Esempio n. 1
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    def __train__(self, data, labels):
        l = labels.reshape((-1,1))
        self.__trainingData__ = data
        self.__trainingLabels__ = l
        N = len(l)
        H = zeros((N,N))
        for i in range(N):
            for j in range(N):
                H[i,j] = self.__trainingLabels__[i]*self.__trainingLabels__[j]*self.__kernelFunc__(self.__trainingData__[i],self.__trainingData__[j])
        f = -1.0*ones(labels.shape)
        lb = zeros(labels.shape)
        ub = self.C * ones(labels.shape)
        Aeq = labels
        beq = 0.0
        suppressOut = True
        if suppressOut:
            devnull = open('/dev/null', 'w')
            oldstdout_fno = os.dup(sys.stdout.fileno())
            os.dup2(devnull.fileno(), 1)
        p = QP(matrix(H),f.tolist(),lb=lb.tolist(),ub=ub.tolist(),Aeq=Aeq.tolist(),beq=beq)
        r = p.solve('cvxopt_qp')
        if suppressOut:
            os.dup2(oldstdout_fno, 1)
        lim = 1e-4
        r.xf[where(abs(r.xf)<lim)] = 0
        self.__lambdas__ = r.xf
        nonzeroindexes = where(r.xf>lim)[0]
#        l1 = nonzeroindexes[0]
#        self.w0 = 1.0/labels[l1]-dot(self.w,data[l1])
        self.numSupportVectors = len(nonzeroindexes)
def triu(m, k=0):
    """
    Upper triangle of an array.

    Return a copy of a matrix with the elements below the `k`-th diagonal
    zeroed.

    Please refer to the documentation for `tril` for further details.

    See Also
    --------
    tril : lower triangle of an array

    Examples
    --------
    >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 1,  2,  3],
           [ 4,  5,  6],
           [ 0,  8,  9],
           [ 0,  0, 12]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k-1, dtype=bool)

    return where(mask, zeros(1, m.dtype), m)
Esempio n. 3
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def calcN(classKernels, trainLabels):
    N = zeros((len(trainLabels), len(trainLabels)))
    for i, l in enumerate(unique(trainLabels)):
        numExamplesWithLabel = len(where(trainLabels == l)[0])
        Idiff = identity(numExamplesWithLabel, Float64) - (1.0 / numExamplesWithLabel) * ones(numExamplesWithLabel, Float64)
        firstDot = dot(classKernels[i], Idiff)
        labelTerm = dot(firstDot, transpose(classKernels[i]))
        N += labelTerm
    N = nan_to_num(N)
    #make N more numerically stable
    #if I had more time, I would train this parameter, but I don't
    additionToN = ((mean(diag(N)) + 1) / 100.0) * identity(N.shape[0], Float64) 
    N += additionToN
            
    #make sure N is invertable
    for i in range(1000):
        try:
            inv(N)
        except LinAlgError:
            #doing this to make sure the maxtrix is invertable
            #large value supported by section titled
            #"numerical issues and regularization" in the paper
            N += additionToN

    return N
Esempio n. 4
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def triu(m, k=0):
    """
    Upper triangle of an array.

    Return a copy of a matrix with the elements below the `k`-th diagonal
    zeroed.

    Please refer to the documentation for `tril` for further details.

    See Also
    --------
    tril : lower triangle of an array

    Examples
    --------
    >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 1,  2,  3],
           [ 4,  5,  6],
           [ 0,  8,  9],
           [ 0,  0, 12]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k - 1, dtype=bool)

    return where(mask, zeros(1, m.dtype), m)
Esempio n. 5
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 def train(self, data, labels):
     l = labels.reshape((-1,1))
     xy = data * l
     H = dot(xy,transpose(xy))
     f = -1.0*ones(labels.shape)
     lb = zeros(labels.shape)
     ub = self.C * ones(labels.shape)
     Aeq = labels
     beq = 0.0
     p = QP(matrix(H),f.tolist(),lb=lb.tolist(),ub=ub.tolist(),Aeq=Aeq.tolist(),beq=beq)
     r = p.solve('cvxopt_qp')
     r.xf[where(r.xf<1e-3)] = 0
     self.w = dot(r.xf*labels,data)
     nonzeroindexes = where(r.xf>1e-4)[0]
     l1 = nonzeroindexes[0]
     self.w0 = 1.0/labels[l1]-dot(self.w,data[l1])
     self.numSupportVectors = len(nonzeroindexes)
Esempio n. 6
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def bartlett(M):
    """bartlett(M) returns the M-point Bartlett window.
    """
    if M < 1:
        return array([])
    if M == 1:
        return ones(1, float)
    n = arange(0,M)
    return where(less_equal(n,(M-1)/2.0),2.0*n/(M-1),2.0-2.0*n/(M-1))
Esempio n. 7
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def tril(m, k=0):
    """
    Lower triangle of an array.

    Return a copy of an array with elements above the `k`-th diagonal zeroed.
    For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two
    axes.

    Parameters
    ----------
    m : array_like, shape (..., M, N)
        Input array.
    k : int, optional
        Diagonal above which to zero elements.  `k = 0` (the default) is the
        main diagonal, `k < 0` is below it and `k > 0` is above.

    Returns
    -------
    tril : ndarray, shape (..., M, N)
        Lower triangle of `m`, of same shape and data-type as `m`.

    See Also
    --------
    triu : same thing, only for the upper triangle

    Examples
    --------
    >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 0,  0,  0],
           [ 4,  0,  0],
           [ 7,  8,  0],
           [10, 11, 12]])

    >>> np.tril(np.arange(3*4*5).reshape(3, 4, 5))
    array([[[ 0,  0,  0,  0,  0],
            [ 5,  6,  0,  0,  0],
            [10, 11, 12,  0,  0],
            [15, 16, 17, 18,  0]],
           [[20,  0,  0,  0,  0],
            [25, 26,  0,  0,  0],
            [30, 31, 32,  0,  0],
            [35, 36, 37, 38,  0]],
           [[40,  0,  0,  0,  0],
            [45, 46,  0,  0,  0],
            [50, 51, 52,  0,  0],
            [55, 56, 57, 58,  0]]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k, dtype=bool)

    return where(mask, m, zeros(1, m.dtype))
Esempio n. 8
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 def __train__(self, data, labels):
     l = labels.reshape((-1,1))
     xy = data * l
     H = dot(xy,transpose(xy))
     f = -1.0*ones(labels.shape)
     lb = zeros(labels.shape)
     ub = self.C * ones(labels.shape)
     Aeq = labels
     beq = 0.0
     devnull = open('/dev/null', 'w')
     oldstdout_fno = os.dup(sys.stdout.fileno())
     os.dup2(devnull.fileno(), 1)
     p = QP(matrix(H),f.tolist(),lb=lb.tolist(),ub=ub.tolist(),Aeq=Aeq.tolist(),beq=beq)
     r = p.solve('cvxopt_qp')
     os.dup2(oldstdout_fno, 1)
     lim = 1e-4
     r.xf[where(r.xf<lim)] = 0
     self.w = dot(r.xf*labels,data)
     nonzeroindexes = where(r.xf>lim)[0]
     l1 = nonzeroindexes[0]
     self.w0 = 1.0/labels[l1]-dot(self.w,data[l1])
     self.numSupportVectors = len(nonzeroindexes)
Esempio n. 9
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def getClassKernels(fullKernelMatrix, trainLabels):
    #create a matrix where rows correspond to all examples
    #and columns correspond to examples of a specific class
    #so if l is the total number of examples, and lj is the number of examples in class j
    #then we're creating an l x lj matrix
    uniqueLabels = unique(trainLabels)
    ret = []
    for l in uniqueLabels:
        labelIndexes = where(trainLabels == l)[0]
        k = zeros((len(fullKernelMatrix), len(labelIndexes)))
        for r in range(len(k)):
            for c in range(len(k[r])):
                k[r][c] = fullKernelMatrix[r][labelIndexes[c]]
        ret.append(k)
    return ret        
Esempio n. 10
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def triu(m, k=0):
    """
    Upper triangle of an array.

    Return a copy of an array with the elements below the `k`-th diagonal
    zeroed. For arrays with ``ndim`` exceeding 2, `triu` will apply to the final
    two axes.

    Please refer to the documentation for `tril` for further details.

    See Also
    --------
    tril : lower triangle of an array

    Examples
    --------
    >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 1,  2,  3],
           [ 4,  5,  6],
           [ 0,  8,  9],
           [ 0,  0, 12]])

    >>> np.triu(np.arange(3*4*5).reshape(3, 4, 5))
    array([[[ 0,  1,  2,  3,  4],
            [ 0,  6,  7,  8,  9],
            [ 0,  0, 12, 13, 14],
            [ 0,  0,  0, 18, 19]],
           [[20, 21, 22, 23, 24],
            [ 0, 26, 27, 28, 29],
            [ 0,  0, 32, 33, 34],
            [ 0,  0,  0, 38, 39]],
           [[40, 41, 42, 43, 44],
            [ 0, 46, 47, 48, 49],
            [ 0,  0, 52, 53, 54],
            [ 0,  0,  0, 58, 59]]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k-1, dtype=bool)

    return where(mask, zeros(1, m.dtype), m)
Esempio n. 11
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def fix(x, y=None):
    """
    Round to nearest integer towards zero.

    Round an array of floats element-wise to nearest integer towards zero.
    The rounded values are returned as floats.

    Parameters
    ----------
    x : array_like
        An array of floats to be rounded
    y : ndarray, optional
        Output array

    Returns
    -------
    out : ndarray of floats
        The array of rounded numbers

    See Also
    --------
    trunc, floor, ceil
    around : Round to given number of decimals

    Examples
    --------
    >>> np.fix(3.14)
    3.0
    >>> np.fix(3)
    3.0
    >>> np.fix([2.1, 2.9, -2.1, -2.9])
    array([ 2.,  2., -2., -2.])

    """
    x = nx.asanyarray(x)
    y1 = nx.floor(x)
    y2 = nx.ceil(x)
    if y is None:
        y = nx.asanyarray(y1)
    y[...] = nx.where(x >= 0, y1, y2)
    return y
Esempio n. 12
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def fix(x, y=None):
    """
    Round to nearest integer towards zero.

    Round an array of floats element-wise to nearest integer towards zero.
    The rounded values are returned as floats.

    Parameters
    ----------
    x : array_like
        An array of floats to be rounded
    y : ndarray, optional
        Output array

    Returns
    -------
    out : ndarray of floats
        The array of rounded numbers

    See Also
    --------
    trunc, floor, ceil
    around : Round to given number of decimals

    Examples
    --------
    >>> np.fix(3.14)
    3.0
    >>> np.fix(3)
    3.0
    >>> np.fix([2.1, 2.9, -2.1, -2.9])
    array([ 2.,  2., -2., -2.])

    """
    x = nx.asanyarray(x)
    y1 = nx.floor(x)
    y2 = nx.ceil(x)
    if y is None:
        y = nx.asanyarray(y1)
    y[...] = nx.where(x >= 0, y1, y2)
    return y
Esempio n. 13
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def tril(m, k=0):
    """
    Lower triangle of an array.

    Return a copy of an array with elements above the `k`-th diagonal zeroed.

    Parameters
    ----------
    m : array_like, shape (M, N)
        Input array.
    k : int, optional
        Diagonal above which to zero elements.  `k = 0` (the default) is the
        main diagonal, `k < 0` is below it and `k > 0` is above.

    Returns
    -------
    tril : ndarray, shape (M, N)
        Lower triangle of `m`, of same shape and data-type as `m`.

    See Also
    --------
    triu : same thing, only for the upper triangle

    Examples
    --------
    >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 0,  0,  0],
           [ 4,  0,  0],
           [ 7,  8,  0],
           [10, 11, 12]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k, dtype=bool)

    return where(mask, m, zeros(1, m.dtype))
Esempio n. 14
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def tril(m, k=0):
    """
    Lower triangle of an array.

    Return a copy of an array with elements above the `k`-th diagonal zeroed.

    Parameters
    ----------
    m : array_like, shape (M, N)
        Input array.
    k : int, optional
        Diagonal above which to zero elements.  `k = 0` (the default) is the
        main diagonal, `k < 0` is below it and `k > 0` is above.

    Returns
    -------
    tril : ndarray, shape (M, N)
        Lower triangle of `m`, of same shape and data-type as `m`.

    See Also
    --------
    triu : same thing, only for the upper triangle

    Examples
    --------
    >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 0,  0,  0],
           [ 4,  0,  0],
           [ 7,  8,  0],
           [10, 11, 12]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k, dtype=bool)

    return where(mask, m, zeros(1, m.dtype))
Esempio n. 15
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def sinhc(x):
    x = np.asanyarray(x)
    y = where(x == 0, 1.0e-20, x)
    return np.sinh(y)/y
Esempio n. 16
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def mask_indices(n, mask_func, k=0):
    """
    Return the indices to access (n, n) arrays, given a masking function.

    Assume `mask_func` is a function that, for a square array a of size
    ``(n, n)`` with a possible offset argument `k`, when called as
    ``mask_func(a, k)`` returns a new array with zeros in certain locations
    (functions like `triu` or `tril` do precisely this). Then this function
    returns the indices where the non-zero values would be located.

    Parameters
    ----------
    n : int
        The returned indices will be valid to access arrays of shape (n, n).
    mask_func : callable
        A function whose call signature is similar to that of `triu`, `tril`.
        That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`.
        `k` is an optional argument to the function.
    k : scalar
        An optional argument which is passed through to `mask_func`. Functions
        like `triu`, `tril` take a second argument that is interpreted as an
        offset.

    Returns
    -------
    indices : tuple of arrays.
        The `n` arrays of indices corresponding to the locations where
        ``mask_func(np.ones((n, n)), k)`` is True.

    See Also
    --------
    triu, tril, triu_indices, tril_indices

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    These are the indices that would allow you to access the upper triangular
    part of any 3x3 array:

    >>> iu = np.mask_indices(3, np.triu)

    For example, if `a` is a 3x3 array:

    >>> a = np.arange(9).reshape(3, 3)
    >>> a
    array([[0, 1, 2],
           [3, 4, 5],
           [6, 7, 8]])
    >>> a[iu]
    array([0, 1, 2, 4, 5, 8])

    An offset can be passed also to the masking function.  This gets us the
    indices starting on the first diagonal right of the main one:

    >>> iu1 = np.mask_indices(3, np.triu, 1)

    with which we now extract only three elements:

    >>> a[iu1]
    array([1, 2, 5])

    """
    m = ones((n,n), int)
    a = mask_func(m, k)
    return where(a != 0)
Esempio n. 17
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def triu_indices(n, k=0, m=None):
    """
    Return the indices for the upper-triangle of an (n, m) array.

    Parameters
    ----------
    n : int
        The size of the arrays for which the returned indices will
        be valid.
    k : int, optional
        Diagonal offset (see `triu` for details).
    m : int, optional
        .. versionadded:: 1.9.0

        The column dimension of the arrays for which the returned
        arrays will be valid.
        By default `m` is taken equal to `n`.


    Returns
    -------
    inds : tuple, shape(2) of ndarrays, shape(`n`)
        The indices for the triangle. The returned tuple contains two arrays,
        each with the indices along one dimension of the array.  Can be used
        to slice a ndarray of shape(`n`, `n`).

    See also
    --------
    tril_indices : similar function, for lower-triangular.
    mask_indices : generic function accepting an arbitrary mask function.
    triu, tril

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    Compute two different sets of indices to access 4x4 arrays, one for the
    upper triangular part starting at the main diagonal, and one starting two
    diagonals further right:

    >>> iu1 = np.triu_indices(4)
    >>> iu2 = np.triu_indices(4, 2)

    Here is how they can be used with a sample array:

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Both for indexing:

    >>> a[iu1]
    array([ 0,  1,  2,  3,  5,  6,  7, 10, 11, 15])

    And for assigning values:

    >>> a[iu1] = -1
    >>> a
    array([[-1, -1, -1, -1],
           [ 4, -1, -1, -1],
           [ 8,  9, -1, -1],
           [12, 13, 14, -1]])

    These cover only a small part of the whole array (two diagonals right
    of the main one):

    >>> a[iu2] = -10
    >>> a
    array([[ -1,  -1, -10, -10],
           [  4,  -1,  -1, -10],
           [  8,   9,  -1,  -1],
           [ 12,  13,  14,  -1]])

    """
    return where(~tri(n, m, k=k - 1, dtype=bool))
Esempio n. 18
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def sinhc(x):
    x = np.asanyarray(x)
    y = where(x == 0, 1.0e-20, x)
    return np.sinh(y)/y
Esempio n. 19
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def triu_indices(n, k=0, m=None):
    """
    Return the indices for the upper-triangle of an (n, m) array.

    Parameters
    ----------
    n : int
        The size of the arrays for which the returned indices will
        be valid.
    k : int, optional
        Diagonal offset (see `triu` for details).
    m : int, optional
        .. versionadded:: 1.9.0

        The column dimension of the arrays for which the returned
        arrays will be valid.
        By default `m` is taken equal to `n`.


    Returns
    -------
    inds : tuple, shape(2) of ndarrays, shape(`n`)
        The indices for the triangle. The returned tuple contains two arrays,
        each with the indices along one dimension of the array.  Can be used
        to slice a ndarray of shape(`n`, `n`).

    See also
    --------
    tril_indices : similar function, for lower-triangular.
    mask_indices : generic function accepting an arbitrary mask function.
    triu, tril

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    Compute two different sets of indices to access 4x4 arrays, one for the
    upper triangular part starting at the main diagonal, and one starting two
    diagonals further right:

    >>> iu1 = np.triu_indices(4)
    >>> iu2 = np.triu_indices(4, 2)

    Here is how they can be used with a sample array:

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Both for indexing:

    >>> a[iu1]
    array([ 0,  1,  2,  3,  5,  6,  7, 10, 11, 15])

    And for assigning values:

    >>> a[iu1] = -1
    >>> a
    array([[-1, -1, -1, -1],
           [ 4, -1, -1, -1],
           [ 8,  9, -1, -1],
           [12, 13, 14, -1]])

    These cover only a small part of the whole array (two diagonals right
    of the main one):

    >>> a[iu2] = -10
    >>> a
    array([[ -1,  -1, -10, -10],
           [  4,  -1,  -1, -10],
           [  8,   9,  -1,  -1],
           [ 12,  13,  14,  -1]])

    """
    return where(~tri(n, m, k=k-1, dtype=bool))
def sinc(x):
    """sinc(x) returns sin(pi*x)/(pi*x) at all points of array x.
    """
    y = pi* where(x == 0, 1.0e-20, x)
    return sin(y)/y
Esempio n. 21
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def histogramdd(sample, bins=10, range=None, normed=False, weights=None):
    """histogramdd(sample, bins=10, range=None, normed=False, weights=None)

    Return the N-dimensional histogram of the sample.

    Parameters:

        sample : sequence or array
            A sequence containing N arrays or an NxM array. Input data.

        bins : sequence or scalar
            A sequence of edge arrays, a sequence of bin counts, or a scalar
            which is the bin count for all dimensions. Default is 10.

        range : sequence
            A sequence of lower and upper bin edges. Default is [min, max].

        normed : boolean
            If False, return the number of samples in each bin, if True,
            returns the density.

        weights : array
            Array of weights.  The weights are normed only if normed is True.
            Should the sum of the weights not equal N, the total bin count will
            not be equal to the number of samples.

    Returns:

        hist : array
            Histogram array.

        edges : list
            List of arrays defining the lower bin edges.

    SeeAlso:

        histogram

    Example

        >>> x = random.randn(100,3)
        >>> hist3d, edges = histogramdd(x, bins = (5, 6, 7))

    """

    try:
        # Sample is an ND-array.
        N, D = sample.shape
    except (AttributeError, ValueError):
        # Sample is a sequence of 1D arrays.
        sample = atleast_2d(sample).T
        N, D = sample.shape

    nbin = empty(D, int)
    edges = D * [None]
    dedges = D * [None]
    if weights is not None:
        weights = asarray(weights)

    try:
        M = len(bins)
        if M != D:
            raise AttributeError, 'The dimension of bins must be a equal to the dimension of the sample x.'
    except TypeError:
        bins = D * [bins]

    # Select range for each dimension
    # Used only if number of bins is given.
    if range is None:
        smin = atleast_1d(array(sample.min(0), float))
        smax = atleast_1d(array(sample.max(0), float))
    else:
        smin = zeros(D)
        smax = zeros(D)
        for i in arange(D):
            smin[i], smax[i] = range[i]

    # Make sure the bins have a finite width.
    for i in arange(len(smin)):
        if smin[i] == smax[i]:
            smin[i] = smin[i] - .5
            smax[i] = smax[i] + .5

    # Create edge arrays
    for i in arange(D):
        if isscalar(bins[i]):
            nbin[i] = bins[i] + 2  # +2 for outlier bins
            edges[i] = linspace(smin[i], smax[i], nbin[i] - 1)
        else:
            edges[i] = asarray(bins[i], float)
            nbin[i] = len(edges[i]) + 1  # +1 for outlier bins
        dedges[i] = diff(edges[i])

    nbin = asarray(nbin)

    # Compute the bin number each sample falls into.
    Ncount = {}
    for i in arange(D):
        Ncount[i] = digitize(sample[:, i], edges[i])

    # Using digitize, values that fall on an edge are put in the right bin.
    # For the rightmost bin, we want values equal to the right
    # edge to be counted in the last bin, and not as an outlier.
    outliers = zeros(N, int)
    for i in arange(D):
        # Rounding precision
        decimal = int(-log10(dedges[i].min())) + 6
        # Find which points are on the rightmost edge.
        on_edge = where(
            around(sample[:, i], decimal) == around(edges[i][-1], decimal))[0]
        # Shift these points one bin to the left.
        Ncount[i][on_edge] -= 1

    # Flattened histogram matrix (1D)
    hist = zeros(nbin.prod(), float)

    # Compute the sample indices in the flattened histogram matrix.
    ni = nbin.argsort()
    shape = []
    xy = zeros(N, int)
    for i in arange(0, D - 1):
        xy += Ncount[ni[i]] * nbin[ni[i + 1:]].prod()
    xy += Ncount[ni[-1]]

    # Compute the number of repetitions in xy and assign it to the flattened histmat.
    if len(xy) == 0:
        return zeros(nbin - 2, int), edges

    flatcount = bincount(xy, weights)
    a = arange(len(flatcount))
    hist[a] = flatcount

    # Shape into a proper matrix
    hist = hist.reshape(sort(nbin))
    for i in arange(nbin.size):
        j = ni[i]
        hist = hist.swapaxes(i, j)
        ni[i], ni[j] = ni[j], ni[i]

    # Remove outliers (indices 0 and -1 for each dimension).
    core = D * [slice(1, -1)]
    hist = hist[core]

    # Normalize if normed is True
    if normed:
        s = hist.sum()
        for i in arange(D):
            shape = ones(D, int)
            shape[i] = nbin[i] - 2
            hist = hist / dedges[i].reshape(shape)
        hist /= s

    return hist, edges
Esempio n. 22
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def sinc(x):
    """sinc(x) returns sin(pi*x)/(pi*x) at all points of array x.
    """
    y = pi * where(x == 0, 1.0e-20, x)
    return sin(y) / y
Esempio n. 23
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def mask_indices(n,mask_func,k=0):
    """Return the indices to access (n,n) arrays, given a masking function.

    Assume mask_func() is a function that, for a square array a of size (n,n)
    with a possible offset argument k, when called as mask_func(a,k) returns a
    new array with zeros in certain locations (functions like triu() or tril()
    do precisely this).  Then this function returns the indices where the
    non-zero values would be located.

    Parameters
    ----------
    n : int
      The returned indices will be valid to access arrays of shape (n,n).

    mask_func : callable
      A function whose api is similar to that of numpy.tri{u,l}.  That is,
      mask_func(x,k) returns a boolean array, shaped like x.  k is an optional
      argument to the function.

    k : scalar
      An optional argument which is passed through to mask_func().  Functions
      like tri{u,l} take a second argument that is interpreted as an offset.

    Returns
    -------
    indices : an n-tuple of index arrays.
      The indices corresponding to the locations where mask_func(ones((n,n)),k)
      is True.

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    These are the indices that would allow you to access the upper triangular
    part of any 3x3 array:
    >>> iu = mask_indices(3,np.triu)

    For example, if `a` is a 3x3 array:
    >>> a = np.arange(9).reshape(3,3)
    >>> a
    array([[0, 1, 2],
           [3, 4, 5],
           [6, 7, 8]])

    Then:
    >>> a[iu]
    array([0, 1, 2, 4, 5, 8])

    An offset can be passed also to the masking function.  This gets us the
    indices starting on the first diagonal right of the main one:
    >>> iu1 = mask_indices(3,np.triu,1)

    with which we now extract only three elements:
    >>> a[iu1]
    array([1, 2, 5])
    """ 
    m = ones((n,n),int)
    a = mask_func(m,k)
    return where(a != 0)
def histogramdd(sample, bins=10, range=None, normed=False, weights=None):
    """histogramdd(sample, bins=10, range=None, normed=False, weights=None)

    Return the N-dimensional histogram of the sample.

    Parameters:

        sample : sequence or array
            A sequence containing N arrays or an NxM array. Input data.

        bins : sequence or scalar
            A sequence of edge arrays, a sequence of bin counts, or a scalar
            which is the bin count for all dimensions. Default is 10.

        range : sequence
            A sequence of lower and upper bin edges. Default is [min, max].

        normed : boolean
            If False, return the number of samples in each bin, if True,
            returns the density.

        weights : array
            Array of weights.  The weights are normed only if normed is True.
            Should the sum of the weights not equal N, the total bin count will
            not be equal to the number of samples.

    Returns:

        hist : array
            Histogram array.

        edges : list
            List of arrays defining the lower bin edges.

    SeeAlso:

        histogram

    Example

        >>> x = random.randn(100,3)
        >>> hist3d, edges = histogramdd(x, bins = (5, 6, 7))

    """

    try:
        # Sample is an ND-array.
        N, D = sample.shape
    except (AttributeError, ValueError):
        # Sample is a sequence of 1D arrays.
        sample = atleast_2d(sample).T
        N, D = sample.shape

    nbin = empty(D, int)
    edges = D*[None]
    dedges = D*[None]
    if weights is not None:
        weights = asarray(weights)

    try:
        M = len(bins)
        if M != D:
            raise AttributeError, 'The dimension of bins must be a equal to the dimension of the sample x.'
    except TypeError:
        bins = D*[bins]

    # Select range for each dimension
    # Used only if number of bins is given.
    if range is None:
        smin = atleast_1d(array(sample.min(0), float))
        smax = atleast_1d(array(sample.max(0), float))
    else:
        smin = zeros(D)
        smax = zeros(D)
        for i in arange(D):
            smin[i], smax[i] = range[i]

    # Make sure the bins have a finite width.
    for i in arange(len(smin)):
        if smin[i] == smax[i]:
            smin[i] = smin[i] - .5
            smax[i] = smax[i] + .5

    # Create edge arrays
    for i in arange(D):
        if isscalar(bins[i]):
            nbin[i] = bins[i] + 2 # +2 for outlier bins
            edges[i] = linspace(smin[i], smax[i], nbin[i]-1)
        else:
            edges[i] = asarray(bins[i], float)
            nbin[i] = len(edges[i])+1  # +1 for outlier bins
        dedges[i] = diff(edges[i])

    nbin =  asarray(nbin)

    # Compute the bin number each sample falls into.
    Ncount = {}
    for i in arange(D):
        Ncount[i] = digitize(sample[:,i], edges[i])

    # Using digitize, values that fall on an edge are put in the right bin.
    # For the rightmost bin, we want values equal to the right
    # edge to be counted in the last bin, and not as an outlier.
    outliers = zeros(N, int)
    for i in arange(D):
        # Rounding precision
        decimal = int(-log10(dedges[i].min())) +6
        # Find which points are on the rightmost edge.
        on_edge = where(around(sample[:,i], decimal) == around(edges[i][-1], decimal))[0]
        # Shift these points one bin to the left.
        Ncount[i][on_edge] -= 1

    # Flattened histogram matrix (1D)
    hist = zeros(nbin.prod(), float)

    # Compute the sample indices in the flattened histogram matrix.
    ni = nbin.argsort()
    shape = []
    xy = zeros(N, int)
    for i in arange(0, D-1):
        xy += Ncount[ni[i]] * nbin[ni[i+1:]].prod()
    xy += Ncount[ni[-1]]

    # Compute the number of repetitions in xy and assign it to the flattened histmat.
    if len(xy) == 0:
        return zeros(nbin-2, int), edges

    flatcount = bincount(xy, weights)
    a = arange(len(flatcount))
    hist[a] = flatcount

    # Shape into a proper matrix
    hist = hist.reshape(sort(nbin))
    for i in arange(nbin.size):
        j = ni[i]
        hist = hist.swapaxes(i,j)
        ni[i],ni[j] = ni[j],ni[i]

    # Remove outliers (indices 0 and -1 for each dimension).
    core = D*[slice(1,-1)]
    hist = hist[core]

    # Normalize if normed is True
    if normed:
        s = hist.sum()
        for i in arange(D):
            shape = ones(D, int)
            shape[i] = nbin[i]-2
            hist = hist / dedges[i].reshape(shape)
        hist /= s

    return hist, edges
Esempio n. 25
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    def inv_by_gauss_elimination(mat):
        """Caculate inverse matrix by gauss elimination.

        Parameters
        ----------
        mat : ndarray
            matrix.

        Returns
        -------
        mat_inv : ndarray
            inverse matrix.
        mat_null : ndarray
            null space matrix.

        """
        n_row, n_col = mat.shape

        if n_row != n_col:
            raise ValueError("n_row and n_col are different.")

        data = GF2array(hstack([mat, eye(n_row)]))

        n_null_dim = 0
        mat_null = array([])

        # Row echelon form
        for idx_row_src in range(n_row - 1):
            idx_pivot_candidate = where(data[idx_row_src:,
                                             idx_row_src] == 1)[0]

            if len(idx_pivot_candidate) > 0:
                idx_pivot = idx_pivot_candidate[0] + idx_row_src
            else:
                n_null_dim += 1
                continue

            if idx_pivot != idx_row_src:
                tmp = data[idx_row_src, :].copy()
                data[idx_row_src, :] = data[idx_pivot, :]
                data[idx_pivot, :] = tmp

            for idx_row_dst in range(idx_row_src + 1, n_row):
                data[idx_row_dst, :] += (data[idx_row_src, :] *
                                         data[idx_row_dst, idx_row_src])

        if np.sum(data[-1, :n_col]) == 0:
            n_null_dim += 1

        # inverse matrix
        for idx_row_src in range(n_row - 1, 0, -1):
            for idx_row_dst in range(idx_row_src - 1, -1, -1):
                data[idx_row_dst, :] += (data[idx_row_src, :] *
                                         data[idx_row_dst, idx_row_src])

        # Find Null space
        if n_null_dim > 0:
            mat_diag = data[:, :n_col]
            mat_null = vstack([
                mat_diag[:n_row - n_null_dim, -n_null_dim:],
                GF2array(eye(n_null_dim))
            ])

        mat_inv = data[-n_row:, -n_col:]

        return mat_inv, mat_null