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scipy.linalg.

# svdvals

scipy.linalg.svdvals(a, overwrite_a=False, check_finite=True)

  Compute singular values of a matrix.

  Parameters:
    a(M, N) array_like

      Matrix to decompose.

    overwrite_a bool, optional

      Whether to overwrite a; may improve performance. Default is False.

    check_finite bool, optional

      Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

  Returns:
    s(min(M, N),) ndarray

      The singular values, sorted in decreasing order.

  Raises:
    LinAlgError

      If SVD computation does not converge.

  See also

  `svd`

    Compute the full singular value decomposition of a matrix.

  `diagsvd`

    Construct the Sigma matrix, given the vector s.

  Examples

      >>> import numpy as np
      >>> from scipy.linalg import svdvals
      >>> m = np.array([[1.0, 0.0],
      ...               [2.0, 3.0],
      ...               [1.0, 1.0],
      ...               [0.0, 2.0],
      ...               [1.0, 0.0]])
      >>> svdvals(m)
      array([ 4.28091555,  1.63516424])

  We can verify the maximum singular value of m by computing the maximum length of m.dot(u) over all the unit vectors u in the (x,y) plane. We approximate “all” the unit vectors with a large sample. Because of linearity, we only need the unit vectors with angles in [0, pi].

      >>> t = np.linspace(0, np.pi, 2000)
      >>> u = np.array([np.cos(t), np.sin(t)])
      >>> np.linalg.norm(m.dot(u), axis=0).max()
      4.2809152422538475

  p is a projection matrix with rank 1. With exact arithmetic, its singular values would be [1, 0, 0, 0].

      >>> v = np.array([0.1, 0.3, 0.9, 0.3])
      >>> p = np.outer(v, v)
      >>> svdvals(p)
      array([  1.00000000e+00,   2.02021698e-17,   1.56692500e-17,
               8.15115104e-34])

  The singular values of an orthogonal matrix are all 1. Here, we create a random orthogonal matrix by using the rvs() method of `scipy.stats.ortho_group`.

      >>> from scipy.stats import ortho_group
      >>> orth = ortho_group.rvs(4)
      >>> svdvals(orth)
      array([ 1.,  1.,  1.,  1.])