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Perf: Implement performance improvements #162

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122 changes: 77 additions & 45 deletions pyhope/basis/basis_basis.py
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Original file line number Diff line number Diff line change
Expand Up @@ -661,55 +661,87 @@ def change_basis_1D(Vdm: npt.NDArray[np.float64], x1D_In: npt.NDArray[np.float64
return Vdm @ x1D_In


def evaluate_jacobian(xGeo_In: npt.NDArray[np.float64],
VdmGLtoAP: npt.NDArray[np.float64],
D_EqToGL: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
""" Calculate the Jacobian of the mapping for a given element
"""
dim1 = xGeo_In.shape[0]
n_In = xGeo_In.shape[1]
n_Out = D_EqToGL.shape[0]

# Perform tensor contraction for the first derivative (Xi direction)
# dXdXiGL = np.tensordot(D_EqToGL, xGeo_In, axes=(1, 1))
# dXdXiGL = np.moveaxis(dXdXiGL , 1, 0) # Correct the shape to (3, nGeoRef, nGeoRef, nGeoRef)
_X1 = xGeo_In.reshape(dim1, n_In, n_In * n_In)
dXdXiGL = (D_EqToGL @ _X1).reshape(dim1, n_Out, n_In, n_In)

# Perform tensor contraction for the second derivative (Eta direction)
dXdEtaGL = np.tensordot(D_EqToGL, xGeo_In, axes=(1, 2))
dXdEtaGL = np.transpose(dXdEtaGL, (1, 2, 0, 3))
# PERF: This is actually slower than the individual contractions
# dXdEtaGL = np.einsum('qj,dijk->dqik', D_EqToGL, xGeo_In, optimize=True)

# Perform tensor contraction for the third derivative (Zeta direction)
# dXdZetaGL = np.tensordot(D_EqToGL, xGeo_In, axes=(1, 3))
# dXdZetaGL = np.moveaxis(dXdZetaGL, 1, 0) # Correct the shape to (3, nGeoRef, nGeoRef, nGeoRef)
_X3 = xGeo_In.reshape(dim1, n_In * n_In, n_In)
dXdZetaGL = (_X3 @ D_EqToGL.T).reshape(dim1, n_In, n_In, n_Out)
dXdZetaGL = np.transpose(dXdZetaGL, (0, 3, 1, 2))
# PERF: This is actually slower than the individual contractions
# dXdZetaGL = np.einsum('rk,dijk->drij', D_EqToGL, xGeo_In, optimize=True)
if not NUMBA_AVAILABLE:
def evaluate_jacobian(xGeo_In: npt.NDArray[np.float64],
VdmGLtoAP: npt.NDArray[np.float64],
D_EqToGL: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
""" Calculate the Jacobian of the mapping for a given element
"""
dim1 = xGeo_In.shape[0]
n_In = xGeo_In.shape[1]
n_Out = D_EqToGL.shape[0]

# Perform tensor contraction for the first derivative (Xi direction)
# dXdXiGL = np.tensordot(D_EqToGL, xGeo_In, axes=(1, 1))
# dXdXiGL = np.moveaxis(dXdXiGL , 1, 0) # Correct the shape to (3, nGeoRef, nGeoRef, nGeoRef)
_X1 = xGeo_In.reshape(dim1, n_In, n_In * n_In)
dXdXiGL = (D_EqToGL @ _X1).reshape(dim1, n_Out, n_In, n_In)

# Perform tensor contraction for the second derivative (Eta direction)
dXdEtaGL = np.tensordot(D_EqToGL, xGeo_In, axes=(1, 2))
dXdEtaGL = np.transpose(dXdEtaGL, (1, 2, 0, 3))
# PERF: This is actually slower than the individual contractions
# dXdEtaGL = np.einsum('qj,dijk->dqik', D_EqToGL, xGeo_In, optimize=True)

# Perform tensor contraction for the third derivative (Zeta direction)
# dXdZetaGL = np.tensordot(D_EqToGL, xGeo_In, axes=(1, 3))
# dXdZetaGL = np.moveaxis(dXdZetaGL, 1, 0) # Correct the shape to (3, nGeoRef, nGeoRef, nGeoRef)
_X3 = xGeo_In.reshape(dim1, n_In * n_In, n_In)
dXdZetaGL = (_X3 @ D_EqToGL.T).reshape(dim1, n_In, n_In, n_Out)
dXdZetaGL = np.transpose(dXdZetaGL, (0, 3, 1, 2))
# PERF: This is actually slower than the individual contractions
# dXdZetaGL = np.einsum('rk,dijk->drij', D_EqToGL, xGeo_In, optimize=True)

# Change basis for each direction
dXdXiAP = change_basis_3D(VdmGLtoAP, dXdXiGL )
dXdEtaAP = change_basis_3D(VdmGLtoAP, dXdEtaGL )
dXdZetaAP = change_basis_3D(VdmGLtoAP, dXdZetaGL)

# Precompute cross products between dXdEtaAP and dXdZetaAP for all points
# cross_eta_zeta = np.cross(dXdEtaAP, dXdZetaAP, axis=0) # Shape: (3, nGeoRef, nGeoRef, nGeoRef)
# > Manually compute cross product
cross_eta_zeta = np.empty_like(dXdEtaAP)
cross_eta_zeta[0] = dXdEtaAP[1] * dXdZetaAP[2] - dXdEtaAP[2] * dXdZetaAP[1]
cross_eta_zeta[1] = dXdEtaAP[2] * dXdZetaAP[0] - dXdEtaAP[0] * dXdZetaAP[2]
cross_eta_zeta[2] = dXdEtaAP[0] * dXdZetaAP[1] - dXdEtaAP[1] * dXdZetaAP[0]

# Fill output Jacobian array
# jacOut = np.einsum('ijkl,ijkl->jkl', dXdXiAP, cross_eta_zeta)
# PERF: This is actually slower than the individual contractions
# jacOut = np.sum(dXdXiAP * cross_eta_zeta, axis=0)

# Change basis for each direction
dXdXiAP = change_basis_3D(VdmGLtoAP, dXdXiGL )
dXdEtaAP = change_basis_3D(VdmGLtoAP, dXdEtaGL )
dXdZetaAP = change_basis_3D(VdmGLtoAP, dXdZetaGL)
return np.einsum('ijkl,ijkl->jkl', dXdXiAP, cross_eta_zeta)
else:
@jit(nopython=True, cache=True, nogil=True)
def evaluate_jacobian(xGeo_In: npt.NDArray[np.float64],
VdmGLtoAP: npt.NDArray[np.float64],
D_EqToGL: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
""" Calculate the Jacobian of the mapping for a given element
"""
dim1 = xGeo_In.shape[0]
n_In = xGeo_In.shape[1]
n_Out = D_EqToGL.shape[0]

# Precompute cross products between dXdEtaAP and dXdZetaAP for all points
# cross_eta_zeta = np.cross(dXdEtaAP, dXdZetaAP, axis=0) # Shape: (3, nGeoRef, nGeoRef, nGeoRef)
# > Manually compute cross product
cross_eta_zeta = np.empty_like(dXdEtaAP)
cross_eta_zeta[0] = dXdEtaAP[1] * dXdZetaAP[2] - dXdEtaAP[2] * dXdZetaAP[1]
cross_eta_zeta[1] = dXdEtaAP[2] * dXdZetaAP[0] - dXdEtaAP[0] * dXdZetaAP[2]
cross_eta_zeta[2] = dXdEtaAP[0] * dXdZetaAP[1] - dXdEtaAP[1] * dXdZetaAP[0]
dXdXiGL = np.zeros((dim1, n_Out, n_In, n_In), dtype=np.float64)
for d in range(dim1):
_X1 = np.ascontiguousarray(xGeo_In[d]).reshape(n_In, n_In * n_In)
dXdXiGL[d] = (D_EqToGL @ _X1).reshape(n_Out, n_In, n_In)

# Fill output Jacobian array
# jacOut = np.einsum('ijkl,ijkl->jkl', dXdXiAP, cross_eta_zeta)
# PERF: This is actually slower than the individual contractions
# jacOut = np.sum(dXdXiAP * cross_eta_zeta, axis=0)
_X2 = np.ascontiguousarray(xGeo_In.transpose(0, 1, 3, 2)).reshape(-1, n_In)
dXdEtaGL = (_X2 @ D_EqToGL.T).reshape(dim1, n_In, n_In, n_Out).transpose(0, 1, 3, 2)

_X3 = np.ascontiguousarray(xGeo_In).reshape(-1, n_In)
dXdZetaGL = (_X3 @ D_EqToGL.T).reshape(dim1, n_In, n_In, n_Out).transpose(0, 3, 1, 2)

dXdXiAP = change_basis_3D(VdmGLtoAP, dXdXiGL )
dXdEtaAP = change_basis_3D(VdmGLtoAP, dXdEtaGL )
dXdZetaAP = change_basis_3D(VdmGLtoAP, dXdZetaGL)

cross_0 = dXdEtaAP[1] * dXdZetaAP[2] - dXdEtaAP[2] * dXdZetaAP[1]
cross_1 = dXdEtaAP[2] * dXdZetaAP[0] - dXdEtaAP[0] * dXdZetaAP[2]
cross_2 = dXdEtaAP[0] * dXdZetaAP[1] - dXdEtaAP[1] * dXdZetaAP[0]

return np.einsum('ijkl,ijkl->jkl', dXdXiAP, cross_eta_zeta)
return dXdXiAP[0] * cross_0 + dXdXiAP[1] * cross_1 + dXdXiAP[2] * cross_2


def evaluate_jacobian_simplex(xGeo_In: npt.NDArray[np.float64],
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