Python tensorflow.python.ops.linalg_ops.cholesky_solve() Examples

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Example #1
Source File: linear_operator_matrix.py    From auto-alt-text-lambda-api with MIT License 5 votes vote down vote up 
def _solve(self, rhs, adjoint=False):
    if self._is_spd:
      return linalg_ops.cholesky_solve(self._chol, rhs)
    return linalg_ops.matrix_solve(self._matrix, rhs, adjoint=adjoint)
Example #2
Source File: linear_operator_matrix.py    From keras-lambda with MIT License 5 votes vote down vote up 
def _solve(self, rhs, adjoint=False):
    if self._is_spd:
      return linalg_ops.cholesky_solve(self._chol, rhs)
    return linalg_ops.matrix_solve(self._matrix, rhs, adjoint=adjoint)
Example #3
Source File: operator_pd_vdvt_update.py    From keras-lambda with MIT License 5 votes vote down vote up 
def _batch_sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=True)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.matmul(v, minv_rhs, adjoint_a=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs
Example #4
Source File: operator_pd_vdvt_update.py    From keras-lambda with MIT License 5 votes vote down vote up 
def _sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    # TODO(jvdillon) Determine if recursively applying rank-1 updates is more
    # efficient.  May not be possible because a general n x n matrix can be
    # represeneted as n rank-1 updates, and solving with this matrix is always
    # done in O(n^3) time.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=False)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.matmul(v, minv_rhs, transpose_a=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs
Example #5
Source File: operator_pd_cholesky.py    From keras-lambda with MIT License 5 votes vote down vote up 
def _batch_solve(self, rhs):
    return linalg_ops.cholesky_solve(self._chol, rhs)
Example #6
Source File: utils.py    From noisy-K-FAC with Apache License 2.0 5 votes vote down vote up 
def posdef_inv_cholesky(tensor, identity, damping):
    """Computes inverse(tensor + damping * identity) with Cholesky."""
    chol = linalg_ops.cholesky(tensor + damping * identity)
    return linalg_ops.cholesky_solve(chol, identity)
Example #7
Source File: operator_pd_vdvt_update.py    From deep_image_model with Apache License 2.0 5 votes vote down vote up 
def _batch_sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=True)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.batch_matmul(v, minv_rhs, adj_x=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.batch_matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs
Example #8
Source File: operator_pd_vdvt_update.py    From deep_image_model with Apache License 2.0 5 votes vote down vote up 
def _sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    # TODO(jvdillon) Determine if recursively applying rank-1 updates is more
    # efficient.  May not be possible because a general n x n matrix can be
    # represeneted as n rank-1 updates, and solving with this matrix is always
    # done in O(n^3) time.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=False)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.matmul(v, minv_rhs, transpose_a=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs
Example #9
Source File: operator_pd_cholesky.py    From deep_image_model with Apache License 2.0 5 votes vote down vote up 
def _batch_solve(self, rhs):
    return linalg_ops.cholesky_solve(self._chol, rhs)
Example #10
Source File: operator_pd_cholesky.py    From lambda-packs with MIT License 5 votes vote down vote up 
def _batch_solve(self, rhs):
    return linalg_ops.cholesky_solve(self._chol, rhs)
Example #11
Source File: operator_pd_vdvt_update.py    From auto-alt-text-lambda-api with MIT License 5 votes vote down vote up 
def _batch_sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=True)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.matmul(v, minv_rhs, adjoint_a=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs
Example #12
Source File: operator_pd_vdvt_update.py    From auto-alt-text-lambda-api with MIT License 5 votes vote down vote up 
def _sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    # TODO(jvdillon) Determine if recursively applying rank-1 updates is more
    # efficient.  May not be possible because a general n x n matrix can be
    # represeneted as n rank-1 updates, and solving with this matrix is always
    # done in O(n^3) time.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=False)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.matmul(v, minv_rhs, transpose_a=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs
Example #13
Source File: operator_pd_cholesky.py    From auto-alt-text-lambda-api with MIT License 5 votes vote down vote up 
def _batch_solve(self, rhs):
    return linalg_ops.cholesky_solve(self._chol, rhs)
Example #14
Source File: linear_operator_udvh_update.py    From lambda-packs with MIT License 5 votes vote down vote up 
def _solve(self, rhs, adjoint=False, adjoint_arg=False):
    if self.base_operator.is_non_singular is False:
      raise ValueError(
          "Solve not implemented unless this is a perturbation of a "
          "non-singular LinearOperator.")
    # The Woodbury formula gives:
    # https://en.wikipedia.org/wiki/Woodbury_matrix_identity
    #   (L + UDV^H)^{-1}
    #   = L^{-1} - L^{-1} U (D^{-1} + V^H L^{-1} U)^{-1} V^H L^{-1}
    #   = L^{-1} - L^{-1} U C^{-1} V^H L^{-1}
    # where C is the capacitance matrix, C := D^{-1} + V^H L^{-1} U
    # Note also that, with ^{-H} being the inverse of the adjoint,
    #   (L + UDV^H)^{-H}
    #   = L^{-H} - L^{-H} V C^{-H} U^H L^{-H}
    l = self.base_operator
    if adjoint:
      v = self.u
      u = self.v
    else:
      v = self.v
      u = self.u

    # L^{-1} rhs
    linv_rhs = l.solve(rhs, adjoint=adjoint, adjoint_arg=adjoint_arg)
    # V^H L^{-1} rhs
    vh_linv_rhs = math_ops.matmul(v, linv_rhs, adjoint_a=True)
    # C^{-1} V^H L^{-1} rhs
    if self._use_cholesky:
      capinv_vh_linv_rhs = linalg_ops.cholesky_solve(
          self._chol_capacitance, vh_linv_rhs)
    else:
      capinv_vh_linv_rhs = linalg_ops.matrix_solve(
          self._capacitance, vh_linv_rhs, adjoint=adjoint)
    # U C^{-1} V^H M^{-1} rhs
    u_capinv_vh_linv_rhs = math_ops.matmul(u, capinv_vh_linv_rhs)
    # L^{-1} U C^{-1} V^H L^{-1} rhs
    linv_u_capinv_vh_linv_rhs = l.solve(u_capinv_vh_linv_rhs, adjoint=adjoint)

    # L^{-1} - L^{-1} U C^{-1} V^H L^{-1}
    return linv_rhs - linv_u_capinv_vh_linv_rhs
Example #15
Source File: linear_operator.py    From lambda-packs with MIT License 5 votes vote down vote up 
def _solve(self, rhs, adjoint=False, adjoint_arg=False):
    """Default implementation of _solve."""
    if self.is_square is False:
      raise NotImplementedError(
          "Solve is not yet implemented for non-square operators.")
    logging.warn(
        "Using (possibly slow) default implementation of solve."
        "  Requires conversion to a dense matrix and O(N^3) operations.")
    rhs = linear_operator_util.matrix_adjoint(rhs) if adjoint_arg else rhs
    if self._can_use_cholesky():
      return linalg_ops.cholesky_solve(self._get_cached_chol(), rhs)
    return linalg_ops.matrix_solve(
        self._get_cached_dense_matrix(), rhs, adjoint=adjoint)
Example #16
Source File: operator_pd_vdvt_update.py    From lambda-packs with MIT License 5 votes vote down vote up 
def _batch_sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=True)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.matmul(v, minv_rhs, adjoint_a=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs
Example #17
Source File: operator_pd_vdvt_update.py    From lambda-packs with MIT License 5 votes vote down vote up 
def _sqrt_solve(self, rhs):
    # Recall the square root of this operator is M + VDV^T.
    # The Woodbury formula gives:
    # (M + VDV^T)^{-1}
    # = M^{-1} - M^{-1} V (D^{-1} + V^T M^{-1} V)^{-1} V^T M^{-1}
    # = M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    # where C is the capacitance matrix.
    # TODO(jvdillon) Determine if recursively applying rank-1 updates is more
    # efficient.  May not be possible because a general n x n matrix can be
    # represeneted as n rank-1 updates, and solving with this matrix is always
    # done in O(n^3) time.
    m = self._operator
    v = self._v
    cchol = self._chol_capacitance(batch_mode=False)

    # The operators will use batch/singleton mode automatically.  We don't
    # override.
    # M^{-1} rhs
    minv_rhs = m.solve(rhs)
    # V^T M^{-1} rhs
    vt_minv_rhs = math_ops.matmul(v, minv_rhs, transpose_a=True)
    # C^{-1} V^T M^{-1} rhs
    cinv_vt_minv_rhs = linalg_ops.cholesky_solve(cchol, vt_minv_rhs)
    # V C^{-1} V^T M^{-1} rhs
    v_cinv_vt_minv_rhs = math_ops.matmul(v, cinv_vt_minv_rhs)
    # M^{-1} V C^{-1} V^T M^{-1} rhs
    minv_v_cinv_vt_minv_rhs = m.solve(v_cinv_vt_minv_rhs)

    # M^{-1} - M^{-1} V C^{-1} V^T M^{-1}
    return minv_rhs - minv_v_cinv_vt_minv_rhs