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# scipy.linalg.svd

`scipy.linalg.``svd`(a, full_matrices=True, compute_uv=True, overwrite_a=False)

  Singular Value Decomposition.

  Factorizes the matrix a into two unitary matrices U and Vh and an 1d-array s of singular values (real, non-negative) such that a == U S Vh if S is an suitably shaped matrix of zeros whose main diagonal is s.

  Parameters : | a : array, shape (M, N) Matrix to decompose full_matrices : boolean If true, U, Vh are shaped (M,M), (N,N) If false, the shapes are (M,K), (K,N) where K = min(M,N) compute_uv : boolean Whether to compute also U, Vh in addition to s (Default: true) overwrite_a : boolean Whether data in a is overwritten (may improve performance)
  Returns : | U: array, shape (M,M) or (M,K) depending on full_matrices : s: array, shape (K,) : The singular values, sorted so that s[i] >= s[i+1]. K = min(M, N) Vh: array, shape (N,N) or (K,N) depending on full_matrices : For compute_uv = False, only s is returned. : Raises LinAlgError if SVD computation does not converge :

  See also

  `svdvals`
    return singular values of a matrix
  `diagsvd`
    return the Sigma matrix, given the vector s

  Examples

      >>> from scipy import random, linalg, allclose, dot
      >>> a = random.randn(9, 6) + 1j*random.randn(9, 6)
      >>> U, s, Vh = linalg.svd(a)
      >>> U.shape, Vh.shape, s.shape
      ((9, 9), (6, 6), (6,))

      >>> U, s, Vh = linalg.svd(a, full_matrices=False)
      >>> U.shape, Vh.shape, s.shape
      ((9, 6), (6, 6), (6,))
      >>> S = linalg.diagsvd(s, 6, 6)
      >>> allclose(a, dot(U, dot(S, Vh)))
      True

      >>> s2 = linalg.svd(a, compute_uv=False)
      >>> allclose(s, s2)
      True

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