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scipy.linalg.

# svdvals

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

  Compute singular values of a matrix.

  The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

  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.])