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# scipy.signal.convolve2d

scipy.signal.convolve2d(in1, in2, mode='full', boundary='fill', fillvalue=0)

  Convolve two 2-dimensional arrays.

  Convolve in1 and in2 with output size determined by mode, and boundary conditions determined by boundary and fillvalue.

  Parameters:
    in1 array_like

      First input.

    in2 array_like

      Second input. Should have the same number of dimensions as in1.

    mode str {‘full’, ‘valid’, ‘same’}, optional

      A string indicating the size of the output:

      `full`

        The output is the full discrete linear convolution of the inputs. (Default)

      `valid`

        The output consists only of those elements that do not rely on the zero-padding. In ‘valid’ mode, either in1 or in2 must be at least as large as the other in every dimension.

      `same`

        The output is the same size as in1, centered with respect to the ‘full’ output.

    boundary str {‘fill’, ‘wrap’, ‘symm’}, optional

      A flag indicating how to handle boundaries:

      `fill`

        pad input arrays with fillvalue. (default)

      `wrap`

        circular boundary conditions.

      `symm`

        symmetrical boundary conditions.

    fillvalue scalar, optional

      Value to fill pad input arrays with. Default is 0.

  Returns:
    out ndarray

      A 2-dimensional array containing a subset of the discrete linear convolution of in1 with in2.

  Examples

  Compute the gradient of an image by 2D convolution with a complex Scharr operator. (Horizontal operator is real, vertical is imaginary.) Use symmetric boundary condition to avoid creating edges at the image boundaries.

      >>> import numpy as np
      >>> from scipy import signal
      >>> from scipy import datasets
      >>> ascent = datasets.ascent()
      >>> scharr = np.array([[ -3-3j, 0-10j,  +3 -3j],
      ...                    [-10+0j, 0+ 0j, +10 +0j],
      ...                    [ -3+3j, 0+10j,  +3 +3j]]) # Gx + j*Gy
      >>> grad = signal.convolve2d(ascent, scharr, boundary='symm', mode='same')

      >>> import matplotlib.pyplot as plt
      >>> fig, (ax_orig, ax_mag, ax_ang) = plt.subplots(3, 1, figsize=(6, 15))
      >>> ax_orig.imshow(ascent, cmap='gray')
      >>> ax_orig.set_title('Original')
      >>> ax_orig.set_axis_off()
      >>> ax_mag.imshow(np.absolute(grad), cmap='gray')
      >>> ax_mag.set_title('Gradient magnitude')
      >>> ax_mag.set_axis_off()
      >>> ax_ang.imshow(np.angle(grad), cmap='hsv') # hsv is cyclic, like angles
      >>> ax_ang.set_title('Gradient orientation')
      >>> ax_ang.set_axis_off()
      >>> fig.show()