, int ctype=CV_64F)

.. ocv:function:: void calcCovarMatrix( InputArray samples, OutputArray covar, OutputArray mean, int flags, int ctype=CV_64F)

.. ocv:pyfunction:: cv2.calcCovarMatrix(samples, flags[, covar[, mean[, ctype]]]) -> covar, mean

.. ocv:cfunction:: void cvCalcCovarMatrix( const CvArr vects, int count, CvArr cov_mat, CvArr avg, int flags )

.. ocv:pyoldfunction:: cv.CalcCovarMatrix(vects, covMat, avg, flags)-> None

:param samples: samples stored either as separate matrices or as rows/columns of a single matrix.

:param nsamples: number of samples when they are stored separately.

:param covar: output covariance matrix of the type ctype and square size.

:param ctype: type of the matrixl; it equals 'CV_64F' by default.

:param mean: input or output (depending on the flags) array as the average value of the input vectors.

:param vects: a set of vectors.

:param flags: operation flags as a combination of the following values:

* **CV_COVAR_SCRAMBLED** The output covariance matrix is calculated as:

.. math::

\texttt{scale}   \cdot  [  \texttt{vects}  [0]-  \texttt{mean}  , \texttt{vects}  [1]-  \texttt{mean}  ,...]^T  \cdot  [ \texttt{vects}  [0]- \texttt{mean}  , \texttt{vects}  [1]- \texttt{mean}  ,...],

The covariance matrix will be  nsamples x nsamples. Such an unusual covariance matrix is used for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for face recognition). Eigenvalues of this "scrambled" matrix match the eigenvalues of the true covariance matrix. The "true" eigenvectors can be easily calculated from the eigenvectors of the "scrambled" covariance matrix.

* **CV_COVAR_NORMAL** The output covariance matrix is calculated as:

.. math::

\texttt{scale}   \cdot  [  \texttt{vects}  [0]-  \texttt{mean}  , \texttt{vects}  [1]-  \texttt{mean}  ,...]  \cdot  [ \texttt{vects}  [0]- \texttt{mean}  , \texttt{vects}  [1]- \texttt{mean}  ,...]^T,

covar  will be a square matrix of the same size as the total number of elements in each input vector. One and only one of  CV_COVAR_SCRAMBLED  and CV_COVAR_NORMAL  must be specified.

* **CV_COVAR_USE_AVG** If the flag is specified, the function does not calculate  mean  from the input vectors but, instead, uses the passed  mean  vector. This is useful if  mean  has been pre-calculated or known in advance, or if the covariance matrix is calculated by parts. In this case, mean  is not a mean vector of the input sub-set of vectors but rather the mean vector of the whole set.

* **CV_COVAR_SCALE** If the flag is specified, the covariance matrix is scaled. In the "normal" mode,  scale  is  1./nsamples . In the "scrambled" mode,  scale  is the reciprocal of the total number of elements in each input vector. By default (if the flag is not specified), the covariance matrix is not scaled (  scale=1 ).

* **CV_COVAR_ROWS** [Only useful in the second variant of the function] If the flag is specified, all the input vectors are stored as rows of the  samples  matrix.  mean  should be a single-row vector in this case.

* **CV_COVAR_COLS** [Only useful in the second variant of the function] If the flag is specified, all the input vectors are stored as columns of the  samples  matrix.  mean  should be a single-column vector in this case.


The functions calcCovarMatrix calculate the covariance matrix and, optionally, the mean vector of the set of input vectors.

.. seealso::

:ocv:class:PCA,
:ocv:func:mulTransposed,
:ocv:func:Mahalanobis


## cartToPolar

Calculates the magnitude and angle of 2D vectors.

.. ocv:function:: void cartToPolar(InputArray x, InputArray y, OutputArray magnitude, OutputArray angle, bool angleInDegrees=false)

.. ocv:pyfunction:: cv2.cartToPolar(x, y[, magnitude[, angle[, angleInDegrees]]]) -> magnitude, angle

.. ocv:cfunction:: void cvCartToPolar( const CvArr x, const CvArr y, CvArr magnitude, CvArr angle=NULL, int angle_in_degrees=0 )

.. ocv:pyoldfunction:: cv.CartToPolar(x, y, magnitude, angle=None, angleInDegrees=0)-> None

:param x: array of x-coordinates; this must be a single-precision or double-precision floating-point array.

:param y: array of y-coordinates, that must have the same size and same type as x.

:param magnitude: output array of magnitudes of the same size and type as x.

:param angle: output array of angles that has the same size and type as x; the angles are measured in radians (from 0 to 2*Pi) or in degrees (0 to 360 degrees).

:param angleInDegrees: a flag, indicating whether the angles are measured in radians (which is by default), or in degrees.

:param angle_in_degrees: a flag, indicating whether the angles are measured in radians, or in degrees (specific to C syntax).


The function cartToPolar calculates either the magnitude, angle, or both for every 2D vector (x(I),y(I)):

.. math::

\begin{array}{l} \texttt{magnitude} (I)= \sqrt{\texttt{x}(I)^2+\texttt{y}(I)^2} , \\ \texttt{angle} (I)= \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))[ \cdot180 / \pi ] \end{array}


The angles are calculated with accuracy about 0.3 degrees. For the point (0,0), the angle is set to 0.

.. seealso::

:ocv:func:Sobel,
:ocv:func:Scharr


## checkRange

Checks every element of an input array for invalid values.

.. ocv:function:: bool checkRange( InputArray a, bool quiet=true, Point* pos=0, double minVal=-DBL_MAX, double maxVal=DBL_MAX )

.. ocv:pyfunction:: cv2.checkRange(a[, quiet[, minVal[, maxVal]]]) -> retval, pos

:param a: input array.

:param quiet: a flag, indicating whether the functions quietly return false when the array elements are out of range or they throw an exception.

:param pos: optional output parameter, where the position of the first outlier is stored; in the second function pos, when not NULL, must be a pointer to array of src.dims elements.

:param minVal: inclusive lower boundary of valid values range.

:param maxVal: exclusive upper boundary of valid values range.


The functions checkRange check that every array element is neither NaN nor infinite. When minVal < -DBL_MAX and maxVal < DBL_MAX, the functions also check that each value is between minVal and maxVal. In case of multi-channel arrays, each channel is processed independently. If some values are out of range, position of the first outlier is stored in pos (when pos != NULL). Then, the functions either return false (when quiet=true) or throw an exception.

## compare

Performs the per-element comparison of two arrays or an array and scalar value.

.. ocv:function:: void compare(InputArray src1, InputArray src2, OutputArray dst, int cmpop)

.. ocv:pyfunction:: cv2.compare(src1, src2, cmpop[, dst]) -> dst

.. ocv:cfunction:: void cvCmp( const CvArr src1, const CvArr src2, CvArr* dst, int cmp_op )

.. ocv:pyoldfunction:: cv.Cmp(src1, src2, dst, cmpOp)-> None

.. ocv:cfunction:: void cvCmpS( const CvArr src, double value, CvArr dst, int cmp_op )

.. ocv:pyoldfunction:: cv.CmpS(src, value, dst, cmpOp)-> None

:param src1: first input array or a scalar (in the case of cvCmp, cv.Cmp, cvCmpS, cv.CmpS it is always an array); when it is an array, it must have a single channel.

:param src2: second input array or a scalar (in the case of cvCmp and cv.Cmp it is always an array; in the case of cvCmpS, cv.CmpS it is always a scalar); when it is an array, it must have a single channel.

:param src: single input array.

:param value: scalar value.

:param dst: output array that has the same size and type as the input arrays.

:param cmpop: a flag, that specifies correspondence between the arrays:

* **CMP_EQ** src1 is equal to src2.
* **CMP_GT** src1 is greater than src2.
* **CMP_GE** src1 is greater than or equal to src2.
* **CMP_LT** src1 is less than src2.
* **CMP_LE** src1 is less than or equal to src2.
* **CMP_NE** src1 is unequal to src2.


The function compares:

* Elements of two arrays when src1 and src2 have the same size:

.. math::

   \texttt{dst} (I) =  \texttt{src1} (I)  \,\texttt{cmpop}\, \texttt{src2} (I)


* Elements of src1 with a scalar src2 when src2 is constructed from Scalar or has a single element:

.. math::

   \texttt{dst} (I) =  \texttt{src1}(I) \,\texttt{cmpop}\,  \texttt{src2}


* src1 with elements of src2 when src1 is constructed from Scalar or has a single element:

.. math::

   \texttt{dst} (I) =  \texttt{src1}  \,\texttt{cmpop}\, \texttt{src2} (I)


When the comparison result is true, the corresponding element of output array is set to 255. The comparison operations can be replaced with the equivalent matrix expressions: ::

Mat dst1 = src1 >= src2;
Mat dst2 = src1 < 8;
...


.. seealso::

:ocv:func:checkRange,
:ocv:func:min,
:ocv:func:max,
:ocv:func:threshold,
:ref:MatrixExpressions


## completeSymm

Copies the lower or the upper half of a square matrix to another half.

.. ocv:function:: void completeSymm(InputOutputArray mtx, bool lowerToUpper=false)

.. ocv:pyfunction:: cv2.completeSymm(mtx[, lowerToUpper]) -> None

:param mtx: input-output floating-point square matrix.

:param lowerToUpper: operation flag; if true, the lower half is copied to the upper half. Otherwise, the upper half is copied to the lower half.


The function completeSymm copies the lower half of a square matrix to its another half. The matrix diagonal remains unchanged:

* :math:\texttt{mtx}_{ij}=\texttt{mtx}_{ji} for :math:i > j if lowerToUpper=false

* :math:\texttt{mtx}_{ij}=\texttt{mtx}_{ji} for :math:i < j if lowerToUpper=true

.. seealso::

:ocv:func:flip,
:ocv:func:transpose


## convertScaleAbs

Scales, calculates absolute values, and converts the result to 8-bit.

.. ocv:function:: void convertScaleAbs(InputArray src, OutputArray dst, double alpha=1, double beta=0)

.. ocv:pyfunction:: cv2.convertScaleAbs(src[, dst[, alpha[, beta]]]) -> dst

.. ocv:cfunction:: void cvConvertScaleAbs(const CvArr src, CvArr dst, double scale=1, double shift=0) .. ocv:pyoldfunction:: cv.ConvertScaleAbs(src, dst, scale=1.0, shift=0.0)-> None

:param src: input array.

:param dst: output array.

:param alpha: optional scale factor.

:param beta: optional delta added to the scaled values.


On each element of the input array, the function convertScaleAbs performs three operations sequentially: scaling, taking an absolute value, conversion to an unsigned 8-bit type:

.. math::

\texttt{dst} (I)= \texttt{saturate\_cast<uchar>} (| \texttt{src} (I)* \texttt{alpha} +  \texttt{beta} |)


In case of multi-channel arrays, the function processes each channel independently. When the output is not 8-bit, the operation can be emulated by calling the Mat::convertTo method (or by using matrix expressions) and then by calculating an absolute value of the result. For example: ::

Mat_<float> A(30,30);
randu(A, Scalar(-100), Scalar(100));
Mat_<float> B = A*5 + 3;
B = abs(B);
// Mat_<float> B = abs(A*5+3) will also do the job,
// but it will allocate a temporary matrix


.. seealso::

:ocv:func:Mat::convertTo,
:ocv:func:abs


## countNonZero

Counts non-zero array elements.

.. ocv:function:: int countNonZero( InputArray src )

.. ocv:pyfunction:: cv2.countNonZero(src) -> retval

.. ocv:cfunction:: int cvCountNonZero(const CvArr* arr)

.. ocv:pyoldfunction:: cv.CountNonZero(arr)-> int

:param src: single-channel array.


The function returns the number of non-zero elements in src :

.. math::

\sum _{I: \; \texttt{src} (I) \ne0 } 1


.. seealso::

:ocv:func:mean,
:ocv:func:meanStdDev,
:ocv:func:norm,
:ocv:func:minMaxLoc,
:ocv:func:calcCovarMatrix


## cvarrToMat

Converts CvMat, IplImage , or CvMatND to Mat.

.. ocv:function:: Mat cvarrToMat( const CvArr* arr, bool copyData=false, bool allowND=true, int coiMode=0 )

:param arr: input CvMat, IplImage , or  CvMatND.

:param copyData: when false (default value), no data is copied and only the new header is created, in this case, the original array should not be deallocated while the new matrix header is used; if the parameter is true, all the data is copied and you may deallocate the original array right after the conversion.

:param allowND: when true (default value), CvMatND is converted to 2-dimensional Mat, if it is possible (see the discussion below); if it is not possible, or when the parameter is false, the function will report an error.

:param coiMode: parameter specifying how the IplImage COI (when set) is handled.

*  If  coiMode=0 and COI is set, the function reports an error.

*  If  coiMode=1 , the function never reports an error. Instead, it returns the header to the whole original image and you will have to check and process COI manually. See  :ocv:func:extractImageCOI .


The function cvarrToMat converts CvMat, IplImage , or CvMatND header to :ocv:class:Mat header, and optionally duplicates the underlying data. The constructed header is returned by the function.

When copyData=false , the conversion is done really fast (in O(1) time) and the newly created matrix header will have refcount=0 , which means that no reference counting is done for the matrix data. In this case, you have to preserve the data until the new header is destructed. Otherwise, when copyData=true , the new buffer is allocated and managed as if you created a new matrix from scratch and copied the data there. That is, cvarrToMat(arr, true) is equivalent to cvarrToMat(arr, false).clone() (assuming that COI is not set). The function provides a uniform way of supporting CvArr paradigm in the code that is migrated to use new-style data structures internally. The reverse transformation, from Mat to CvMat or IplImage can be done by a simple assignment: ::

CvMat* A = cvCreateMat(10, 10, CV_32F);
cvSetIdentity(A);
IplImage A1; cvGetImage(A, &A1);
Mat B = cvarrToMat(A);
Mat B1 = cvarrToMat(&A1);
IplImage C = B;
CvMat C1 = B1;
// now A, A1, B, B1, C and C1 are different headers
// for the same 10x10 floating-point array.
// note that you will need to use "&"
// to pass C & C1 to OpenCV functions, for example:
printf("%g\n", cvNorm(&C1, 0, CV_L2));


Normally, the function is used to convert an old-style 2D array ( CvMat or IplImage ) to Mat . However, the function can also take CvMatND as an input and create :ocv:func:Mat for it, if it is possible. And, for CvMatND A , it is possible if and only if A.dim[i].size*A.dim.step[i] == A.dim.step[i-1] for all or for all but one i, 0 < i < A.dims . That is, the matrix data should be continuous or it should be representable as a sequence of continuous matrices. By using this function in this way, you can process CvMatND using an arbitrary element-wise function.

The last parameter, coiMode , specifies how to deal with an image with COI set. By default, it is 0 and the function reports an error when an image with COI comes in. And coiMode=1 means that no error is signalled. You have to check COI presence and handle it manually. The modern structures, such as :ocv:class:Mat and MatND do not support COI natively. To process an individual channel of a new-style array, you need either to organize a loop over the array (for example, using matrix iterators) where the channel of interest will be processed, or extract the COI using :ocv:func:mixChannels (for new-style arrays) or :ocv:func:extractImageCOI (for old-style arrays), process this individual channel, and insert it back to the output array if needed (using :ocv:func:mixChannels or :ocv:func:insertImageCOI , respectively).

.. seealso::

:ocv:cfunc:cvGetImage,
:ocv:cfunc:cvGetMat,
:ocv:func:extractImageCOI,
:ocv:func:insertImageCOI,
:ocv:func:mixChannels


## dct

Performs a forward or inverse discrete Cosine transform of 1D or 2D array.

.. ocv:function:: void dct(InputArray src, OutputArray dst, int flags=0)

.. ocv:pyfunction:: cv2.dct(src[, dst[, flags]]) -> dst

.. ocv:cfunction:: void cvDCT(const CvArr src, CvArr dst, int flags) .. ocv:pyoldfunction:: cv.DCT(src, dst, flags)-> None

:param src: input floating-point array.

:param dst: output array of the same size and type as  src .

:param flags: transformation flags as a combination of the following values:

* **DCT_INVERSE** performs an inverse 1D or 2D transform instead of the default forward transform.

* **DCT_ROWS** performs a forward or inverse transform of every individual row of the input matrix. This flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transforms and so forth.


The function dct performs a forward or inverse discrete Cosine transform (DCT) of a 1D or 2D floating-point array:

* Forward Cosine transform of a 1D vector of N elements:

.. math::

Y = C^{(N)}  \cdot X

where

.. math::

C^{(N)}_{jk}= \sqrt{\alpha_j/N} \cos \left ( \frac{\pi(2k+1)j}{2N} \right )

and

:math:\alpha_0=1, :math:\alpha_j=2 for *j > 0*.


* Inverse Cosine transform of a 1D vector of N elements:

.. math::

X =  \left (C^{(N)} \right )^{-1}  \cdot Y =  \left (C^{(N)} \right )^T  \cdot Y

(since
:math:C^{(N)} is an orthogonal matrix,
:math:C^{(N)} \cdot \left(C^{(N)}\right)^T = I )


* Forward 2D Cosine transform of M x N matrix:

.. math::

Y = C^{(N)}  \cdot X  \cdot \left (C^{(N)} \right )^T


* Inverse 2D Cosine transform of M x N matrix:

.. math::

X =  \left (C^{(N)} \right )^T  \cdot X  \cdot C^{(N)}


The function chooses the mode of operation by looking at the flags and size of the input array:

* If (flags & DCT_INVERSE) == 0 , the function does a forward 1D or 2D transform. Otherwise, it is an inverse 1D or 2D transform.

* If (flags & DCT_ROWS) != 0 , the function performs a 1D transform of each row.

* If the array is a single column or a single row, the function performs a 1D transform.

* If none of the above is true, the function performs a 2D transform.

.. note::

Currently dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation, you can pad the array when necessary.

Also, the function performance depends very much, and not monotonically, on the array size (see
:ocv:func:getOptimalDFTSize ). In the current implementation DCT of a vector of size N is calculated via DFT of a vector of size N/2 . Thus, the optimal DCT size N1 >= N can be calculated as: ::

size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
N1 = getOptimalDCTSize(N);


.. seealso:: :ocv:func:dft , :ocv:func:getOptimalDFTSize , :ocv:func:idct

## dft

Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.

.. ocv:function:: void dft(InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)

.. ocv:pyfunction:: cv2.dft(src[, dst[, flags[, nonzeroRows]]]) -> dst

.. ocv:cfunction:: void cvDFT( const CvArr src, CvArr dst, int flags, int nonzero_rows=0 )

.. ocv:pyoldfunction:: cv.DFT(src, dst, flags, nonzeroRows=0)-> None

:param src: input array that could be real or complex.

:param dst: output array whose size and type depends on the  flags .

:param flags: transformation flags, representing a combination of the following values:

* **DFT_INVERSE** performs an inverse 1D or 2D transform instead of the default forward transform.

* **DFT_SCALE** scales the result: divide it by the number of array elements. Normally, it is combined with  DFT_INVERSE.
* **DFT_ROWS** performs a forward or inverse transform of every individual row of the input matrix; this flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transformations and so forth.

* **DFT_COMPLEX_OUTPUT** performs a forward transformation of 1D or 2D real array; the result, though being a complex array, has complex-conjugate symmetry (*CCS*, see the function description below for details), and such an array can be packed into a real array of the same size as input, which is the fastest option and which is what the function does by default; however, you may wish to get a full complex array (for simpler spectrum analysis, and so on) - pass the flag to enable the function to produce a full-size complex output array.

* **DFT_REAL_OUTPUT** performs an inverse transformation of a 1D or 2D complex array; the result is normally a complex array of the same size, however, if the input array has conjugate-complex symmetry (for example, it is a result of forward transformation with  DFT_COMPLEX_OUTPUT  flag), the output is a real array; while the function itself does not check whether the input is symmetrical or not, you can pass the flag and then the function will assume the symmetry and produce the real output array (note that when the input is packed into a real array and inverse transformation is executed, the function treats the input as a packed complex-conjugate symmetrical array, and the output will also be a real array).

:param nonzeroRows: when the parameter is not zero, the function assumes that only the first nonzeroRows rows of the input array (DFT_INVERSE is not set) or only the first nonzeroRows of the output array (DFT_INVERSE is set) contain non-zeros, thus, the function can handle the rest of the rows more efficiently and save some time; this technique is very useful for calculating array cross-correlation or convolution using DFT.


The function performs one of the following:

* Forward the Fourier transform of a 1D vector of N elements:

.. math::

Y = F^{(N)}  \cdot X,

where
:math:F^{(N)}_{jk}=\exp(-2\pi i j k/N) and
:math:i=\sqrt{-1}


* Inverse the Fourier transform of a 1D vector of N elements:

.. math::

\begin{array}{l} X'=  \left (F^{(N)} \right )^{-1}  \cdot Y =  \left (F^{(N)} \right )^*  \cdot y  \\ X = (1/N)  \cdot X, \end{array}

where
:math:F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T


* Forward the 2D Fourier transform of a M x N matrix:

.. math::

Y = F^{(M)}  \cdot X  \cdot F^{(N)}


* Inverse the 2D Fourier transform of a M x N matrix:

.. math::

\begin{array}{l} X'=  \left (F^{(M)} \right )^*  \cdot Y  \cdot \left (F^{(N)} \right )^* \\ X =  \frac{1}{M \cdot N} \cdot X' \end{array}


In case of real (single-channel) data, the output spectrum of the forward Fourier transform or input spectrum of the inverse Fourier transform can be represented in a packed format called CCS (complex-conjugate-symmetrical). It was borrowed from IPL (Intel Image Processing Library). Here is how 2D CCS* spectrum looks:

.. math::

\begin{bmatrix} Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} &  \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2}  \\ Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} &  \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2}  \\ Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} &  \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2}  \\ \hdotsfor{9} \\ Re Y_{M/2-1,0} &  Re Y_{M-3,1}  & Im Y_{M-3,1} &  \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2}  \\ Im Y_{M/2-1,0} &  Re Y_{M-2,1}  & Im Y_{M-2,1} &  \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2}  \\ Re Y_{M/2,0}  &  Re Y_{M-1,1} &  Im Y_{M-1,1} &  \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2} \end{bmatrix}


In case of 1D transform of a real vector, the output looks like the first row of the matrix above.

So, the function chooses an operation mode depending on the flags and size of the input array:

• If DFT_ROWS is set or the input array has a single row or single column, the function performs a 1D forward or inverse transform of each row of a matrix when DFT_ROWS is set. Otherwise, it performs a 2D transform.

• If the input array is real and DFT_INVERSE is not set, the function performs a forward 1D or 2D transform:

• When DFT_COMPLEX_OUTPUT is set, the output is a complex matrix of the same size as input.

• When DFT_COMPLEX_OUTPUT is not set, the output is a real matrix of the same size as input. In case of 2D transform, it uses the packed format as shown above. In case of a single 1D transform, it looks like the first row of the matrix above. In case of multiple 1D transforms (when using the DFT_ROWS flag), each row of the output matrix looks like the first row of the matrix above.

• If the input array is complex and either DFT_INVERSE or DFT_REAL_OUTPUT are not set, the output is a complex array of the same size as input. The function performs a forward or inverse 1D or 2D transform of the whole input array or each row of the input array independently, depending on the flags DFT_INVERSE and DFT_ROWS.

• When DFT_INVERSE is set and the input array is real, or it is complex but DFT_REAL_OUTPUT is set, the output is a real array of the same size as input. The function performs a 1D or 2D inverse transformation of the whole input array or each individual row, depending on the flags DFT_INVERSE and DFT_ROWS.

If DFT_SCALE is set, the scaling is done after the transformation.

Unlike :ocv:func:dct , the function supports arrays of arbitrary size. But only those arrays are processed efficiently, whose sizes can be factorized in a product of small prime numbers (2, 3, and 5 in the current implementation). Such an efficient DFT size can be calculated using the :ocv:func:getOptimalDFTSize method.

The sample below illustrates how to calculate a DFT-based convolution of two 2D real arrays: ::

void convolveDFT(InputArray A, InputArray B, OutputArray C)
{
// reallocate the output array if needed
C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type());
Size dftSize;
// calculate the size of DFT transform
dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1);
dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1);

// allocate temporary buffers and initialize them with 0's
Mat tempA(dftSize, A.type(), Scalar::all(0));
Mat tempB(dftSize, B.type(), Scalar::all(0));

// copy A and B to the top-left corners of tempA and tempB, respectively
Mat roiA(tempA, Rect(0,0,A.cols,A.rows));
A.copyTo(roiA);
Mat roiB(tempB, Rect(0,0,B.cols,B.rows));
B.copyTo(roiB);

// now transform the padded A & B in-place;
// use "nonzeroRows" hint for faster processing
dft(tempA, tempA, 0, A.rows);
dft(tempB, tempB, 0, B.rows);

// multiply the spectrums;
// the function handles packed spectrum representations well
mulSpectrums(tempA, tempB, tempA);

// transform the product back from the frequency domain.
// Even though all the result rows will be non-zero,
// you need only the first C.rows of them, and thus you
// pass nonzeroRows == C.rows
dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows);

// now copy the result back to C.
tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C);

// all the temporary buffers will be deallocated automatically
}


To optimize this sample, consider the following approaches:

* Since nonzeroRows != 0 is passed to the forward transform calls and since A and B are copied to the top-left corners of tempA and tempB, respectively, it is not necessary to clear the whole tempA and tempB. It is only necessary to clear the tempA.cols - A.cols ( tempB.cols - B.cols) rightmost columns of the matrices.

* This DFT-based convolution does not have to be applied to the whole big arrays, especially if B is significantly smaller than A or vice versa. Instead, you can calculate convolution by parts. To do this, you need to split the output array C into multiple tiles. For each tile, estimate which parts of A and B are required to calculate convolution in this tile. If the tiles in C are too small, the speed will decrease a lot because of repeated work. In the ultimate case, when each tile in C is a single pixel, the algorithm becomes equivalent to the naive convolution algorithm. If the tiles are too big, the temporary arrays tempA and tempB become too big and there is also a slowdown because of bad cache locality. So, there is an optimal tile size somewhere in the middle.

* If different tiles in C can be calculated in parallel and, thus, the convolution is done by parts, the loop can be threaded.

All of the above improvements have been implemented in :ocv:func:matchTemplate and :ocv:func:filter2D . Therefore, by using them, you can get the performance even better than with the above theoretically optimal implementation. Though, those two functions actually calculate cross-correlation, not convolution, so you need to “flip” the second convolution operand B vertically and horizontally using :ocv:func:flip .

.. seealso:: :ocv:func:dct , :ocv:func:getOptimalDFTSize , :ocv:func:mulSpectrums, :ocv:func:filter2D , :ocv:func:matchTemplate , :ocv:func:flip , :ocv:func:cartToPolar , :ocv:func:magnitude , :ocv:func:phase

.. note::

• An example using the discrete fourier transform can be found at opencv_source_code/samples/cpp/dft.cpp

• (Python) An example using the dft functionality to perform Wiener deconvolution can be found at opencv_source/samples/python2/deconvolution.py

• (Python) An example rearranging the quadrants of a Fourier image can be found at opencv_source/samples/python2/dft.py

## divide

Performs per-element division of two arrays or a scalar by an array.

.. ocv:function:: void divide(InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)

.. ocv:function:: void divide(double scale, InputArray src2, OutputArray dst, int dtype=-1)

.. ocv:pyfunction:: cv2.divide(src1, src2[, dst[, scale[, dtype]]]) -> dst .. ocv:pyfunction:: cv2.divide(scale, src2[, dst[, dtype]]) -> dst

.. ocv:cfunction:: void cvDiv(const CvArr src1, const CvArr src2, CvArr* dst, double scale=1) .. ocv:pyoldfunction:: cv.Div(src1, src2, dst, scale=1) -> None

:param src1: first input array.

:param src2: second input array of the same size and type as src1.

:param scale: scalar factor.

:param dst: output array of the same size and type as src2.

:param dtype: optional depth of the output array; if -1, dst will have depth src2.depth(), but in case of an array-by-array division, you can only pass -1 when src1.depth()==src2.depth().


The functions divide divide one array by another:

.. math::

\texttt{dst(I) = saturate(src1(I)*scale/src2(I))}


or a scalar by an array when there is no src1 :

.. math::

\texttt{dst(I) = saturate(scale/src2(I))}


When src2(I) is zero, dst(I) will also be zero. Different channels of multi-channel arrays are processed independently.

.. note:: Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

.. seealso::

:ocv:func:multiply,
:ocv:func:add,
:ocv:func:subtract,
:ref:MatrixExpressions


## determinant

Returns the determinant of a square floating-point matrix.

.. ocv:function:: double determinant(InputArray mtx)

.. ocv:pyfunction:: cv2.determinant(mtx) -> retval

.. ocv:cfunction:: double cvDet( const CvArr* mat )

.. ocv:pyoldfunction:: cv.Det(mat) -> float

:param mtx: input matrix that must have CV_32FC1 or CV_64FC1 type and square size.

:param mat: input matrix that must have CV_32FC1 or CV_64FC1 type and square size.


The function determinant calculates and returns the determinant of the specified matrix. For small matrices ( mtx.cols=mtx.rows<=3 ), the direct method is used. For larger matrices, the function uses LU factorization with partial pivoting.

For symmetric positively-determined matrices, it is also possible to use :ocv:func:eigen decomposition to calculate the determinant.

.. seealso::

:ocv:func:trace,
:ocv:func:invert,
:ocv:func:solve,
:ocv:func:eigen,
:ref:MatrixExpressions


## eigen

Calculates eigenvalues and eigenvectors of a symmetric matrix.

.. ocv:function:: bool eigen(InputArray src, OutputArray eigenvalues, int lowindex=-1, int highindex=-1)

.. ocv:function:: bool eigen(InputArray src, OutputArray eigenvalues, OutputArray eigenvectors, int lowindex=-1,int highindex=-1)

.. ocv:pyfunction:: cv2.eigen(src, computeEigenvectors[, eigenvalues[, eigenvectors]]) -> retval, eigenvalues, eigenvectors

.. ocv:cfunction:: void cvEigenVV( CvArr mat, CvArr evects, CvArr* evals, double eps=0, int lowindex=-1, int highindex=-1 )

.. ocv:pyoldfunction:: cv.EigenVV(mat, evects, evals, eps, lowindex=-1, highindex=-1)-> None

:param src: input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical (src :sup:T == src).

:param eigenvalues: output vector of eigenvalues of the same type as src; the eigenvalues are stored in the descending order.

:param eigenvectors: output matrix of eigenvectors; it has the same size and type as src; the eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues.

:param lowindex: optional index of largest eigenvalue/-vector to calculate; the parameter is ignored in the current implementation.

:param highindex: optional index of smallest eigenvalue/-vector to calculate; the parameter is ignored in the current implementation.


The functions eigen calculate just eigenvalues, or eigenvalues and eigenvectors of the symmetric matrix src : ::

src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()


.. note:: in the new and the old interfaces different ordering of eigenvalues and eigenvectors parameters is used.

.. seealso:: :ocv:func:completeSymm , :ocv:class:PCA

## exp

Calculates the exponent of every array element.

.. ocv:function:: void exp(InputArray src, OutputArray dst)

.. ocv:pyfunction:: cv2.exp(src[, dst]) -> dst

.. ocv:cfunction:: void cvExp(const CvArr src, CvArr dst) .. ocv:pyoldfunction:: cv.Exp(src, dst)-> None

:param src: input array.

:param dst: output array of the same size and type as src.


The function exp calculates the exponent of every element of the input array:

.. math::

\texttt{dst} [I] = e^{ src(I) }


The maximum relative error is about 7e-6 for single-precision input and less than 1e-10 for double-precision input. Currently, the function converts denormalized values to zeros on output. Special values (NaN, Inf) are not handled.

.. seealso:: :ocv:func:log , :ocv:func:cartToPolar , :ocv:func:polarToCart , :ocv:func:phase , :ocv:func:pow , :ocv:func:sqrt , :ocv:func:magnitude

## extractImageCOI

Extracts the selected image channel.

.. ocv:function:: void extractImageCOI( const CvArr* arr, OutputArray coiimg, int coi=-1 )

:param arr: input array; it should be a pointer to CvMat or IplImage.

:param coiimg: output array with a single channel and the same size and depth as arr.

:param coi: if the parameter is >=0, it specifies the channel to extract, if it is <0 and arr is a pointer to IplImage with a valid COI set, the selected COI is extracted.


The function extractImageCOI is used to extract an image COI from an old-style array and put the result to the new-style C++ matrix. As usual, the output matrix is reallocated using Mat::create if needed.

To extract a channel from a new-style matrix, use :ocv:func:mixChannels or :ocv:func:split .

.. seealso:: :ocv:func:mixChannels , :ocv:func:split , :ocv:func:merge , :ocv:func:cvarrToMat , :ocv:cfunc:cvSetImageCOI , :ocv:cfunc:cvGetImageCOI

## insertImageCOI

Copies the selected image channel from a new-style C++ matrix to the old-style C array.

.. ocv:function:: void insertImageCOI( InputArray coiimg, CvArr* arr, int coi=-1 )

:param coiimg: input array with a single channel and the same size and depth as arr.

:param arr: output array, it should be a pointer to CvMat or IplImage.

:param coi: if the parameter is >=0, it specifies the channel to insert, if it is <0 and arr is a pointer to IplImage with a  valid COI set, the selected COI is extracted.


The function insertImageCOI is used to extract an image COI from a new-style C++ matrix and put the result to the old-style array.

The sample below illustrates how to use the function: ::

Mat temp(240, 320, CV_8UC1, Scalar(255));
IplImage* img = cvCreateImage(cvSize(320,240), IPL_DEPTH_8U, 3);
insertImageCOI(temp, img, 1); //insert to the first channel
cvNamedWindow("window",1);
cvShowImage("window", img); //you should see green image, because channel number 1 is green (BGR)
cvWaitKey(0);
cvDestroyAllWindows();
cvReleaseImage(&img);


To insert a channel to a new-style matrix, use :ocv:func:merge .

.. seealso:: :ocv:func:mixChannels , :ocv:func:split , :ocv:func:merge , :ocv:func:cvarrToMat , :ocv:cfunc:cvSetImageCOI , :ocv:cfunc:cvGetImageCOI

## flip

Flips a 2D array around vertical, horizontal, or both axes.

.. ocv:function:: void flip(InputArray src, OutputArray dst, int flipCode)

.. ocv:pyfunction:: cv2.flip(src, flipCode[, dst]) -> dst

.. ocv:cfunction:: void cvFlip( const CvArr src, CvArr dst=NULL, int flip_mode=0 )

.. ocv:pyoldfunction:: cv.Flip(src, dst=None, flipMode=0)-> None

:param src: input array.

:param dst: output array of the same size and type as src.

:param flipCode: a flag to specify how to flip the array; 0 means flipping around the x-axis and positive value (for example, 1) means flipping around y-axis. Negative value (for example, -1) means flipping around both axes (see the discussion below for the formulas).


The function flip flips the array in one of three different ways (row and column indices are 0-based):

.. math::

\texttt{dst} _{ij} =
\left\{
\begin{array}{l l}
\texttt{src} _{\texttt{src.rows}-i-1,j} & if\;  \texttt{flipCode} = 0 \\
\texttt{src} _{i, \texttt{src.cols} -j-1} & if\;  \texttt{flipCode} > 0 \\
\texttt{src} _{ \texttt{src.rows} -i-1, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} < 0 \\
\end{array}
\right.


The example scenarios of using the function are the following:

* Vertical flipping of the image (flipCode == 0) to switch between top-left and bottom-left image origin. This is a typical operation in video processing on Microsoft Windows* OS.

* Horizontal flipping of the image with the subsequent horizontal shift and absolute difference calculation to check for a vertical-axis symmetry (flipCode > 0).

* Simultaneous horizontal and vertical flipping of the image with the subsequent shift and absolute difference calculation to check for a central symmetry (flipCode < 0).

* Reversing the order of point arrays (flipCode > 0 or flipCode == 0).

.. seealso:: :ocv:func:transpose , :ocv:func:repeat , :ocv:func:completeSymm

## gemm

Performs generalized matrix multiplication.

.. ocv:function:: void gemm( InputArray src1, InputArray src2, double alpha, InputArray src3, double beta, OutputArray dst, int flags=0 )

.. ocv:pyfunction:: cv2.gemm(src1, src2, alpha, src3, beta[, dst[, flags]]) -> dst

.. ocv:cfunction:: void cvGEMM( const CvArr src1, const CvArr src2, double alpha, const CvArr src3, double beta, CvArr dst, int tABC=0)

.. ocv:pyoldfunction:: cv.GEMM(src1, src2, alpha, src3, beta, dst, tABC=0)-> None

:param src1: first multiplied input matrix that should have CV_32FC1, CV_64FC1, CV_32FC2, or CV_64FC2 type.

:param src2: second multiplied input matrix of the same type as src1.

:param alpha: weight of the matrix product.

:param src3: third optional delta matrix added to the matrix product; it should have the same type as src1 and src2.

:param beta: weight of src3.

:param dst: output matrix; it has the proper size and the same type as input matrices.

:param flags: operation flags:

* **GEMM_1_T** transposes src1.
* **GEMM_2_T** transposes src2.
* **GEMM_3_T** transposes src3.


The function performs generalized matrix multiplication similar to the gemm functions in BLAS level 3. For example, gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T) corresponds to

.. math::

\texttt{dst} =  \texttt{alpha} \cdot \texttt{src1} ^T  \cdot \texttt{src2} +  \texttt{beta} \cdot \texttt{src3} ^T


The function can be replaced with a matrix expression. For example, the above call can be replaced with: ::

dst = alpha*src1.t()*src2 + beta*src3.t();


.. seealso:: :ocv:func:mulTransposed , :ocv:func:transform , :ref:MatrixExpressions

## getConvertElem

Returns a conversion function for a single pixel.

.. ocv:function:: ConvertData getConvertElem(int fromType, int toType)

.. ocv:function:: ConvertScaleData getConvertScaleElem(int fromType, int toType)

:param fromType: input pixel type.

:param toType: output pixel type.

:param from: callback parameter: pointer to the input pixel.

:param to: callback parameter: pointer to the output pixel

:param cn: callback parameter: the number of channels; it can be arbitrary, 1, 100, 100000, etc.

:param alpha: ConvertScaleData callback optional parameter: the scale factor.

:param beta: ConvertScaleData callback optional parameter: the delta or offset.


The functions getConvertElem and getConvertScaleElem return pointers to the functions for converting individual pixels from one type to another. While the main function purpose is to convert single pixels (actually, for converting sparse matrices from one type to another), you can use them to convert the whole row of a dense matrix or the whole matrix at once, by setting cn = matrix.cols*matrix.rows*matrix.channels() if the matrix data is continuous.

ConvertData and ConvertScaleData are defined as: ::

typedef void (*ConvertData)(const void* from, void* to, int cn)
typedef void (*ConvertScaleData)(const void* from, void* to,
int cn, double alpha, double beta)


.. seealso:: :ocv:func:Mat::convertTo , :ocv:func:SparseMat::convertTo

## getOptimalDFTSize

Returns the optimal DFT size for a given vector size.

.. ocv:function:: int getOptimalDFTSize(int vecsize)

.. ocv:pyfunction:: cv2.getOptimalDFTSize(vecsize) -> retval

.. ocv:cfunction:: int cvGetOptimalDFTSize(int size0) .. ocv:pyoldfunction:: cv.GetOptimalDFTSize(size0)-> int

:param vecsize: vector size.


DFT performance is not a monotonic function of a vector size. Therefore, when you calculate convolution of two arrays or perform the spectral analysis of an array, it usually makes sense to pad the input data with zeros to get a bit larger array that can be transformed much faster than the original one. Arrays whose size is a power-of-two (2, 4, 8, 16, 32, …) are the fastest to process. Though, the arrays whose size is a product of 2’s, 3’s, and 5’s (for example, 300 = 55322) are also processed quite efficiently.

The function getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize so that the DFT of a vector of size N can be processed efficiently. In the current implementation N = 2 :sup:p * 3 :sup:q * 5 :sup:r for some integer p, q, r.

The function returns a negative number if vecsize is too large (very close to INT_MAX ).

While the function cannot be used directly to estimate the optimal vector size for DCT transform (since the current DCT implementation supports only even-size vectors), it can be easily processed as getOptimalDFTSize((vecsize+1)/2)*2.

.. seealso:: :ocv:func:dft , :ocv:func:dct , :ocv:func:idft , :ocv:func:idct , :ocv:func:mulSpectrums

## idct

Calculates the inverse Discrete Cosine Transform of a 1D or 2D array.

.. ocv:function:: void idct(InputArray src, OutputArray dst, int flags=0)

.. ocv:pyfunction:: cv2.idct(src[, dst[, flags]]) -> dst

:param src: input floating-point single-channel array.

:param dst: output array of the same size and type as src.

:param flags: operation flags.


idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE).

.. seealso::

:ocv:func:dct,
:ocv:func:dft,
:ocv:func:idft,
:ocv:func:getOptimalDFTSize


## idft

Calculates the inverse Discrete Fourier Transform of a 1D or 2D array.

.. ocv:function:: void idft(InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)

.. ocv:pyfunction:: cv2.idft(src[, dst[, flags[, nonzeroRows]]]) -> dst

:param src: input floating-point real or complex array.

:param dst: output array whose size and type depend on the flags.

:param flags: operation flags (see :ocv:func:dft).

:param nonzeroRows: number of dst rows to process; the rest of the rows have undefined content (see the convolution sample in  :ocv:func:dft description.


idft(src, dst, flags) is equivalent to dft(src, dst, flags | DFT_INVERSE) .

See :ocv:func:dft for details.

.. note:: None of dft and idft scales the result by default. So, you should pass DFT_SCALE to one of dft or idft explicitly to make these transforms mutually inverse.

.. seealso::

:ocv:func:dft,
:ocv:func:dct,
:ocv:func:idct,
:ocv:func:mulSpectrums,
:ocv:func:getOptimalDFTSize


## inRange

Checks if array elements lie between the elements of two other arrays.

.. ocv:function:: void inRange(InputArray src, InputArray lowerb, InputArray upperb, OutputArray dst)

.. ocv:pyfunction:: cv2.inRange(src, lowerb, upperb[, dst]) -> dst

.. ocv:cfunction:: void cvInRange(const CvArr src, const CvArr lower, const CvArr upper, CvArr dst) .. ocv:cfunction:: void cvInRangeS(const CvArr src, CvScalar lower, CvScalar upper, CvArr dst) .. ocv:pyoldfunction:: cv.InRange(src, lower, upper, dst)-> None .. ocv:pyoldfunction:: cv.InRangeS(src, lower, upper, dst)-> None

:param src: first input array.

:param lowerb: inclusive lower boundary array or a scalar.

:param upperb: inclusive upper boundary array or a scalar.

:param dst: output array of the same size as src and CV_8U type.


The function checks the range as follows:

• For every element of a single-channel input array:

.. math::

\texttt{dst} (I)= \texttt{lowerb} (I)0 \leq \texttt{src} (I)0 \leq \texttt{upperb} (I)_0

• For two-channel arrays:

.. math::

\texttt{dst} (I)= \texttt{lowerb} (I)0 \leq \texttt{src} (I)0 \leq \texttt{upperb} (I)0 \land \texttt{lowerb} (I)1 \leq \texttt{src} (I)1 \leq \texttt{upperb} (I)1

• and so forth.

That is, dst (I) is set to 255 (all 1 -bits) if src (I) is within the specified 1D, 2D, 3D, … box and 0 otherwise.

When the lower and/or upper boundary parameters are scalars, the indexes (I) at lowerb and upperb in the above formulas should be omitted.

## invert

Finds the inverse or pseudo-inverse of a matrix.

.. ocv:function:: double invert(InputArray src, OutputArray dst, int flags=DECOMP_LU)

.. ocv:pyfunction:: cv2.invert(src[, dst[, flags]]) -> retval, dst

.. ocv:cfunction:: double cvInvert( const CvArr src, CvArr dst, int method=CV_LU )

.. ocv:pyoldfunction:: cv.Invert(src, dst, method=CV_LU) -> float

:param src: input floating-point M x N matrix.

:param dst: output matrix of N x M size and the same type as src.

:param flags: inversion method :

* **DECOMP_LU** Gaussian elimination with the optimal pivot element chosen.

* **DECOMP_SVD** singular value decomposition (SVD) method.

* **DECOMP_CHOLESKY** Cholesky decomposition; the matrix must be symmetrical and positively defined.


The function invert inverts the matrix src and stores the result in dst . When the matrix src is singular or non-square, the function calculates the pseudo-inverse matrix (the dst matrix) so that norm(src*dst - I) is minimal, where I is an identity matrix.

In case of the DECOMP_LU method, the function returns non-zero value if the inverse has been successfully calculated and 0 if src is singular.

In case of the DECOMP_SVD method, the function returns the inverse condition number of src (the ratio of the smallest singular value to the largest singular value) and 0 if src is singular. The SVD method calculates a pseudo-inverse matrix if src is singular.

Similarly to DECOMP_LU , the method DECOMP_CHOLESKY works only with non-singular square matrices that should also be symmetrical and positively defined. In this case, the function stores the inverted matrix in dst and returns non-zero. Otherwise, it returns 0.

.. seealso::

:ocv:func:solve,
:ocv:class:SVD


## log

Calculates the natural logarithm of every array element.

.. ocv:function:: void log(InputArray src, OutputArray dst)

.. ocv:pyfunction:: cv2.log(src[, dst]) -> dst

.. ocv:cfunction:: void cvLog(const CvArr src, CvArr dst) .. ocv:pyoldfunction:: cv.Log(src, dst)-> None

:param src: input array.

:param dst: output array of the same size and type as  src .


The function log calculates the natural logarithm of the absolute value of every element of the input array:

.. math::

\texttt{dst} (I) =  \fork{\log |\texttt{src}(I)|}{if $\texttt{src}(I) \ne 0$ }{\texttt{C}}{otherwise}


where C is a large negative number (about -700 in the current implementation). The maximum relative error is about 7e-6 for single-precision input and less than 1e-10 for double-precision input. Special values (NaN, Inf) are not handled.

.. seealso::

:ocv:func:exp,
:ocv:func:cartToPolar,
:ocv:func:polarToCart,
:ocv:func:phase,
:ocv:func:pow,
:ocv:func:sqrt,
:ocv:func:magnitude


## LUT

Performs a look-up table transform of an array.

.. ocv:function:: void LUT( InputArray src, InputArray lut, OutputArray dst, int interpolation=0 )

.. ocv:pyfunction:: cv2.LUT(src, lut[, dst[, interpolation]]) -> dst

.. ocv:cfunction:: void cvLUT(const CvArr src, CvArr dst, const CvArr* lut) .. ocv:pyoldfunction:: cv.LUT(src, dst, lut)-> None

:param src: input array of 8-bit elements.

:param lut: look-up table of 256 elements; in case of multi-channel input array, the table should either have a single channel (in this case the same table is used for all channels) or the same number of channels as in the input array.

:param dst: output array of the same size and number of channels as src, and the same depth as lut.


The function LUT fills the output array with values from the look-up table. Indices of the entries are taken from the input array. That is, the function processes each element of src as follows:

.. math::

\texttt{dst} (I)  \leftarrow \texttt{lut(src(I) + d)}


where

.. math::

d =  \fork{0}{if \texttt{src} has depth \texttt{CV\_8U}}{128}{if \texttt{src} has depth \texttt{CV\_8S}}


.. seealso::

:ocv:func:convertScaleAbs,
:ocv:func:Mat::convertTo


## magnitude

Calculates the magnitude of 2D vectors.

.. ocv:function:: void magnitude(InputArray x, InputArray y, OutputArray magnitude)

.. ocv:pyfunction:: cv2.magnitude(x, y[, magnitude]) -> magnitude

:param x: floating-point array of x-coordinates of the vectors.

:param y: floating-point array of y-coordinates of the vectors; it must have the same size as x.

:param magnitude: output array of the same size and type as x.


The function magnitude calculates the magnitude of 2D vectors formed from the corresponding elements of x and y arrays:

.. math::

\texttt{dst} (I) =  \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}


.. seealso::

:ocv:func:cartToPolar,
:ocv:func:polarToCart,
:ocv:func:phase,
:ocv:func:sqrt


## Mahalanobis

Calculates the Mahalanobis distance between two vectors.

.. ocv:function:: double Mahalanobis( InputArray v1, InputArray v2, InputArray icovar )

.. ocv:pyfunction:: cv2.Mahalanobis(v1, v2, icovar) -> retval

.. ocv:cfunction:: double cvMahalanobis( const CvArr vec1, const CvArr vec2, const CvArr* mat )

.. ocv:pyoldfunction:: cv.Mahalonobis(vec1, vec2, mat) -> None

:param vec1: first 1D input vector.

:param vec2: second 1D input vector.

:param icovar: inverse covariance matrix.


The function Mahalanobis calculates and returns the weighted distance between two vectors:

.. math::

d( \texttt{vec1} , \texttt{vec2} )= \sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})} }


The covariance matrix may be calculated using the :ocv:func:calcCovarMatrix function and then inverted using the :ocv:func:invert function (preferably using the DECOMP_SVD method, as the most accurate).

## max

Calculates per-element maximum of two arrays or an array and a scalar.

.. ocv:function:: MatExpr max( const Mat& a, const Mat& b )

.. ocv:function:: MatExpr max( const Mat& a, double s )

.. ocv:function:: MatExpr max( double s, const Mat& a )

.. ocv:function:: void max(InputArray src1, InputArray src2, OutputArray dst)

.. ocv:function:: void max(const Mat& src1, const Mat& src2, Mat& dst)

.. ocv:function:: void max( const Mat& src1, double src2, Mat& dst )

.. ocv:pyfunction:: cv2.max(src1, src2[, dst]) -> dst

.. ocv:cfunction:: void cvMax(const CvArr src1, const CvArr src2, CvArr dst) .. ocv:cfunction:: void cvMaxS(const CvArr src, double value, CvArr* dst) .. ocv:pyoldfunction:: cv.Max(src1, src2, dst)-> None .. ocv:pyoldfunction:: cv.MaxS(src, value, dst)-> None

:param src1: first input array.

:param src2: second input array of the same size and type as  src1 .

:param value: real scalar value.

:param dst: output array of the same size and type as src1.


The functions max calculate the per-element maximum of two arrays:

.. math::

\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{src2} (I))


or array and a scalar:

.. math::

\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{value} )


In the second variant, when the input array is multi-channel, each channel is compared with value independently.

The first 3 variants of the function listed above are actually a part of :ref:MatrixExpressions . They return an expression object that can be further either transformed/ assigned to a matrix, or passed to a function, and so on.

.. seealso::

:ocv:func:min,
:ocv:func:compare,
:ocv:func:inRange,
:ocv:func:minMaxLoc,
:ref:MatrixExpressions


## mean

Calculates an average (mean) of array elements.

.. ocv:function:: Scalar mean(InputArray src, InputArray mask=noArray())

.. ocv:pyfunction:: cv2.mean(src[, mask]) -> retval

.. ocv:cfunction:: CvScalar cvAvg( const CvArr arr, const CvArr mask=NULL )

.. ocv:pyoldfunction:: cv.Avg(arr, mask=None) -> scalar

:param src: input array that should have from 1 to 4 channels so that the result can be stored in :ocv:class:Scalar_ .



The function mean calculates the mean value M of array elements, independently for each channel, and return it:

.. math::

\begin{array}{l} N =  \sum _{I: \; \texttt{mask} (I) \ne 0} 1 \\ M_c =  \left ( \sum _{I: \; \texttt{mask} (I) \ne 0}{ \texttt{mtx} (I)_c} \right )/N \end{array}


When all the mask elements are 0’s, the functions return Scalar::all(0) .

.. seealso::

:ocv:func:countNonZero,
:ocv:func:meanStdDev,
:ocv:func:norm,
:ocv:func:minMaxLoc


## meanStdDev

Calculates a mean and standard deviation of array elements.

.. ocv:function:: void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev, InputArray mask=noArray())

.. ocv:pyfunction:: cv2.meanStdDev(src[, mean[, stddev[, mask]]]) -> mean, stddev

.. ocv:cfunction:: void cvAvgSdv( const CvArr arr, CvScalar mean, CvScalar std_dev, const CvArr mask=NULL )

.. ocv:pyoldfunction:: cv.AvgSdv(arr, mask=None) -> (mean, stdDev)

:param src: input array that should have from 1 to 4 channels so that the results can be stored in  :ocv:class:Scalar_ 's.

:param mean: output parameter: calculated mean value.

:param stddev: output parameter: calculateded standard deviation.



The function meanStdDev calculates the mean and the standard deviation M of array elements independently for each channel and returns it via the output parameters:

.. math::

\begin{array}{l} N =  \sum _{I, \texttt{mask} (I)  \ne 0} 1 \\ \texttt{mean} _c =  \frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \texttt{src} (I)_c}{N} \\ \texttt{stddev} _c =  \sqrt{\frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \left ( \texttt{src} (I)_c -  \texttt{mean} _c \right )^2}{N}} \end{array}


When all the mask elements are 0’s, the functions return mean=stddev=Scalar::all(0) .

.. note:: The calculated standard deviation is only the diagonal of the complete normalized covariance matrix. If the full matrix is needed, you can reshape the multi-channel array M x N to the single-channel array M*N x mtx.channels() (only possible when the matrix is continuous) and then pass the matrix to :ocv:func:calcCovarMatrix .

.. seealso::

:ocv:func:countNonZero,
:ocv:func:mean,
:ocv:func:norm,
:ocv:func:minMaxLoc,
:ocv:func:calcCovarMatrix


## merge

Creates one multichannel array out of several single-channel ones.

.. ocv:function:: void merge(const Mat* mv, size_t count, OutputArray dst)

.. ocv:function:: void merge( InputArrayOfArrays mv, OutputArray dst )

.. ocv:pyfunction:: cv2.merge(mv[, dst]) -> dst

.. ocv:cfunction:: void cvMerge(const CvArr src0, const CvArr src1, const CvArr src2, const CvArr src3, CvArr* dst) .. ocv:pyoldfunction:: cv.Merge(src0, src1, src2, src3, dst)-> None

:param mv: input array or vector of matrices to be merged; all the matrices in mv must have the same size and the same depth.

:param count: number of input matrices when mv is a plain C array; it must be greater than zero.

:param dst: output array of the same size and the same depth as mv[0]; The number of channels will be the total number of channels in the matrix array.


The functions merge merge several arrays to make a single multi-channel array. That is, each element of the output array will be a concatenation of the elements of the input arrays, where elements of i-th input array are treated as mv[i].channels()-element vectors.

The function :ocv:func:split does the reverse operation. If you need to shuffle channels in some other advanced way, use :ocv:func:mixChannels .

.. seealso::

:ocv:func:mixChannels,
:ocv:func:split,
:ocv:func:Mat::reshape


## min

Calculates per-element minimum of two arrays or an array and a scalar.

.. ocv:function:: MatExpr min( const Mat& a, const Mat& b )

.. ocv:function:: MatExpr min( const Mat& a, double s )

.. ocv:function:: MatExpr min( double s, const Mat& a )

.. ocv:function:: void min(InputArray src1, InputArray src2, OutputArray dst)

.. ocv:function:: void min(const Mat& src1, const Mat& src2, Mat& dst)

.. ocv:function:: void min( const Mat& src1, double src2, Mat& dst )

.. ocv:pyfunction:: cv2.min(src1, src2[, dst]) -> dst

.. ocv:cfunction:: void cvMin(const CvArr src1, const CvArr src2, CvArr dst) .. ocv:cfunction:: void cvMinS(const CvArr src, double value, CvArr* dst) .. ocv:pyoldfunction:: cv.Min(src1, src2, dst)-> None .. ocv:pyoldfunction:: cv.MinS(src, value, dst)-> None

:param src1: first input array.

:param src2: second input array of the same size and type as src1.

:param value: real scalar value.

:param dst: output array of the same size and type as src1.


The functions min calculate the per-element minimum of two arrays:

.. math::

\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{src2} (I))


or array and a scalar:

.. math::

\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{value} )


In the second variant, when the input array is multi-channel, each channel is compared with value independently.

The first three variants of the function listed above are actually a part of :ref:MatrixExpressions . They return the expression object that can be further either transformed/assigned to a matrix, or passed to a function, and so on.

.. seealso::

:ocv:func:max,
:ocv:func:compare,
:ocv:func:inRange,
:ocv:func:minMaxLoc,
:ref:MatrixExpressions


## minMaxIdx

Finds the global minimum and maximum in an array

.. ocv:function:: void minMaxIdx(InputArray src, double minVal, double maxVal, int minIdx=0, int maxIdx=0, InputArray mask=noArray())

:param src: input single-channel array.

:param minVal: pointer to the returned minimum value; NULL is used if not required.

:param maxVal: pointer to the returned maximum value; NULL is used if not required.

:param minIdx: pointer to the returned minimum location (in nD case); NULL is used if not required; Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element in each dimension are stored there sequentially.

.. note::

When minIdx is not NULL, it must have at least 2 elements (as well as maxIdx), even if src is a single-row or single-column matrix. In OpenCV (following MATLAB) each array has at least 2 dimensions, i.e. single-column matrix is Mx1 matrix (and therefore minIdx/maxIdx will be (i1,0)/(i2,0)) and single-row matrix is 1xN matrix (and therefore minIdx/maxIdx will be (0,j1)/(0,j2)).

:param maxIdx: pointer to the returned maximum location (in nD case). NULL is used if not required.

The function minMaxIdx finds the minimum and maximum element values and their positions. The extremums are searched across the whole array or, if mask is not an empty array, in the specified array region.

The function does not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use
:ocv:func:Mat::reshape first to reinterpret the array as single-channel. Or you may extract the particular channel using either
:ocv:func:extractImageCOI , or
:ocv:func:mixChannels , or
:ocv:func:split .

In case of a sparse matrix, the minimum is found among non-zero elements only.


## minMaxLoc

Finds the global minimum and maximum in an array.

.. ocv:function:: void minMaxLoc(InputArray src, double minVal, double maxVal=0, Point minLoc=0, Point maxLoc=0, InputArray mask=noArray())

.. ocv:function:: void minMaxLoc( const SparseMat& a, double minVal, double maxVal, int minIdx=0, int maxIdx=0 )

.. ocv:pyfunction:: cv2.minMaxLoc(src[, mask]) -> minVal, maxVal, minLoc, maxLoc

.. ocv:cfunction:: void cvMinMaxLoc( const CvArr arr, double min_val, double max_val, CvPoint min_loc=NULL, CvPoint max_loc=NULL, const CvArr mask=NULL )

.. ocv:pyoldfunction:: cv.MinMaxLoc(arr, mask=None)-> (minVal, maxVal, minLoc, maxLoc)

:param src: input single-channel array.

:param minVal: pointer to the returned minimum value;  NULL is used if not required.

:param maxVal: pointer to the returned maximum value;  NULL is used if not required.

:param minLoc: pointer to the returned minimum location (in 2D case);  NULL is used if not required.

:param maxLoc: pointer to the returned maximum location (in 2D case);  NULL is used if not required.



The functions minMaxLoc find the minimum and maximum element values and their positions. The extremums are searched across the whole array or, if mask is not an empty array, in the specified array region.

The functions do not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use :ocv:func:Mat::reshape first to reinterpret the array as single-channel. Or you may extract the particular channel using either :ocv:func:extractImageCOI , or :ocv:func:mixChannels , or :ocv:func:split .

.. seealso::

:ocv:func:max,
:ocv:func:min,
:ocv:func:compare,
:ocv:func:inRange,
:ocv:func:extractImageCOI,
:ocv:func:mixChannels,
:ocv:func:split,
:ocv:func:Mat::reshape


## mixChannels

Copies specified channels from input arrays to the specified channels of output arrays.

.. ocv:function:: void mixChannels( const Mat src, size_t nsrcs, Mat dst, size_t ndsts, const int* fromTo, size_t npairs )

.. ocv:function:: void mixChannels( const vector& src, vector& dst, const int* fromTo, size_t npairs )

.. ocv:pyfunction:: cv2.mixChannels(src, dst, fromTo) -> None

.. ocv:cfunction:: void cvMixChannels( const CvArr src, int src_count, CvArr dst, int dst_count, const int* from_to, int pair_count )

.. ocv:pyoldfunction:: cv.MixChannels(src, dst, fromTo) -> None

:param src: input array or vector of matricesl; all of the matrices must have the same size and the same depth.

:param nsrcs: number of matrices in src.

:param dst: output array or vector of matrices; all the matrices *must be allocated*; their size and depth must be the same as in src[0].

:param ndsts: number of matrices in dst.

:param fromTo: array of index pairs specifying which channels are copied and where; fromTo[k*2] is a 0-based index of the input channel in src, fromTo[k*2+1] is an index of the output channel in dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to src[0].channels()-1, the second input image channels are indexed from src[0].channels() to src[0].channels() + src[1].channels()-1,  and so on, the same scheme is used for the output image channels; as a special case, when fromTo[k*2] is negative, the corresponding output channel is filled with zero .

:param npairs: number of index pairs in fromTo.


The functions mixChannels provide an advanced mechanism for shuffling image channels.

:ocv:func:split and :ocv:func:merge and some forms of :ocv:func:cvtColor are partial cases of mixChannels .

In the example below, the code splits a 4-channel RGBA image into a 3-channel BGR (with R and B channels swapped) and a separate alpha-channel image: ::

Mat rgba( 100, 100, CV_8UC4, Scalar(1,2,3,4) );
Mat bgr( rgba.rows, rgba.cols, CV_8UC3 );
Mat alpha( rgba.rows, rgba.cols, CV_8UC1 );

// forming an array of matrices is a quite efficient operation,
// because the matrix data is not copied, only the headers
Mat out[] = { bgr, alpha };
// rgba[0] -> bgr[2], rgba[1] -> bgr[1],
// rgba[2] -> bgr[0], rgba[3] -> alpha[0]
int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
mixChannels( &rgba, 1, out, 2, from_to, 4 );


.. note:: Unlike many other new-style C++ functions in OpenCV (see the introduction section and :ocv:func:Mat::create ), mixChannels requires the output arrays to be pre-allocated before calling the function.

.. seealso::

:ocv:func:split,
:ocv:func:merge,
:ocv:func:cvtColor


## mulSpectrums

Performs the per-element multiplication of two Fourier spectrums.

.. ocv:function:: void mulSpectrums( InputArray a, InputArray b, OutputArray c, int flags, bool conjB=false )

.. ocv:pyfunction:: cv2.mulSpectrums(a, b, flags[, c[, conjB]]) -> c

.. ocv:cfunction:: void cvMulSpectrums( const CvArr src1, const CvArr src2, CvArr* dst, int flags) .. ocv:pyoldfunction:: cv.MulSpectrums(src1, src2, dst, flags)-> None

:param src1: first input array.

:param src2: second input array of the same size and type as src1 .

:param dst: output array of the same size and type as src1 .

:param flags: operation flags; currently, the only supported flag is DFT_ROWS, which indicates that each row of src1 and src2 is an independent 1D Fourier spectrum. If you do not want to use this flag, then simply add a 0 as value.

:param conjB: optional flag that conjugates the second input array before the multiplication (true) or not (false).


The function mulSpectrums performs the per-element multiplication of the two CCS-packed or complex matrices that are results of a real or complex Fourier transform.

The function, together with :ocv:func:dft and :ocv:func:idft , may be used to calculate convolution (pass conjB=false ) or correlation (pass conjB=true ) of two arrays rapidly. When the arrays are complex, they are simply multiplied (per element) with an optional conjugation of the second-array elements. When the arrays are real, they are assumed to be CCS-packed (see :ocv:func:dft for details).

## multiply

Calculates the per-element scaled product of two arrays.

.. ocv:function:: void multiply( InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1 )

.. ocv:pyfunction:: cv2.multiply(src1, src2[, dst[, scale[, dtype]]]) -> dst

.. ocv:cfunction:: void cvMul(const CvArr src1, const CvArr src2, CvArr* dst, double scale=1) .. ocv:pyoldfunction:: cv.Mul(src1, src2, dst, scale=1) -> None

:param src1: first input array.

:param src2: second input array of the same size and the same type as src1.

:param dst: output array of the same size and type as src1.

:param scale: optional scale factor.


The function multiply calculates the per-element product of two arrays:

.. math::

\texttt{dst} (I)= \texttt{saturate} ( \texttt{scale} \cdot \texttt{src1} (I)  \cdot \texttt{src2} (I))


There is also a :ref:MatrixExpressions -friendly variant of the first function. See :ocv:func:Mat::mul .

For a not-per-element matrix product, see :ocv:func:gemm .

.. note:: Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

.. seealso::

:ocv:func:add,
:ocv:func:subtract,
:ocv:func:divide,
:ref:MatrixExpressions,
:ocv:func:scaleAdd,
:ocv:func:addWeighted,
:ocv:func:accumulate,
:ocv:func:accumulateProduct,
:ocv:func:accumulateSquare,
:ocv:func:Mat::convertTo


## mulTransposed

Calculates the product of a matrix and its transposition.

.. ocv:function:: void mulTransposed( InputArray src, OutputArray dst, bool aTa, InputArray delta=noArray(), double scale=1, int dtype=-1 )

.. ocv:pyfunction:: cv2.mulTransposed(src, aTa[, dst[, delta[, scale[, dtype]]]]) -> dst

.. ocv:cfunction:: void cvMulTransposed( const CvArr src, CvArr dst, int order, const CvArr* delta=NULL, double scale=1. )

.. ocv:pyoldfunction:: cv.MulTransposed(src, dst, order, delta=None, scale=1.0) -> None

:param src: input single-channel matrix. Note that unlike :ocv:func:gemm, the function can multiply not only floating-point matrices.

:param dst: output square matrix.

:param aTa: Flag specifying the multiplication ordering. See the description below.

:param delta: Optional delta matrix subtracted from  src  before the multiplication. When the matrix is empty ( delta=noArray() ), it is assumed to be zero, that is, nothing is subtracted. If it has the same size as  src , it is simply subtracted. Otherwise, it is "repeated" (see  :ocv:func:repeat ) to cover the full  src  and then subtracted. Type of the delta matrix, when it is not empty, must be the same as the type of created output matrix. See the  dtype  parameter description below.

:param scale: Optional scale factor for the matrix product.

:param dtype: Optional type of the output matrix. When it is negative, the output matrix will have the same type as  src . Otherwise, it will be type=CV_MAT_DEPTH(dtype) that should be either  CV_32F  or  CV_64F .


The function mulTransposed calculates the product of src and its transposition:

.. math::

\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} )^T ( \texttt{src} - \texttt{delta} )


if aTa=true , and

.. math::

\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} ) ( \texttt{src} - \texttt{delta} )^T


otherwise. The function is used to calculate the covariance matrix. With zero delta, it can be used as a faster substitute for general matrix product A*B when B=A'

.. seealso::

:ocv:func:calcCovarMatrix,
:ocv:func:gemm,
:ocv:func:repeat,
:ocv:func:reduce


## norm

Calculates an absolute array norm, an absolute difference norm, or a relative difference norm.

.. ocv:function:: double norm(InputArray src1, int normType=NORM_L2, InputArray mask=noArray())

.. ocv:function:: double norm( InputArray src1, InputArray src2, int normType=NORM_L2, InputArray mask=noArray() )

.. ocv:function:: double norm( const SparseMat& src, int normType )

.. ocv:pyfunction:: cv2.norm(src1[, normType[, mask]]) -> retval .. ocv:pyfunction:: cv2.norm(src1, src2[, normType[, mask]]) -> retval

.. ocv:cfunction:: double cvNorm( const CvArr arr1, const CvArr arr2=NULL, int norm_type=CV_L2, const CvArr* mask=NULL )

.. ocv:pyoldfunction:: cv.Norm(arr1, arr2, normType=CV_L2, mask=None) -> float

:param src1: first input array.

:param src2: second input array of the same size and the same type as src1.

:param normType: type of the norm (see the details below).

:param mask: optional operation mask; it must have the same size as src1 and CV_8UC1 type.


The functions norm calculate an absolute norm of src1 (when there is no src2 ):

.. math::

norm =  \forkthree{\|\texttt{src1}\|_{L_{\infty}} =  \max _I | \texttt{src1} (I)|}{if  $\texttt{normType} = \texttt{NORM\_INF}$ }
{ \| \texttt{src1} \| _{L_1} =  \sum _I | \texttt{src1} (I)|}{if  $\texttt{normType} = \texttt{NORM\_L1}$ }
{ \| \texttt{src1} \| _{L_2} =  \sqrt{\sum_I \texttt{src1}(I)^2} }{if  $\texttt{normType} = \texttt{NORM\_L2}$ }


or an absolute or relative difference norm if src2 is there:

.. math::

norm =  \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} =  \max _I | \texttt{src1} (I) -  \texttt{src2} (I)|}{if  $\texttt{normType} = \texttt{NORM\_INF}$ }
{ \| \texttt{src1} - \texttt{src2} \| _{L_1} =  \sum _I | \texttt{src1} (I) -  \texttt{src2} (I)|}{if  $\texttt{normType} = \texttt{NORM\_L1}$ }
{ \| \texttt{src1} - \texttt{src2} \| _{L_2} =  \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if  $\texttt{normType} = \texttt{NORM\_L2}$ }


or

.. math::

norm =  \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}}    }{\|\texttt{src2}\|_{L_{\infty}} }}{if  $\texttt{normType} = \texttt{NORM\_RELATIVE\_INF}$ }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if  $\texttt{normType} = \texttt{NORM\_RELATIVE\_L1}$ }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if  $\texttt{normType} = \texttt{NORM\_RELATIVE\_L2}$ }


The functions norm return the calculated norm.

When the mask parameter is specified and it is not empty, the norm is calculated only over the region specified by the mask.

A multi-channel input arrays are treated as a single-channel, that is, the results for all channels are combined.

## normalize

Normalizes the norm or value range of an array.

.. ocv:function:: void normalize( InputArray src, OutputArray dst, double alpha=1, double beta=0, int norm_type=NORM_L2, int dtype=-1, InputArray mask=noArray() )

.. ocv:function:: void normalize(const SparseMat& src, SparseMat& dst, double alpha, int normType)

.. ocv:pyfunction:: cv2.normalize(src[, dst[, alpha[, beta[, norm_type[, dtype[, mask]]]]]]) -> dst

:param src: input array.

:param dst: output array of the same size as  src .

:param alpha: norm value to normalize to or the lower range boundary in case of the range normalization.

:param beta: upper range boundary in case of the range normalization; it is not used for the norm normalization.

:param normType: normalization type (see the details below).

:param dtype: when negative, the output array has the same type as src; otherwise, it has the same number of channels as  src and the depth =CV_MAT_DEPTH(dtype).



The functions normalize scale and shift the input array elements so that

.. math::

\| \texttt{dst} \| _{L_p}= \texttt{alpha}


(where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that

.. math::

\min _I  \texttt{dst} (I)= \texttt{alpha} , \, \, \max _I  \texttt{dst} (I)= \texttt{beta}


when normType=NORM_MINMAX (for dense arrays only). The optional mask specifies a sub-array to be normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or min-max but modify the whole array, you can use :ocv:func:norm and :ocv:func:Mat::convertTo.

In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this, the range transformation for sparse matrices is not allowed since it can shift the zero level.

.. seealso::

:ocv:func:norm,
:ocv:func:Mat::convertTo,
:ocv:func:SparseMat::convertTo


## PCA

.. ocv:class:: PCA

Principal Component Analysis class.

The class is used to calculate a special basis for a set of vectors. The basis will consist of eigenvectors of the covariance matrix calculated from the input set of vectors. The class PCA can also transform vectors to/from the new coordinate space defined by the basis. Usually, in this new coordinate system, each vector from the original set (and any linear combination of such vectors) can be quite accurately approximated by taking its first few components, corresponding to the eigenvectors of the largest eigenvalues of the covariance matrix. Geometrically it means that you calculate a projection of the vector to a subspace formed by a few eigenvectors corresponding to the dominant eigenvalues of the covariance matrix. And usually such a projection is very close to the original vector. So, you can represent the original vector from a high-dimensional space with a much shorter vector consisting of the projected vector’s coordinates in the subspace. Such a transformation is also known as Karhunen-Loeve Transform, or KLT. See http://en.wikipedia.org/wiki/Principal_component_analysis .

The sample below is the function that takes two matrices. The first function stores a set of vectors (a row per vector) that is used to calculate PCA. The second function stores another “test” set of vectors (a row per vector). First, these vectors are compressed with PCA, then reconstructed back, and then the reconstruction error norm is computed and printed for each vector. ::

PCA compressPCA(InputArray pcaset, int maxComponents,
const Mat& testset, OutputArray compressed)
{
PCA pca(pcaset, // pass the data
Mat(), // there is no pre-computed mean vector,
// so let the PCA engine to compute it
CV_PCA_DATA_AS_ROW, // indicate that the vectors
// are stored as matrix rows
// (use CV_PCA_DATA_AS_COL if the vectors are
// the matrix columns)
maxComponents // specify how many principal components to retain
);
// if there is no test data, just return the computed basis, ready-to-use
if( !testset.data )
return pca;
CV_Assert( testset.cols == pcaset.cols );

compressed.create(testset.rows, maxComponents, testset.type());

Mat reconstructed;
for( int i = 0; i < testset.rows; i++ )
{
Mat vec = testset.row(i), coeffs = compressed.row(i);
// compress the vector, the result will be stored
// in the i-th row of the output matrix
pca.project(vec, coeffs);
// and then reconstruct it
pca.backProject(coeffs, reconstructed);
// and measure the error
printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2));
}
return pca;
}


.. seealso::

:ocv:func:calcCovarMatrix,
:ocv:func:mulTransposed,
:ocv:class:SVD,
:ocv:func:dft,
:ocv:func:dct


.. note::

• An example using PCA for dimensionality reduction while maintaining an amount of variance can be found at opencv_source_code/samples/cpp/pca.cpp

## PCA::PCA

PCA constructors

.. ocv:function:: PCA::PCA()

.. ocv:function:: PCA::PCA(InputArray data, InputArray mean, int flags, int maxComponents=0)

.. ocv:function:: PCA::PCA(InputArray data, InputArray mean, int flags, double retainedVariance)

:param data: input samples stored as matrix rows or matrix columns.

:param mean: optional mean value; if the matrix is empty (noArray()), the mean is computed from the data.

:param flags: operation flags; currently the parameter is only used to specify the data layout:

* **CV_PCA_DATA_AS_ROW** indicates that the input samples are stored as matrix rows.

* **CV_PCA_DATA_AS_COL** indicates that the input samples are stored as matrix columns.

:param maxComponents: maximum number of components that PCA should retain; by default, all the components are retained.

:param retainedVariance: Percentage of variance that PCA should retain. Using this parameter will let the PCA decided how many components to retain but it will always keep at least 2.


The default constructor initializes an empty PCA structure. The other constructors initialize the structure and call :ocv:funcx:PCA::operator() .

## PCA::operator ()

Performs Principal Component Analysis of the supplied dataset.

.. ocv:function:: PCA& PCA::operator()(InputArray data, InputArray mean, int flags, int maxComponents=0)

.. ocv:function:: PCA& PCA::computeVar(InputArray data, InputArray mean, int flags, double retainedVariance)

.. ocv:pyfunction:: cv2.PCACompute(data[, mean[, eigenvectors[, maxComponents]]]) -> mean, eigenvectors

.. ocv:pyfunction:: cv2.PCAComputeVar(data, retainedVariance[, mean[, eigenvectors]]) -> mean, eigenvectors

:param data: input samples stored as the matrix rows or as the matrix columns.

:param mean: optional mean value; if the matrix is empty (noArray()), the mean is computed from the data.

:param flags: operation flags; currently the parameter is only used to specify the data layout.

* **CV_PCA_DATA_AS_ROW** indicates that the input samples are stored as matrix rows.

* **CV_PCA_DATA_AS_COL** indicates that the input samples are stored as matrix columns.

:param maxComponents: maximum number of components that PCA should retain; by default, all the components are retained.

:param retainedVariance: Percentage of variance that PCA should retain. Using this parameter will let the PCA decided how many components to retain but it will always keep at least 2.


The operator performs PCA of the supplied dataset. It is safe to reuse the same PCA structure for multiple datasets. That is, if the structure has been previously used with another dataset, the existing internal data is reclaimed and the new eigenvalues, eigenvectors , and mean are allocated and computed.

The computed eigenvalues are sorted from the largest to the smallest and the corresponding eigenvectors are stored as PCA::eigenvectors rows.

## PCA::project

Projects vector(s) to the principal component subspace.

.. ocv:function:: Mat PCA::project(InputArray vec) const

.. ocv:function:: void PCA::project(InputArray vec, OutputArray result) const

.. ocv:pyfunction:: cv2.PCAProject(data, mean, eigenvectors[, result]) -> result

:param vec: input vector(s); must have the same dimensionality and the same layout as the input data used at PCA phase, that is, if CV_PCA_DATA_AS_ROW are specified, then vec.cols==data.cols (vector dimensionality) and vec.rows is the number of vectors to project, and the same is true for the CV_PCA_DATA_AS_COL case.

:param result: output vectors; in case of CV_PCA_DATA_AS_COL, the output matrix has as many columns as the number of input vectors, this means that result.cols==vec.cols and the number of rows match the number of principal components (for example, maxComponents parameter passed to the constructor).


The methods project one or more vectors to the principal component subspace, where each vector projection is represented by coefficients in the principal component basis. The first form of the method returns the matrix that the second form writes to the result. So the first form can be used as a part of expression while the second form can be more efficient in a processing loop.

## PCA::backProject

Reconstructs vectors from their PC projections.

.. ocv:function:: Mat PCA::backProject(InputArray vec) const

.. ocv:function:: void PCA::backProject(InputArray vec, OutputArray result) const

.. ocv:pyfunction:: cv2.PCABackProject(data, mean, eigenvectors[, result]) -> result

:param vec: coordinates of the vectors in the principal component subspace, the layout and size are the same as of PCA::project output vectors.

:param result: reconstructed vectors; the layout and size are the same as of PCA::project input vectors.


The methods are inverse operations to :ocv:func:PCA::project. They take PC coordinates of projected vectors and reconstruct the original vectors. Unless all the principal components have been retained, the reconstructed vectors are different from the originals. But typically, the difference is small if the number of components is large enough (but still much smaller than the original vector dimensionality). As a result, PCA is used.

## perspectiveTransform

Performs the perspective matrix transformation of vectors.

.. ocv:function:: void perspectiveTransform( InputArray src, OutputArray dst, InputArray m )

.. ocv:pyfunction:: cv2.perspectiveTransform(src, m[, dst]) -> dst

.. ocv:cfunction:: void cvPerspectiveTransform(const CvArr src, CvArr dst, const CvMat* mat) .. ocv:pyoldfunction:: cv.PerspectiveTransform(src, dst, mat)-> None

:param src: input two-channel or three-channel floating-point array; each element is a 2D/3D vector to be transformed.

:param dst: output array of the same size and type as src.

:param m: 3x3 or 4x4 floating-point transformation matrix.


The function perspectiveTransform transforms every element of src by treating it as a 2D or 3D vector, in the following way:

.. math::

(x, y, z)  \rightarrow (x'/w, y'/w, z'/w)


where

.. math::

(x', y', z', w') =  \texttt{mat} \cdot \begin{bmatrix} x & y & z & 1  \end{bmatrix}


and

.. math::

w =  \fork{w'}{if $w' \ne 0$}{\infty}{otherwise}


Here a 3D vector transformation is shown. In case of a 2D vector transformation, the z component is omitted.

.. note:: The function transforms a sparse set of 2D or 3D vectors. If you want to transform an image using perspective transformation, use :ocv:func:warpPerspective . If you have an inverse problem, that is, you want to compute the most probable perspective transformation out of several pairs of corresponding points, you can use :ocv:func:getPerspectiveTransform or :ocv:func:findHomography .

.. seealso::

:ocv:func:transform,
:ocv:func:warpPerspective,
:ocv:func:getPerspectiveTransform,
:ocv:func:findHomography


## phase

Calculates the rotation angle of 2D vectors.

.. ocv:function:: void phase(InputArray x, InputArray y, OutputArray angle, bool angleInDegrees=false)

.. ocv:pyfunction:: cv2.phase(x, y[, angle[, angleInDegrees]]) -> angle

:param x: input floating-point array of x-coordinates of 2D vectors.

:param y: input array of y-coordinates of 2D vectors; it must have the same size and the same type as x.

:param angle: output array of vector angles; it has the same size and same type as  x .

:param angleInDegrees: when true, the function calculates the angle in degrees, otherwise, they are measured in radians.


The function phase calculates the rotation angle of each 2D vector that is formed from the corresponding elements of x and y :

.. math::

\texttt{angle} (I) =  \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))


The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0 , the corresponding angle(I) is set to 0.

## polarToCart

Calculates x and y coordinates of 2D vectors from their magnitude and angle.

.. ocv:function:: void polarToCart(InputArray magnitude, InputArray angle, OutputArray x, OutputArray y, bool angleInDegrees=false)

.. ocv:pyfunction:: cv2.polarToCart(magnitude, angle[, x[, y[, angleInDegrees]]]) -> x, y

.. ocv:cfunction:: void cvPolarToCart( const CvArr magnitude, const CvArr angle, CvArr x, CvArr y, int angle_in_degrees=0 )

.. ocv:pyoldfunction:: cv.PolarToCart(magnitude, angle, x, y, angleInDegrees=0)-> None

:param magnitude: input floating-point array of magnitudes of 2D vectors; it can be an empty matrix (=Mat()), in this case, the function assumes that all the magnitudes are =1; if it is not empty, it must have the same size and type as angle.

:param angle: input floating-point array of angles of 2D vectors.

:param x: output array of x-coordinates of 2D vectors; it has the same size and type as angle.

:param y: output array of y-coordinates of 2D vectors; it has the same size and type as angle.

:param angleInDegrees: when true, the input angles are measured in degrees, otherwise, they are measured in radians.


The function polarToCart calculates the Cartesian coordinates of each 2D vector represented by the corresponding elements of magnitude and angle :

.. math::

\begin{array}{l} \texttt{x} (I) =  \texttt{magnitude} (I) \cos ( \texttt{angle} (I)) \\ \texttt{y} (I) =  \texttt{magnitude} (I) \sin ( \texttt{angle} (I)) \\ \end{array}


The relative accuracy of the estimated coordinates is about 1e-6.

.. seealso::

:ocv:func:cartToPolar,
:ocv:func:magnitude,
:ocv:func:phase,
:ocv:func:exp,
:ocv:func:log,
:ocv:func:pow,
:ocv:func:sqrt


## pow

Raises every array element to a power.

.. ocv:function:: void pow( InputArray src, double power, OutputArray dst )

.. ocv:pyfunction:: cv2.pow(src, power[, dst]) -> dst

.. ocv:cfunction:: void cvPow( const CvArr src, CvArr dst, double power) .. ocv:pyoldfunction:: cv.Pow(src, dst, power)-> None

:param src: input array.

:param power: exponent of power.

:param dst: output array of the same size and type as src.


The function pow raises every element of the input array to power :

.. math::

\texttt{dst} (I) =  \fork{\texttt{src}(I)^power}{if \texttt{power} is integer}{|\texttt{src}(I)|^power}{otherwise}


So, for a non-integer power exponent, the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations. In the example below, computing the 5th root of array src shows: ::

Mat mask = src < 0;
pow(src, 1./5, dst);


For some values of power , such as integer values, 0.5 and -0.5, specialized faster algorithms are used.

Special values (NaN, Inf) are not handled.

.. seealso::

:ocv:func:sqrt,
:ocv:func:exp,
:ocv:func:log,
:ocv:func:cartToPolar,
:ocv:func:polarToCart


## RNG

.. ocv:class:: RNG

Random number generator. It encapsulates the state (currently, a 64-bit integer) and has methods to return scalar random values and to fill arrays with random values. Currently it supports uniform and Gaussian (normal) distributions. The generator uses Multiply-With-Carry algorithm, introduced by G. Marsaglia ( http://en.wikipedia.org/wiki/Multiply-with-carry ). Gaussian-distribution random numbers are generated using the Ziggurat algorithm ( http://en.wikipedia.org/wiki/Ziggurat_algorithm ), introduced by G. Marsaglia and W. W. Tsang.

## RNG::RNG

The constructors

.. ocv:function:: RNG::RNG()

.. ocv:function:: RNG::RNG(uint64 state)

:param state: 64-bit value used to initialize the RNG.


These are the RNG constructors. The first form sets the state to some pre-defined value, equal to 2**32-1 in the current implementation. The second form sets the state to the specified value. If you passed state=0 , the constructor uses the above default value instead to avoid the singular random number sequence, consisting of all zeros.

## RNG::next

Returns the next random number.

.. ocv:function:: unsigned RNG::next()

The method updates the state using the MWC algorithm and returns the next 32-bit random number.

## RNG::operator T

Returns the next random number of the specified type.

.. ocv:function:: RNG::operator uchar()

.. ocv:function:: RNG::operator schar()

.. ocv:function:: RNG::operator ushort()

.. ocv:function:: RNG::operator short()

.. ocv:function:: RNG::operator int()

.. ocv:function:: RNG::operator unsigned()

.. ocv:function:: RNG::operator float()

.. ocv:function:: RNG::operator double()

Each of the methods updates the state using the MWC algorithm and returns the next random number of the specified type. In case of integer types, the returned number is from the available value range for the specified type. In case of floating-point types, the returned value is from [0,1) range.

## RNG::operator ()

Returns the next random number.

.. ocv:function:: unsigned RNG::operator ()()

.. ocv:function:: unsigned RNG::operator ()(unsigned N)

:param N: upper non-inclusive boundary of the returned random number.


The methods transform the state using the MWC algorithm and return the next random number. The first form is equivalent to :ocv:func:RNG::next . The second form returns the random number modulo N , which means that the result is in the range [0, N) .

## RNG::uniform

Returns the next random number sampled from the uniform distribution.

.. ocv:function:: int RNG::uniform(int a, int b)

.. ocv:function:: float RNG::uniform(float a, float b)

.. ocv:function:: double RNG::uniform(double a, double b)

:param a: lower inclusive boundary of the returned random numbers.

:param b: upper non-inclusive boundary of the returned random numbers.


The methods transform the state using the MWC algorithm and return the next uniformly-distributed random number of the specified type, deduced from the input parameter type, from the range [a, b) . There is a nuance illustrated by the following sample: ::

RNG rng;

// always produces 0
double a = rng.uniform(0, 1);

// produces double from [0, 1)
double a1 = rng.uniform((double)0, (double)1);

// produces float from [0, 1)
double b = rng.uniform(0.f, 1.f);

// produces double from [0, 1)
double c = rng.uniform(0., 1.);

// may cause compiler error because of ambiguity:
//  RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)?
double d = rng.uniform(0, 0.999999);


The compiler does not take into account the type of the variable to which you assign the result of RNG::uniform . The only thing that matters to the compiler is the type of a and b parameters. So, if you want a floating-point random number, but the range boundaries are integer numbers, either put dots in the end, if they are constants, or use explicit type cast operators, as in the a1 initialization above.

## RNG::gaussian

Returns the next random number sampled from the Gaussian distribution.

.. ocv:function:: double RNG::gaussian(double sigma)

:param sigma: standard deviation of the distribution.


The method transforms the state using the MWC algorithm and returns the next random number from the Gaussian distribution N(0,sigma) . That is, the mean value of the returned random numbers is zero and the standard deviation is the specified sigma .

## RNG::fill

Fills arrays with random numbers.

.. ocv:function:: void RNG::fill( InputOutputArray mat, int distType, InputArray a, InputArray b, bool saturateRange=false )

:param mat: 2D or N-dimensional matrix; currently matrices with more than 4 channels are not supported by the methods, use  :ocv:func:Mat::reshape as a possible workaround.

:param distType: distribution type, RNG::UNIFORM or RNG::NORMAL.

:param a: first distribution parameter; in case of the uniform distribution, this is an inclusive lower boundary, in case of the normal distribution, this is a mean value.

:param b: second distribution parameter; in case of the uniform distribution, this is a non-inclusive upper boundary, in case of the normal distribution, this is a standard deviation (diagonal of the standard deviation matrix or the full standard deviation matrix).

:param saturateRange: pre-saturation flag; for uniform distribution only; if true, the method will first convert a and b to the acceptable value range (according to the mat datatype) and then will generate uniformly distributed random numbers within the range [saturate(a), saturate(b)), if saturateRange=false, the method will generate uniformly distributed random numbers in the original range [a, b) and then will saturate them, it means, for example, that theRNG().fill(mat_8u, RNG::UNIFORM, -DBL_MAX, DBL_MAX) will likely produce array mostly filled with 0's and 255's, since the range (0, 255) is significantly smaller than [-DBL_MAX, DBL_MAX).


Each of the methods fills the matrix with the random values from the specified distribution. As the new numbers are generated, the RNG state is updated accordingly. In case of multiple-channel images, every channel is filled independently, which means that RNG cannot generate samples from the multi-dimensional Gaussian distribution with non-diagonal covariance matrix directly. To do that, the method generates samples from multi-dimensional standard Gaussian distribution with zero mean and identity covariation matrix, and then transforms them using :ocv:func:transform to get samples from the specified Gaussian distribution.

## randu

Generates a single uniformly-distributed random number or an array of random numbers.

.. ocv:function:: template _Tp randu()

.. ocv:function:: void randu( InputOutputArray dst, InputArray low, InputArray high )

.. ocv:pyfunction:: cv2.randu(dst, low, high) -> None

:param dst: output array of random numbers; the array must be pre-allocated.

:param low: inclusive lower boundary of the generated random numbers.

:param high: exclusive upper boundary of the generated random numbers.


The template functions randu generate and return the next uniformly-distributed random value of the specified type. randu<int>() is an equivalent to (int)theRNG(); , and so on. See :ocv:class:RNG description.

The second non-template variant of the function fills the matrix dst with uniformly-distributed random numbers from the specified range:

.. math::

\texttt{low} _c  \leq \texttt{dst} (I)_c <  \texttt{high} _c


.. seealso::

:ocv:class:RNG,
:ocv:func:randn,
:ocv:func:theRNG


## randn

Fills the array with normally distributed random numbers.

.. ocv:function:: void randn( InputOutputArray dst, InputArray mean, InputArray stddev )

.. ocv:pyfunction:: cv2.randn(dst, mean, stddev) -> None

:param dst: output array of random numbers; the array must be pre-allocated and have 1 to 4 channels.

:param mean: mean value (expectation) of the generated random numbers.

:param stddev: standard deviation of the generated random numbers; it can be either a vector (in which case a diagonal standard deviation matrix is assumed) or a square matrix.


The function randn fills the matrix dst with normally distributed random numbers with the specified mean vector and the standard deviation matrix. The generated random numbers are clipped to fit the value range of the output array data type.

.. seealso::

:ocv:class:RNG,
:ocv:func:randu


## randShuffle

Shuffles the array elements randomly.

.. ocv:function:: void randShuffle( InputOutputArray dst, double iterFactor=1., RNG* rng=0 )

.. ocv:pyfunction:: cv2.randShuffle(dst[, iterFactor]) -> None

:param dst: input/output numerical 1D array.

:param iterFactor: scale factor that determines the number of random swap operations (see the details below).

:param rng: optional random number generator used for shuffling; if it is zero, :ocv:func:theRNG () is used instead.


The function randShuffle shuffles the specified 1D array by randomly choosing pairs of elements and swapping them. The number of such swap operations will be dst.rows*dst.cols*iterFactor .

.. seealso::

:ocv:class:RNG,
:ocv:func:sort


## reduce

Reduces a matrix to a vector.

.. ocv:function:: void reduce( InputArray src, OutputArray dst, int dim, int rtype, int dtype=-1 )

.. ocv:pyfunction:: cv2.reduce(src, dim, rtype[, dst[, dtype]]) -> dst

.. ocv:cfunction:: void cvReduce(const CvArr src, CvArr dst, int dim=-1, int op=CV_REDUCE_SUM) .. ocv:pyoldfunction:: cv.Reduce(src, dst, dim=-1, op=CV_REDUCE_SUM)-> None

:param src: input 2D matrix.

:param dst: output vector. Its size and type is defined by  dim  and  dtype  parameters.

:param dim: dimension index along which the matrix is reduced. 0 means that the matrix is reduced to a single row. 1 means that the matrix is reduced to a single column.

:param rtype: reduction operation that could be one of the following:

* **CV_REDUCE_SUM**: the output is the sum of all rows/columns of the matrix.

* **CV_REDUCE_AVG**: the output is the mean vector of all rows/columns of the matrix.

* **CV_REDUCE_MAX**: the output is the maximum (column/row-wise) of all rows/columns of the matrix.

* **CV_REDUCE_MIN**: the output is the minimum (column/row-wise) of all rows/columns of the matrix.

:param dtype: when negative, the output vector will have the same type as the input matrix, otherwise, its type will be CV_MAKE_TYPE(CV_MAT_DEPTH(dtype), src.channels()).


The function reduce reduces the matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of a raster image. In case of CV_REDUCE_SUM and CV_REDUCE_AVG , the output may have a larger element bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction modes.

.. seealso:: :ocv:func:repeat

## repeat

Fills the output array with repeated copies of the input array.

.. ocv:function:: void repeat(InputArray src, int ny, int nx, OutputArray dst)

.. ocv:function:: Mat repeat( const Mat& src, int ny, int nx )

.. ocv:pyfunction:: cv2.repeat(src, ny, nx[, dst]) -> dst

.. ocv:cfunction:: void cvRepeat(const CvArr src, CvArr dst)

.. ocv:pyoldfunction:: cv.Repeat(src, dst)-> None

:param src: input array to replicate.

:param dst: output array of the same type as src.

:param ny: Flag to specify how many times the src is repeated along the vertical axis.

:param nx: Flag to specify how many times the src is repeated along the horizontal axis.


The functions :ocv:func:repeat duplicate the input array one or more times along each of the two axes:

.. math::

\texttt{dst} _{ij}= \texttt{src} _{i\mod src.rows, \; j\mod src.cols }


The second variant of the function is more convenient to use with :ref:MatrixExpressions .

.. seealso::

:ocv:func:reduce,
:ref:MatrixExpressions


Calculates the sum of a scaled array and another array.

.. ocv:function:: void scaleAdd( InputArray src1, double alpha, InputArray src2, OutputArray dst )

.. ocv:pyfunction:: cv2.scaleAdd(src1, alpha, src2[, dst]) -> dst

.. ocv:cfunction:: void cvScaleAdd(const CvArr src1, CvScalar scale, const CvArr src2, CvArr* dst) .. ocv:pyoldfunction:: cv.ScaleAdd(src1, scale, src2, dst)-> None

:param src1: first input array.

:param scale: scale factor for the first array.

:param src2: second input array of the same size and type as src1.

:param dst: output array of the same size and type as src1.


The function scaleAdd is one of the classical primitive linear algebra operations, known as DAXPY or SAXPY in BLAS <http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms>_. It calculates the sum of a scaled array and another array:

.. math::

\texttt{dst} (I)= \texttt{scale} \cdot \texttt{src1} (I) +  \texttt{src2} (I)


The function can also be emulated with a matrix expression, for example: ::

Mat A(3, 3, CV_64F);
...
A.row(0) = A.row(1)*2 + A.row(2);


.. seealso::

:ocv:func:add,
:ocv:func:addWeighted,
:ocv:func:subtract,
:ocv:func:Mat::dot,
:ocv:func:Mat::convertTo,
:ref:MatrixExpressions


## setIdentity

Initializes a scaled identity matrix.

.. ocv:function:: void setIdentity( InputOutputArray mtx, const Scalar& s=Scalar(1) )

.. ocv:pyfunction:: cv2.setIdentity(mtx[, s]) -> None

.. ocv:cfunction:: void cvSetIdentity(CvArr* mat, CvScalar value=cvRealScalar(1))

.. ocv:pyoldfunction:: cv.SetIdentity(mat, value=1)-> None

:param mtx: matrix to initialize (not necessarily square).

:param value: value to assign to diagonal elements.


The function :ocv:func:setIdentity initializes a scaled identity matrix:

.. math::

\texttt{mtx} (i,j)= \fork{\texttt{value}}{ if $i=j$}{0}{otherwise}


The function can also be emulated using the matrix initializers and the matrix expressions: ::

Mat A = Mat::eye(4, 3, CV_32F)*5;
// A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]]


.. seealso::

:ocv:func:Mat::zeros,
:ocv:func:Mat::ones,
:ref:MatrixExpressions,
:ocv:func:Mat::setTo,
:ocv:func:Mat::operator=


## solve

Solves one or more linear systems or least-squares problems.

.. ocv:function:: bool solve(InputArray src1, InputArray src2, OutputArray dst, int flags=DECOMP_LU)

.. ocv:pyfunction:: cv2.solve(src1, src2[, dst[, flags]]) -> retval, dst

.. ocv:cfunction:: int cvSolve(const CvArr src1, const CvArr src2, CvArr* dst, int method=CV_LU) .. ocv:pyoldfunction:: cv.Solve(A, B, X, method=CV_LU)-> None

:param src1: input matrix on the left-hand side of the system.

:param src2: input matrix on the right-hand side of the system.

:param dst: output solution.

:param flags: solution (matrix inversion) method.

* **DECOMP_LU** Gaussian elimination with optimal pivot element chosen.

* **DECOMP_CHOLESKY** Cholesky  :math:LL^T  factorization; the matrix src1 must be symmetrical and positively defined.

* **DECOMP_EIG** eigenvalue decomposition; the matrix src1 must be symmetrical.

* **DECOMP_SVD** singular value decomposition (SVD) method; the system can be over-defined and/or the matrix src1 can be singular.

* **DECOMP_QR** QR factorization; the system can be over-defined and/or the matrix src1 can be singular.

* **DECOMP_NORMAL** while all the previous flags are mutually exclusive, this flag can be used together with any of the previous; it means that the normal equations  :math:\texttt{src1}^T\cdot\texttt{src1}\cdot\texttt{dst}=\texttt{src1}^T\texttt{src2}  are solved instead of the original system  :math:\texttt{src1}\cdot\texttt{dst}=\texttt{src2} .


The function solve solves a linear system or least-squares problem (the latter is possible with SVD or QR methods, or by specifying the flag DECOMP_NORMAL ):

.. math::

\texttt{dst} =  \arg \min _X \| \texttt{src1} \cdot \texttt{X} -  \texttt{src2} \|


If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1 if src1 (or :math:\texttt{src1}^T\texttt{src1} ) is non-singular. Otherwise, it returns 0. In the latter case, dst is not valid. Other methods find a pseudo-solution in case of a singular left-hand side part.

.. note:: If you want to find a unity-norm solution of an under-defined singular system :math:\texttt{src1}\cdot\texttt{dst}=0 , the function solve will not do the work. Use :ocv:func:SVD::solveZ instead.

.. seealso::

:ocv:func:invert,
:ocv:class:SVD,
:ocv:func:eigen


## solveCubic

Finds the real roots of a cubic equation.

.. ocv:function:: int solveCubic( InputArray coeffs, OutputArray roots )

.. ocv:pyfunction:: cv2.solveCubic(coeffs[, roots]) -> retval, roots

.. ocv:cfunction:: int cvSolveCubic( const CvMat coeffs, CvMat roots )

.. ocv:pyoldfunction:: cv.SolveCubic(coeffs, roots)-> None

:param coeffs: equation coefficients, an array of 3 or 4 elements.

:param roots: output array of real roots that has 1 or 3 elements.


The function solveCubic finds the real roots of a cubic equation:

• if coeffs is a 4-element vector:

.. math::

\texttt{coeffs} [0] x^3 +  \texttt{coeffs} [1] x^2 +  \texttt{coeffs} [2] x +  \texttt{coeffs} [3] = 0

• if coeffs is a 3-element vector:

.. math::

x^3 +  \texttt{coeffs} [0] x^2 +  \texttt{coeffs} [1] x +  \texttt{coeffs} [2] = 0


The roots are stored in the roots array.

## solvePoly

Finds the real or complex roots of a polynomial equation.

.. ocv:function:: double solvePoly( InputArray coeffs, OutputArray roots, int maxIters=300 )

.. ocv:pyfunction:: cv2.solvePoly(coeffs[, roots[, maxIters]]) -> retval, roots

:param coeffs: array of polynomial coefficients.

:param roots: output (complex) array of roots.

:param maxIters: maximum number of iterations the algorithm does.


The function solvePoly finds real and complex roots of a polynomial equation:

.. math::

\texttt{coeffs} [n] x^{n} +  \texttt{coeffs} [n-1] x^{n-1} + ... +  \texttt{coeffs} [1] x +  \texttt{coeffs} [0] = 0


## sort

Sorts each row or each column of a matrix.

.. ocv:function:: void sort(InputArray src, OutputArray dst, int flags)

.. ocv:pyfunction:: cv2.sort(src, flags[, dst]) -> dst

:param src: input single-channel array.

:param dst: output array of the same size and type as src.

:param flags: operation flags, a combination of the following values:

* **CV_SORT_EVERY_ROW** each matrix row is sorted independently.

* **CV_SORT_EVERY_COLUMN** each matrix column is sorted independently; this flag and the previous one are mutually exclusive.

* **CV_SORT_ASCENDING** each matrix row is sorted in the ascending order.

* **CV_SORT_DESCENDING** each matrix row is sorted in the descending order; this flag and the previous one are also mutually exclusive.


The function sort sorts each matrix row or each matrix column in ascending or descending order. So you should pass two operation flags to get desired behaviour. If you want to sort matrix rows or columns lexicographically, you can use STL std::sort generic function with the proper comparison predicate.

.. seealso::

:ocv:func:sortIdx,
:ocv:func:randShuffle


## sortIdx

Sorts each row or each column of a matrix.

.. ocv:function:: void sortIdx(InputArray src, OutputArray dst, int flags)

.. ocv:pyfunction:: cv2.sortIdx(src, flags[, dst]) -> dst

:param src: input single-channel array.

:param dst: output integer array of the same size as src.

:param flags: operation flags that could be a combination of the following values:

* **CV_SORT_EVERY_ROW** each matrix row is sorted independently.

* **CV_SORT_EVERY_COLUMN** each matrix column is sorted independently; this flag and the previous one are mutually exclusive.

* **CV_SORT_ASCENDING** each matrix row is sorted in the ascending order.

* **CV_SORT_DESCENDING** each matrix row is sorted in the descending order; his flag and the previous one are also mutually exclusive.


The function sortIdx sorts each matrix row or each matrix column in the ascending or descending order. So you should pass two operation flags to get desired behaviour. Instead of reordering the elements themselves, it stores the indices of sorted elements in the output array. For example: ::

Mat A = Mat::eye(3,3,CV_32F), B;
sortIdx(A, B, CV_SORT_EVERY_ROW + CV_SORT_ASCENDING);
// B will probably contain
// (because of equal elements in A some permutations are possible):
// [[1, 2, 0], [0, 2, 1], [0, 1, 2]]


.. seealso::

:ocv:func:sort,
:ocv:func:randShuffle


## split

Divides a multi-channel array into several single-channel arrays.

.. ocv:function:: void split( const Mat& src, Mat* mvbegin )

.. ocv:function:: void split( InputArray m, OutputArrayOfArrays mv )

.. ocv:pyfunction:: cv2.split(m[, mv]) -> mv

.. ocv:cfunction:: void cvSplit(const CvArr src, CvArr dst0, CvArr dst1, CvArr dst2, CvArr* dst3)

.. ocv:pyoldfunction:: cv.Split(src, dst0, dst1, dst2, dst3)-> None

:param src: input multi-channel array.

:param mv: output array or vector of arrays; in the first variant of the function the number of arrays must match src.channels(); the arrays themselves are reallocated, if needed.


The functions split split a multi-channel array into separate single-channel arrays:

.. math::

\texttt{mv} [c](I) =  \texttt{src} (I)_c


If you need to extract a single channel or do some other sophisticated channel permutation, use :ocv:func:mixChannels .

.. seealso::

:ocv:func:merge,
:ocv:func:mixChannels,
:ocv:func:cvtColor


## sqrt

Calculates a square root of array elements.

.. ocv:function:: void sqrt(InputArray src, OutputArray dst)

.. ocv:pyfunction:: cv2.sqrt(src[, dst]) -> dst

.. ocv:cfunction:: float cvSqrt(float value) .. ocv:pyoldfunction:: cv.Sqrt(value)-> float

:param src: input floating-point array.

:param dst: output array of the same size and type as src.


The functions sqrt calculate a square root of each input array element. In case of multi-channel arrays, each channel is processed independently. The accuracy is approximately the same as of the built-in std::sqrt .

.. seealso::

:ocv:func:pow,
:ocv:func:magnitude


## subtract

Calculates the per-element difference between two arrays or array and a scalar.

.. ocv:function:: void subtract(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)

.. ocv:pyfunction:: cv2.subtract(src1, src2[, dst[, mask[, dtype]]]) -> dst

.. ocv:cfunction:: void cvSub(const CvArr src1, const CvArr src2, CvArr dst, const CvArr mask=NULL) .. ocv:cfunction:: void cvSubRS( const CvArr src, CvScalar value, CvArr dst, const CvArr mask=NULL ) .. ocv:cfunction:: void cvSubS( const CvArr src, CvScalar value, CvArr dst, const CvArr mask=NULL )

.. ocv:pyoldfunction:: cv.Sub(src1, src2, dst, mask=None) -> None .. ocv:pyoldfunction:: cv.SubRS(src, value, dst, mask=None) -> None .. ocv:pyoldfunction:: cv.SubS(src, value, dst, mask=None) -> None

:param src1: first input array or a scalar.

:param src2: second input array or a scalar.

:param dst: output array of the same size and the same number of channels as the input array.

:param mask: optional operation mask; this is an 8-bit single channel array that specifies elements of the output array to be changed.

:param dtype: optional depth of the output array (see the details below).


The function subtract calculates:

* Difference between two arrays, when both input arrays have the same size and the same number of channels:

.. math::



* Difference between an array and a scalar, when src2 is constructed from Scalar or has the same number of elements as src1.channels():

.. math::

\texttt{dst}(I) =  \texttt{saturate} ( \texttt{src1}(I) -  \texttt{src2} ) \quad \texttt{if mask}(I) \ne0


* Difference between a scalar and an array, when src1 is constructed from Scalar or has the same number of elements as src2.channels():

.. math::

\texttt{dst}(I) =  \texttt{saturate} ( \texttt{src1} -  \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0


* The reverse difference between a scalar and an array in the case of SubRS:

.. math::

\texttt{dst}(I) =  \texttt{saturate} ( \texttt{src2} -  \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0


where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.

The first function in the list above can be replaced with matrix expressions: ::

dst = src1 - src2;
dst -= src1; // equivalent to subtract(dst, src1, dst);


The input arrays and the output array can all have the same or different depths. For example, you can subtract to 8-bit unsigned arrays and store the difference in a 16-bit signed array. Depth of the output array is determined by dtype parameter. In the second and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this case the output array will have the same depth as the input array, be it src1, src2 or both.

.. note:: Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

.. seealso::

:ocv:func:add,
:ocv:func:addWeighted,
:ocv:func:scaleAdd,
:ocv:func:Mat::convertTo,
:ref:MatrixExpressions


## SVD

.. ocv:class:: SVD

Class for computing Singular Value Decomposition of a floating-point matrix. The Singular Value Decomposition is used to solve least-square problems, under-determined linear systems, invert matrices, compute condition numbers, and so on.

For a faster operation, you can pass flags=SVD::MODIFY_A|... to modify the decomposed matrix when it is not necessary to preserve it. If you want to compute a condition number of a matrix or an absolute value of its determinant, you do not need u and vt . You can pass flags=SVD::NO_UV|... . Another flag FULL_UV indicates that full-size u and vt must be computed, which is not necessary most of the time.

.. seealso::

:ocv:func:invert,
:ocv:func:solve,
:ocv:func:eigen,
:ocv:func:determinant


## SVD::SVD

The constructors.

.. ocv:function:: SVD::SVD()

.. ocv:function:: SVD::SVD( InputArray src, int flags=0 )

:param src: decomposed matrix.

:param flags: operation flags.

* **SVD::MODIFY_A** use the algorithm to modify the decomposed matrix; it can save space and speed up processing.

* **SVD::NO_UV** indicates that only a vector of singular values w is to be processed, while u and vt will be set to empty matrices.

* **SVD::FULL_UV** when the matrix is not square, by default the algorithm produces u and vt matrices of sufficiently large size for the further A reconstruction; if, however,   FULL_UV flag is specified, u and vt will be full-size square orthogonal matrices.


The first constructor initializes an empty SVD structure. The second constructor initializes an empty SVD structure and then calls :ocv:funcx:SVD::operator() .

## SVD::operator ()

Performs SVD of a matrix.

.. ocv:function:: SVD& SVD::operator()( InputArray src, int flags=0 )

:param src: decomposed matrix.

:param flags: operation flags.

* **SVD::MODIFY_A** use the algorithm to modify the decomposed matrix; it can save space and speed up processing.

* **SVD::NO_UV** use only singular values; the algorithm does not compute u and vt matrices.

* **SVD::FULL_UV** when the matrix is not square, by default the algorithm produces u and vt matrices of sufficiently large size for the further A reconstruction; if, however, the FULL_UV  flag is specified, u  and  vt  are full-size square orthogonal matrices.


The operator performs the singular value decomposition of the supplied matrix. The u,vt , and the vector of singular values w are stored in the structure. The same SVD structure can be reused many times with different matrices. Each time, if needed, the previous u,vt , and w are reclaimed and the new matrices are created, which is all handled by :ocv:func:Mat::create .

## SVD::compute

Performs SVD of a matrix

.. ocv:function:: static void SVD::compute( InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags=0 )

.. ocv:function:: static void SVD::compute( InputArray src, OutputArray w, int flags=0 )

.. ocv:pyfunction:: cv2.SVDecomp(src[, w[, u[, vt[, flags]]]]) -> w, u, vt

.. ocv:cfunction:: void cvSVD( CvArr A, CvArr W, CvArr U=NULL, CvArr V=NULL, int flags=0 )

.. ocv:pyoldfunction:: cv.SVD(A, W, U=None, V=None, flags=0) -> None

:param src: decomposed matrix

:param w: calculated singular values

:param u: calculated left singular vectors

:param V: calculated right singular vectors

:param vt: transposed matrix of right singular values

:param flags: operation flags - see :ocv:func:SVD::SVD.


The methods/functions perform SVD of matrix. Unlike SVD::SVD constructor and SVD::operator(), they store the results to the user-provided matrices. ::

Mat A, w, u, vt;
SVD::compute(A, w, u, vt);


## SVD::solveZ

Solves an under-determined singular linear system.

.. ocv:function:: static void SVD::solveZ( InputArray src, OutputArray dst )

:param src: left-hand-side matrix.

:param dst: found solution.


The method finds a unit-length solution x of a singular linear system A*x = 0. Depending on the rank of A, there can be no solutions, a single solution or an infinite number of solutions. In general, the algorithm solves the following problem:

.. math::

dst =  \arg \min _{x:  \| x \| =1}  \| src  \cdot x  \|


## SVD::backSubst

Performs a singular value back substitution.

.. ocv:function:: void SVD::backSubst( InputArray rhs, OutputArray dst ) const

.. ocv:function:: static void SVD::backSubst( InputArray w, InputArray u, InputArray vt, InputArray rhs, OutputArray dst )

.. ocv:pyfunction:: cv2.SVBackSubst(w, u, vt, rhs[, dst]) -> dst

.. ocv:cfunction:: void cvSVBkSb( const CvArr W, const CvArr U, const CvArr V, const CvArr B, CvArr* X, int flags )

.. ocv:pyoldfunction:: cv.SVBkSb(W, U, V, B, X, flags) -> None

:param w: singular values

:param u: left singular vectors

:param V: right singular vectors

:param vt: transposed matrix of right singular vectors.

:param rhs: right-hand side of a linear system (u*w*v')*dst = rhs to be solved, where A has been previously decomposed.

:param dst: found solution of the system.


The method calculates a back substitution for the specified right-hand side:

.. math::

\texttt{x} =  \texttt{vt} ^T  \cdot diag( \texttt{w} )^{-1}  \cdot \texttt{u} ^T  \cdot \texttt{rhs} \sim \texttt{A} ^{-1}  \cdot \texttt{rhs}


Using this technique you can either get a very accurate solution of the convenient linear system, or the best (in the least-squares terms) pseudo-solution of an overdetermined linear system.

.. note:: Explicit SVD with the further back substitution only makes sense if you need to solve many linear systems with the same left-hand side (for example, src ). If all you need is to solve a single system (possibly with multiple rhs immediately available), simply call :ocv:func:solve add pass DECOMP_SVD there. It does absolutely the same thing.

## sum

Calculates the sum of array elements.

.. ocv:function:: Scalar sum( InputArray src )

.. ocv:pyfunction:: cv2.sumElems(src) -> retval

.. ocv:cfunction:: CvScalar cvSum(const CvArr* arr)

.. ocv:pyoldfunction:: cv.Sum(arr) -> scalar

:param arr: input array that must have from 1 to 4 channels.


The functions sum calculate and return the sum of array elements, independently for each channel.

.. seealso::

:ocv:func:countNonZero,
:ocv:func:mean,
:ocv:func:meanStdDev,
:ocv:func:norm,
:ocv:func:minMaxLoc,
:ocv:func:reduce


## theRNG

Returns the default random number generator.

.. ocv:function:: RNG& theRNG()

The function theRNG returns the default random number generator. For each thread, there is a separate random number generator, so you can use the function safely in multi-thread environments. If you just need to get a single random number using this generator or initialize an array, you can use :ocv:func:randu or :ocv:func:randn instead. But if you are going to generate many random numbers inside a loop, it is much faster to use this function to retrieve the generator and then use RNG::operator _Tp() .

.. seealso::

:ocv:class:RNG,
:ocv:func:randu,
:ocv:func:randn


## trace

Returns the trace of a matrix.

.. ocv:function:: Scalar trace( InputArray mtx )

.. ocv:pyfunction:: cv2.trace(mtx) -> retval

.. ocv:cfunction:: CvScalar cvTrace(const CvArr* mat)

.. ocv:pyoldfunction:: cv.Trace(mat) -> scalar

:param mat: input matrix.


The function trace returns the sum of the diagonal elements of the matrix mtx .

.. math::

\mathrm{tr} ( \texttt{mtx} ) =  \sum _i  \texttt{mtx} (i,i)


## transform

Performs the matrix transformation of every array element.

.. ocv:function:: void transform( InputArray src, OutputArray dst, InputArray m )

.. ocv:pyfunction:: cv2.transform(src, m[, dst]) -> dst

.. ocv:cfunction:: void cvTransform( const CvArr src, CvArr dst, const CvMat transmat, const CvMat shiftvec=NULL )

.. ocv:pyoldfunction:: cv.Transform(src, dst, transmat, shiftvec=None)-> None

:param src: input array that must have as many channels (1 to 4) as m.cols or m.cols-1.

:param dst: output array of the same size and depth as src; it has as many channels as m.rows.

:param m: transformation 2x2 or 2x3 floating-point matrix.

:param shiftvec: optional translation vector (when m is 2x2)


The function transform performs the matrix transformation of every element of the array src and stores the results in dst :

.. math::

\texttt{dst} (I) =  \texttt{m} \cdot \texttt{src} (I)


(when m.cols=src.channels() ), or

.. math::

\texttt{dst} (I) =  \texttt{m} \cdot [ \texttt{src} (I); 1]


(when m.cols=src.channels()+1 )

Every element of the N -channel array src is interpreted as N -element vector that is transformed using the M x N or M x (N+1) matrix m to M-element vector - the corresponding element of the output array dst .

The function may be used for geometrical transformation of N -dimensional points, arbitrary linear color space transformation (such as various kinds of RGB to YUV transforms), shuffling the image channels, and so forth.

.. seealso::

:ocv:func:perspectiveTransform,
:ocv:func:getAffineTransform,
:ocv:func:estimateRigidTransform,
:ocv:func:warpAffine,
:ocv:func:warpPerspective


## transpose

Transposes a matrix.

.. ocv:function:: void transpose(InputArray src, OutputArray dst)

.. ocv:pyfunction:: cv2.transpose(src[, dst]) -> dst

.. ocv:cfunction:: void cvTranspose(const CvArr src, CvArr dst) .. ocv:pyoldfunction:: cv.Transpose(src, dst)-> None

:param src: input array.

:param dst: output array of the same type as src.


The function :ocv:func:transpose transposes the matrix src :

.. math::

\texttt{dst} (i,j) =  \texttt{src} (j,i)


.. note:: No complex conjugation is done in case of a complex matrix. It it should be done separately if needed.