python类svd()的实例源码

def pseudo_inverse(mat, eps=1e-10):
  """Computes pseudo-inverse of mat, treating eigenvalues below eps as 0."""

  s, u, v = tf.svd(mat)
  eps = 1e-10   # zero threshold for eigenvalues
  si = tf.where(tf.less(s, eps), s, 1./s)
  return u @ tf.diag(si) @ tf.transpose(v)

def symsqrt(mat, eps=1e-7):
  """Symmetric square root."""
  s, u, v = tf.svd(mat)
  # sqrt is unstable around 0, just use 0 in such case
  print("Warning, cutting off at eps")
  si = tf.where(tf.less(s, eps), s, tf.sqrt(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse_sqrt2(svd, eps=1e-7):
  """half pseduo-inverse, accepting existing values"""
  # zero threshold for eigenvalues
  if svd.__class__.__name__=='SvdTuple':
    (s, u, v) = (svd.s, svd.u, svd.v)
  elif svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  si = tf.where(tf.less(s, eps), s, 1./tf.sqrt(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse2(svd, eps=1e-7):
  """pseudo-inverse, accepting existing values"""
  # use float32 machine precision as cut-off (works for MKL)
  # https://www.wolframcloud.com/objects/927b2aa5-de9c-46f5-89fe-c4a58aa4c04b
  if svd.__class__.__name__=='SvdTuple':
    (s, u, v) = (svd.s, svd.u, svd.v)
  elif svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  max_eigen = tf.reduce_max(s)
  si = tf.where(s/max_eigen<eps, 0.*s, 1./s)
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse_stable(svd, eps=1e-7):
  """pseudo-inverse, accepting existing values"""
  # use float32 machine precision as cut-off (works for MKL)
  # https://www.wolframcloud.com/objects/927b2aa5-de9c-46f5-89fe-c4a58aa4c04b
  if svd.__class__.__name__=='SvdTuple':
    (s, u, v) = (svd.s, svd.u, svd.v)
  elif svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  max_eigen = tf.reduce_max(s)
  si = tf.where(s/max_eigen<eps, 0.*s, tf.pow(s, -0.9))
  return u @ tf.diag(si) @ tf.transpose(v)

# todo: rename l to L

def regularized_inverse2(svd, L=1e-3):
  """Regularized inverse, working from SVD"""
  if svd.__class__.__name__=='SvdTuple' or svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  max_eigen = tf.reduce_max(s)
  #  max_eigen = tf.Print(max_eigen, [max_eigen], "max_eigen")
  #si = 1/(s + L*tf.ones_like(s)/max_eigen)
  si = 1/(s+L*tf.ones_like(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def regularized_inverse3(svd, L=1e-3):
  """Unbiased version of regularized_inverse2"""
  if svd.__class__.__name__=='SvdTuple' or svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"

  if L.__class__.__name__=='Var':
    L = L.var

  max_eigen = tf.reduce_max(s)
  #  max_eigen = tf.Print(max_eigen, [max_eigen], "max_eigen")
  #si = 1/(s + L*tf.ones_like(s)/max_eigen)
  si = (1+L*tf.ones_like(s))/(s+L*tf.ones_like(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse(mat, eps=1e-10):
  """Computes pseudo-inverse of mat, treating eigenvalues below eps as 0."""

  s, u, v = tf.svd(mat)
  eps = 1e-10   # zero threshold for eigenvalues
  si = tf.where(tf.less(s, eps), s, 1./s)
  return u @ tf.diag(si) @ tf.transpose(v)

def symsqrt(mat, eps=1e-7):
  """Symmetric square root."""
  s, u, v = tf.svd(mat)
  # sqrt is unstable around 0, just use 0 in such case
  print("Warning, cutting off at eps")
  si = tf.where(tf.less(s, eps), s, tf.sqrt(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse_sqrt(mat, eps=1e-7):
  """half pseduo-inverse"""
  s, u, v = tf.svd(mat)
  # zero threshold for eigenvalues
  si = tf.where(tf.less(s, eps), s, 1./tf.sqrt(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse2(svd, eps=1e-7):
  """pseudo-inverse, accepting existing values"""
  # use float32 machine precision as cut-off (works for MKL)
  # https://www.wolframcloud.com/objects/927b2aa5-de9c-46f5-89fe-c4a58aa4c04b
  if svd.__class__.__name__=='SvdTuple':
    (s, u, v) = (svd.s, svd.u, svd.v)
  elif svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  max_eigen = tf.reduce_max(s)
  si = tf.where(s/max_eigen<eps, 0.*s, 1./s)
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse_stable(svd, eps=1e-7):
  """pseudo-inverse, accepting existing values"""
  # use float32 machine precision as cut-off (works for MKL)
  # https://www.wolframcloud.com/objects/927b2aa5-de9c-46f5-89fe-c4a58aa4c04b
  if svd.__class__.__name__=='SvdTuple':
    (s, u, v) = (svd.s, svd.u, svd.v)
  elif svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  max_eigen = tf.reduce_max(s)
  si = tf.where(s/max_eigen<eps, 0.*s, tf.pow(s, -0.9))
  return u @ tf.diag(si) @ tf.transpose(v)

# todo: rename l to L

def regularized_inverse2(svd, L=1e-3):
  """Regularized inverse, working from SVD"""
  if svd.__class__.__name__=='SvdTuple' or svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  max_eigen = tf.reduce_max(s)
  #  max_eigen = tf.Print(max_eigen, [max_eigen], "max_eigen")
  #si = 1/(s + L*tf.ones_like(s)/max_eigen)
  si = 1/(s+L*tf.ones_like(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def regularized_inverse3(svd, L=1e-3):
  """Unbiased version of regularized_inverse2"""
  if svd.__class__.__name__=='SvdTuple' or svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"

  if L.__class__.__name__=='Var':
    L = L.var

  max_eigen = tf.reduce_max(s)
  #  max_eigen = tf.Print(max_eigen, [max_eigen], "max_eigen")
  #si = 1/(s + L*tf.ones_like(s)/max_eigen)
  si = (1+L*tf.ones_like(s))/(s+L*tf.ones_like(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def regularized_inverse4(svd, L=1e-3):
  """Uses relative norm"""
  if svd.__class__.__name__=='SvdTuple' or svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"

  if L.__class__.__name__=='Var':
    L = L.var

  max_eigen = tf.reduce_max(s)
  L = L/max_eigen
  si = (1+L*tf.ones_like(s))/(s+L*tf.ones_like(s))
  #  si = tf.ones_like(s)
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse(mat, eps=1e-10):
  """Computes pseudo-inverse of mat, treating eigenvalues below eps as 0."""

  s, u, v = tf.svd(mat)
  eps = 1e-10   # zero threshold for eigenvalues
  si = tf.where(tf.less(s, eps), s, 1./s)
  return u @ tf.diag(si) @ tf.transpose(v)

def symsqrt(mat, eps=1e-7):
  """Symmetric square root."""
  s, u, v = tf.svd(mat)
  # sqrt is unstable around 0, just use 0 in such case
  print("Warning, cutting off at eps")
  si = tf.where(tf.less(s, eps), s, tf.sqrt(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse_sqrt(mat, eps=1e-7):
  """half pseduo-inverse"""
  s, u, v = tf.svd(mat)
  # zero threshold for eigenvalues
  si = tf.where(tf.less(s, eps), s, 1./tf.sqrt(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse_sqrt2(svd, eps=1e-7):
  """half pseduo-inverse, accepting existing values"""
  # zero threshold for eigenvalues
  if svd.__class__.__name__=='SvdTuple':
    (s, u, v) = (svd.s, svd.u, svd.v)
  elif svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  si = tf.where(tf.less(s, eps), s, 1./tf.sqrt(s))
  return u @ tf.diag(si) @ tf.transpose(v)

def pseudo_inverse_stable(svd, eps=1e-7):
  """pseudo-inverse, accepting existing values"""
  # use float32 machine precision as cut-off (works for MKL)
  # https://www.wolframcloud.com/objects/927b2aa5-de9c-46f5-89fe-c4a58aa4c04b
  if svd.__class__.__name__=='SvdTuple':
    (s, u, v) = (svd.s, svd.u, svd.v)
  elif svd.__class__.__name__=='SvdWrapper':
    (s, u, v) = (svd.s, svd.u, svd.v)
  else:
    assert False, "Unknown type"
  max_eigen = tf.reduce_max(s)
  si = tf.where(s/max_eigen<eps, 0.*s, tf.pow(s, -0.9))
  return u @ tf.diag(si) @ tf.transpose(v)

# todo: rename l to L