def sym_eig2x2(A, dt):
"""Compute the eigenvalues and right eigenvectors (Av=lambda v) of a 2x2 real symmetric matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix.
Args:
A (ti.Matrix(2, 2)): input 2x2 symmetric matrix `A`.
dt (DataType): date type of elements in matrix `A`, typically accepts ti.f32 or ti.f64.
Returns:
eigenvalues (ti.Vector(2)): The eigenvalues. Each entry store one eigen value.
eigenvectors (ti.Matrix(2, 2)): The eigenvectors. Each column stores one eigenvector.
"""
tr = A.trace()
det = A.determinant()
gap = tr**2 - 4 * det
lambda1 = (tr + ops.sqrt(gap)) * 0.5
lambda2 = (tr - ops.sqrt(gap)) * 0.5
eigenvalues = Vector([lambda1, lambda2], dt=dt)
A1 = A - lambda1 * Matrix.identity(dt, 2)
A2 = A - lambda2 * Matrix.identity(dt, 2)
v1 = Vector.zero(dt, 2)
v2 = Vector.zero(dt, 2)
if all(A1 == Matrix.zero(dt, 2, 2)) and all(A1 == Matrix.zero(dt, 2, 2)):
v1 = Vector([0.0, 1.0]).cast(dt)
v2 = Vector([1.0, 0.0]).cast(dt)
else:
v1 = Vector([A2[0, 0], A2[1, 0]], dt=dt).normalized()
v2 = Vector([A1[0, 0], A1[1, 0]], dt=dt).normalized()
eigenvectors = Matrix.cols([v1, v2])
return eigenvalues, eigenvectors
def polar_decompose2d(A, dt):
"""Perform polar decomposition (A=UP) for 2x2 matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Polar_decomposition.
Args:
A (ti.Matrix(2, 2)): input 2x2 matrix `A`.
dt (DataType): date type of elements in matrix `A`, typically accepts ti.f32 or ti.f64.
Returns:
Decomposed 2x2 matrices `U` and `P`. `U` is a 2x2 orthogonal matrix
and `P` is a 2x2 positive or semi-positive definite matrix.
"""
U = Matrix.identity(dt, 2)
P = ops.cast(A, dt)
zero = ops.cast(0.0, dt)
# if A is a zero matrix we simply return the pair (I, A)
if (A[0, 0] == zero and A[0, 1] == zero and A[1, 0] == zero
and A[1, 1] == zero):
pass
else:
detA = A[0, 0] * A[1, 1] - A[1, 0] * A[0, 1]
adetA = abs(detA)
B = Matrix([[A[0, 0] + A[1, 1], A[0, 1] - A[1, 0]],
[A[1, 0] - A[0, 1], A[1, 1] + A[0, 0]]], dt)
if detA < zero:
B = Matrix([[A[0, 0] - A[1, 1], A[0, 1] + A[1, 0]],
[A[1, 0] + A[0, 1], A[1, 1] - A[0, 0]]], dt)
# here det(B) != 0 if A is not the zero matrix
adetB = abs(B[0, 0] * B[1, 1] - B[1, 0] * B[0, 1])
k = ops.cast(1.0, dt) / ops.sqrt(adetB)
U = B * k
P = (A.transpose() @ A + adetA * Matrix.identity(dt, 2)) * k
return U, P
def expr_init(rhs):
if rhs is None:
return Expr(get_runtime().prog.current_ast_builder().expr_alloca())
if isinstance(rhs, Matrix) and (hasattr(rhs, "_DIM")):
return type(rhs)(*rhs.to_list())
if isinstance(rhs, Matrix):
return Matrix(rhs.to_list())
if isinstance(rhs, Struct):
return Struct(rhs.to_dict())
if isinstance(rhs, list):
return [expr_init(e) for e in rhs]
if isinstance(rhs, tuple):
return tuple(expr_init(e) for e in rhs)
if isinstance(rhs, dict):
return dict((key, expr_init(val)) for key, val in rhs.items())
if isinstance(rhs, _ti_core.DataType):
return rhs
if isinstance(rhs, _ti_core.Arch):
return rhs
if isinstance(rhs, _Ndrange):
return rhs
if isinstance(rhs, MeshElementFieldProxy):
return rhs
if isinstance(rhs, MeshRelationAccessProxy):
return rhs
if hasattr(rhs, '_data_oriented'):
return rhs
return Expr(get_runtime().prog.current_ast_builder().expr_var(
Expr(rhs).ptr))
def solve(A, b, dt=None):
"""Solve a matrix using Gauss elimination method.
Args:
A (ti.Matrix(n, n)): input nxn matrix `A`.
b (ti.Vector(n, 1)): input nx1 vector `b`.
dt (DataType): The datatype for the `A` and `b`.
Returns:
x (ti.Vector(n, 1)): the solution of Ax=b.
"""
assert A.n == A.m, "Only sqaure matrix is supported"
assert A.n >= 2 and A.n <= 3, "Only 2D and 3D matrices are supported"
assert A.m == b.n, "Matrix and Vector dimension dismatch"
if dt is None:
dt = impl.get_runtime().default_fp
nrow, ncol = static(A.n, A.n + 1)
Ab = expr_init(Matrix.zero(dt, nrow, ncol))
lhs = tuple([e.ptr for e in A.entries])
rhs = tuple([e.ptr for e in b.entries])
for i in range(nrow):
for j in range(nrow):
Ab(i, j)._assign(lhs[nrow * i + j])
for i in range(nrow):
Ab(i, nrow)._assign(rhs[i])
if A.n == 2:
return _gauss_elimination_2x2(Ab, dt)
if A.n == 3:
return _gauss_elimination_3x3(Ab, dt)
raise Exception("Solver only supports 2D and 3D matrices.")
def expr_init(rhs):
if rhs is None:
return Expr(_ti_core.expr_alloca())
if isinstance(rhs, Matrix):
if rhs.in_python_scope or isinstance(rhs, _IntermediateMatrix):
return Matrix(rhs.to_list())
return rhs
if isinstance(rhs, Struct):
if rhs.in_python_scope or isinstance(rhs, _IntermediateStruct):
return Struct(rhs.to_dict())
return rhs
if isinstance(rhs, list):
return [expr_init(e) for e in rhs]
if isinstance(rhs, tuple):
return tuple(expr_init(e) for e in rhs)
if isinstance(rhs, dict):
return dict((key, expr_init(val)) for key, val in rhs.items())
if isinstance(rhs, _ti_core.DataType):
return rhs
if isinstance(rhs, _ti_core.Arch):
return rhs
if isinstance(rhs, ti.ndrange):
return rhs
if isinstance(rhs, MeshElementFieldProxy):
return rhs
if isinstance(rhs, MeshRelationAccessProxy):
return rhs
if hasattr(rhs, '_data_oriented'):
return rhs
return Expr(_ti_core.expr_var(Expr(rhs).ptr))
def eig2x2(A, dt):
"""Compute the eigenvalues and right eigenvectors (Av=lambda v) of a 2x2 real matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix.
Args:
A (ti.Matrix(2, 2)): input 2x2 matrix `A`.
dt (DataType): date type of elements in matrix `A`, typically accepts ti.f32 or ti.f64.
Returns:
eigenvalues (ti.Matrix(2, 2)): The eigenvalues in complex form. Each row stores one eigenvalue. The first number of the eigenvalue represents the real part and the second number represents the imaginary part.
eigenvectors: (ti.Matrix(4, 2)): The eigenvectors in complex form. Each column stores one eigenvector. Each eigenvector consists of 2 entries, each of which is represented by two numbers for its real part and imaginary part.
"""
tr = A.trace()
det = A.determinant()
gap = tr**2 - 4 * det
lambda1 = Vector.zero(dt, 2)
lambda2 = Vector.zero(dt, 2)
v1 = Vector.zero(dt, 4)
v2 = Vector.zero(dt, 4)
if gap > 0:
lambda1 = Vector([tr + ops.sqrt(gap), 0.0], dt=dt) * 0.5
lambda2 = Vector([tr - ops.sqrt(gap), 0.0], dt=dt) * 0.5
A1 = A - lambda1[0] * Matrix.identity(dt, 2)
A2 = A - lambda2[0] * Matrix.identity(dt, 2)
if all(A1 == Matrix.zero(dt, 2, 2)) and all(
A1 == Matrix.zero(dt, 2, 2)):
v1 = Vector([0.0, 0.0, 1.0, 0.0]).cast(dt)
v2 = Vector([1.0, 0.0, 0.0, 0.0]).cast(dt)
else:
v1 = Vector([A2[0, 0], 0.0, A2[1, 0], 0.0], dt=dt).normalized()
v2 = Vector([A1[0, 0], 0.0, A1[1, 0], 0.0], dt=dt).normalized()
else:
lambda1 = Vector([tr, ops.sqrt(-gap)], dt=dt) * 0.5
lambda2 = Vector([tr, -ops.sqrt(-gap)], dt=dt) * 0.5
A1r = A - lambda1[0] * Matrix.identity(dt, 2)
A1i = -lambda1[1] * Matrix.identity(dt, 2)
A2r = A - lambda2[0] * Matrix.identity(dt, 2)
A2i = -lambda2[1] * Matrix.identity(dt, 2)
v1 = Vector([A2r[0, 0], A2i[0, 0], A2r[1, 0], A2i[1, 0]],
dt=dt).normalized()
v2 = Vector([A1r[0, 0], A1i[0, 0], A1r[1, 0], A1i[1, 0]],
dt=dt).normalized()
eigenvalues = Matrix.rows([lambda1, lambda2])
eigenvectors = Matrix.cols([v1, v2])
return eigenvalues, eigenvectors
def produce_injected_args(kernel, symbolic_args=None):
injected_args = []
for i, arg in enumerate(kernel.arguments):
anno = arg.annotation
if isinstance(anno, template_types):
if not isinstance(anno, NdarrayType):
raise TaichiCompilationError(
f'Expected Ndaray type, got {anno}')
if symbolic_args is not None:
element_shape = tuple(symbolic_args[i].element_shape)
element_dim = len(element_shape)
dtype = symbolic_args[i].dtype()
else:
element_shape = anno.element_shape
element_dim = anno.element_dim
dtype = anno.dtype
if element_shape is None or anno.field_dim is None:
raise TaichiCompilationError(
'Please either specify both `element_shape` and `field_dim` '
'in the param annotation, or provide an example '
f'ndarray for param={arg.name}')
if element_dim is None or element_dim == 0:
injected_args.append(
ScalarNdarray(dtype, (2, ) * anno.field_dim))
elif element_dim == 1:
injected_args.append(
VectorNdarray(element_shape[0],
dtype=dtype,
shape=(2, ) * anno.field_dim,
layout=Layout.AOS))
elif element_dim == 2:
injected_args.append(
MatrixNdarray(element_shape[0],
element_shape[1],
dtype=dtype,
shape=(2, ) * anno.field_dim,
layout=Layout.AOS))
else:
raise RuntimeError('')
elif isinstance(anno, MatrixType):
if not isinstance(symbolic_args[i], list):
raise RuntimeError('Expected a symbolic arg with Matrix type.')
symbolic_mat_n = len(symbolic_args[i])
symbolic_mat_m = len(symbolic_args[i][0])
if symbolic_mat_m != anno.m or symbolic_mat_n != anno.n:
raise RuntimeError(
f'Matrix dimension mismatch, expected ({anno.n}, {anno.m}) '
f'but dispathed shape ({symbolic_mat_n}, {symbolic_mat_m}).'
)
injected_args.append(Matrix([0] * anno.n * anno.m, dt=anno.dtype))
else:
# For primitive types, we can just inject a dummy value.
injected_args.append(0)
return injected_args
def polar_decompose2d(A, dt):
"""Perform polar decomposition (A=UP) for 2x2 matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Polar_decomposition.
Args:
A (ti.Matrix(2, 2)): input 2x2 matrix `A`.
dt (DataType): date type of elements in matrix `A`, typically accepts ti.f32 or ti.f64.
Returns:
Decomposed 2x2 matrices `U` and `P`.
"""
x, y = A(0, 0) + A(1, 1), A(1, 0) - A(0, 1)
scale = (1.0 / ops.sqrt(x * x + y * y))
c = x * scale
s = y * scale
r = Matrix([[c, -s], [s, c]], dt=dt)
return r, r.transpose() @ A
def svd3d(A, dt, iters=None):
"""Perform singular value decomposition (A=USV^T) for 3x3 matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Singular_value_decomposition.
Args:
A (ti.Matrix(3, 3)): input 3x3 matrix `A`.
dt (DataType): date type of elements in matrix `A`, typically accepts ti.f32 or ti.f64.
iters (int): iteration number to control algorithm precision.
Returns:
Decomposed 3x3 matrices `U`, 'S' and `V`.
"""
assert A.n == 3 and A.m == 3
inputs = tuple([e.ptr for e in A.entries])
assert dt in [f32, f64]
if iters is None:
if dt == f32:
iters = 5
else:
iters = 8
if dt == f32:
rets = get_runtime().prog.current_ast_builder().sifakis_svd_f32(
*inputs, iters)
else:
rets = get_runtime().prog.current_ast_builder().sifakis_svd_f64(
*inputs, iters)
assert len(rets) == 21
U_entries = rets[:9]
V_entries = rets[9:18]
sig_entries = rets[18:]
U = expr_init(Matrix.zero(dt, 3, 3))
V = expr_init(Matrix.zero(dt, 3, 3))
sigma = expr_init(Matrix.zero(dt, 3, 3))
for i in range(3):
for j in range(3):
U(i, j)._assign(U_entries[i * 3 + j])
V(i, j)._assign(V_entries[i * 3 + j])
sigma(i, i)._assign(sig_entries[i])
return U, sigma, V
def svd2d(A, dt):
"""Perform singular value decomposition (A=USV^T) for 2x2 matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Singular_value_decomposition.
Args:
A (ti.Matrix(2, 2)): input 2x2 matrix `A`.
dt (DataType): date type of elements in matrix `A`, typically accepts ti.f32 or ti.f64.
Returns:
Decomposed 2x2 matrices `U`, 'S' and `V`.
"""
R, S = polar_decompose2d(A, dt)
c, s = ops.cast(0.0, dt), ops.cast(0.0, dt)
s1, s2 = ops.cast(0.0, dt), ops.cast(0.0, dt)
if abs(S[0, 1]) < 1e-5:
c, s = 1, 0
s1, s2 = S[0, 0], S[1, 1]
else:
tao = ops.cast(0.5, dt) * (S[0, 0] - S[1, 1])
w = ops.sqrt(tao**2 + S[0, 1]**2)
t = ops.cast(0.0, dt)
if tao > 0:
t = S[0, 1] / (tao + w)
else:
t = S[0, 1] / (tao - w)
c = 1 / ops.sqrt(t**2 + 1)
s = -t * c
s1 = c**2 * S[0, 0] - 2 * c * s * S[0, 1] + s**2 * S[1, 1]
s2 = s**2 * S[0, 0] + 2 * c * s * S[0, 1] + c**2 * S[1, 1]
V = Matrix.zero(dt, 2, 2)
if s1 < s2:
tmp = s1
s1 = s2
s2 = tmp
V = Matrix([[-s, c], [-c, -s]], dt=dt)
else:
V = Matrix([[c, s], [-s, c]], dt=dt)
U = R @ V
return U, Matrix([[s1, ops.cast(0, dt)], [ops.cast(0, dt), s2]], dt=dt), V
def __init__(self, *args, **kwargs):
# converts lists to matrices and dicts to structs
if len(args) == 1 and kwargs == {} and isinstance(args[0], dict):
self.entries = args[0]
elif len(args) == 0:
self.entries = kwargs
else:
raise TaichiSyntaxError(
"Custom structs need to be initialized using either dictionary or keyword arguments"
)
for k, v in self.entries.items():
if isinstance(v, (list, tuple)):
v = Matrix(v)
if isinstance(v, dict):
v = Struct(v)
self.entries[k] = v if in_python_scope() else impl.expr_init(v)
self._register_members()
def __init__(self, *args, **kwargs):
# converts lists to matrices and dicts to structs
if len(args) == 1 and kwargs == {} and isinstance(args[0], dict):
self.entries = args[0]
elif len(args) == 0:
self.entries = kwargs
else:
raise TaichiSyntaxError(
"Custom structs need to be initialized using either dictionary or keyword arguments"
)
for k, v in self.entries.items():
if isinstance(v, (list, tuple)):
v = Matrix(v)
if isinstance(v, dict):
v = Struct(v)
self.entries[k] = v
self.register_members()
self.local_tensor_proxy = None
self.any_array_access = None
def produce_injected_args(kernel, symbolic_args=None):
injected_args = []
for i, arg in enumerate(kernel.arguments):
anno = arg.annotation
if isinstance(anno, template_types):
if not isinstance(anno, NdarrayType):
raise TaichiCompilationError(
f'Expected Ndaray type, got {anno}')
if symbolic_args is not None:
element_shape = tuple(symbolic_args[i].element_shape)
element_dim = len(element_shape)
field_dim = symbolic_args[i].field_dim
dtype = symbolic_args[i].dtype()
else:
element_shape = anno.element_shape
element_dim = anno.element_dim
field_dim = anno.field_dim
dtype = anno.dtype
if element_shape is None or field_dim is None:
raise TaichiCompilationError(
'Please either specify both `element_shape` and `field_dim` '
'in the param annotation, or provide an example '
f'ndarray for param={arg.name}')
if anno.field_dim is not None and field_dim != anno.field_dim:
raise TaichiCompilationError(
f'{field_dim} from Arg {arg.name} doesn\'t match kernel\'s annotated field_dim={anno.field_dim}'
)
if anno.dtype is not None and not check_type_match(
dtype, anno.dtype):
raise TaichiCompilationError(
f' Arg {arg.name}\'s dtype {dtype.to_string()} doesn\'t match kernel\'s annotated dtype={anno.dtype.to_string()}'
)
if element_dim is None or element_dim == 0:
injected_args.append(ScalarNdarray(dtype, (2, ) * field_dim))
elif element_dim == 1:
injected_args.append(
VectorNdarray(element_shape[0],
dtype=dtype,
shape=(2, ) * field_dim,
layout=Layout.AOS))
elif element_dim == 2:
injected_args.append(
MatrixNdarray(element_shape[0],
element_shape[1],
dtype=dtype,
shape=(2, ) * field_dim,
layout=Layout.AOS))
else:
raise RuntimeError('')
elif isinstance(anno, (TextureType, RWTextureType)):
if symbolic_args is None:
raise RuntimeError(
'Texture type annotation doesn\'t have enough information for aot. Please either specify the channel_format, shape and num_channels in the graph arg declaration.'
)
texture_shape = tuple(symbolic_args[i].texture_shape)
channel_format = symbolic_args[i].channel_format()
num_channels = symbolic_args[i].num_channels
injected_args.append(
Texture(channel_format, num_channels, texture_shape))
elif isinstance(anno, MatrixType):
if not isinstance(symbolic_args[i], list):
raise RuntimeError('Expected a symbolic arg with Matrix type.')
symbolic_mat_n = len(symbolic_args[i])
symbolic_mat_m = len(symbolic_args[i][0])
if symbolic_mat_m != anno.m or symbolic_mat_n != anno.n:
raise RuntimeError(
f'Matrix dimension mismatch, expected ({anno.n}, {anno.m}) '
f'but dispatched shape ({symbolic_mat_n}, {symbolic_mat_m}).'
)
injected_args.append(Matrix([0] * anno.n * anno.m, dt=anno.dtype))
else:
if symbolic_args is not None:
dtype = symbolic_args[i].dtype()
else:
dtype = anno
if not check_type_match(dtype, anno):
raise TaichiCompilationError(
f' Arg {arg.name}\'s dtype {dtype.to_string()} doesn\'t match kernel\'s annotated dtype={anno.to_string()}'
)
# For primitive types, we can just inject a dummy value.
injected_args.append(0)
return injected_args
def sym_eig3x3(A, dt):
"""Compute the eigenvalues and right eigenvectors (Av=lambda v) of a 3x3 real symmetric matrix using Cardano's method.
Mathematical concept refers to https://www.mpi-hd.mpg.de/personalhomes/globes/3x3/.
Args:
A (ti.Matrix(3, 3)): input 3x3 symmetric matrix `A`.
dt (DataType): date type of elements in matrix `A`, typically accepts ti.f32 or ti.f64.
Returns:
eigenvalues (ti.Vector(3)): The eigenvalues. Each entry store one eigen value.
eigenvectors (ti.Matrix(3, 3)): The eigenvectors. Each column stores one eigenvector.
"""
M_SQRT3 = 1.73205080756887729352744634151
m = A.trace()
dd = A[0, 1] * A[0, 1]
ee = A[1, 2] * A[1, 2]
ff = A[0, 2] * A[0, 2]
c1 = A[0, 0] * A[1, 1] + A[0, 0] * A[2, 2] + A[1, 1] * A[2, 2] - (dd + ee +
ff)
c0 = A[2, 2] * dd + A[0, 0] * ee + A[1, 1] * ff - A[0, 0] * A[1, 1] * A[
2, 2] - 2.0 * A[0, 2] * A[0, 1] * A[1, 2]
p = m * m - 3.0 * c1
q = m * (p - 1.5 * c1) - 13.5 * c0
sqrt_p = ops.sqrt(ops.abs(p))
phi = 27.0 * (0.25 * c1 * c1 * (p - c1) + c0 * (q + 6.75 * c0))
phi = (1.0 / 3.0) * ops.atan2(ops.sqrt(ops.abs(phi)), q)
c = sqrt_p * ops.cos(phi)
s = (1.0 / M_SQRT3) * sqrt_p * ops.sin(phi)
eigenvalues = Vector([0.0, 0.0, 0.0], dt=dt)
eigenvalues[2] = (1.0 / 3.0) * (m - c)
eigenvalues[1] = eigenvalues[2] + s
eigenvalues[0] = eigenvalues[2] + c
eigenvalues[2] = eigenvalues[2] - s
t = ops.abs(eigenvalues[0])
u = ops.abs(eigenvalues[1])
if u > t:
t = u
u = ops.abs(eigenvalues[2])
if u > t:
t = u
if t < 1.0:
u = t
else:
u = t * t
Q = Matrix.zero(dt, 3, 3)
Q[0, 1] = A[0, 1] * A[1, 2] - A[0, 2] * A[1, 1]
Q[1, 1] = A[0, 2] * A[0, 1] - A[1, 2] * A[0, 0]
Q[2, 1] = A[0, 1] * A[0, 1]
Q[0, 0] = Q[0, 1] + A[0, 2] * eigenvalues[0]
Q[1, 0] = Q[1, 1] + A[1, 2] * eigenvalues[0]
Q[2, 0] = (A[0, 0] - eigenvalues[0]) * (A[1, 1] - eigenvalues[0]) - Q[2, 1]
norm = Q[0, 0] * Q[0, 0] + Q[1, 0] * Q[1, 0] + Q[2, 0] * Q[2, 0]
norm = ops.sqrt(1.0 / norm)
Q[0, 0] *= norm
Q[1, 0] *= norm
Q[2, 0] *= norm
Q[0, 1] = Q[0, 1] + A[0, 2] * eigenvalues[1]
Q[1, 1] = Q[1, 1] + A[1, 2] * eigenvalues[1]
Q[2, 1] = (A[0, 0] - eigenvalues[1]) * (A[1, 1] - eigenvalues[1]) - Q[2, 1]
norm = Q[0, 1] * Q[0, 1] + Q[1, 1] * Q[1, 1] + Q[2, 1] * Q[2, 1]
norm = ops.sqrt(1.0 / norm)
Q[0, 1] *= norm
Q[1, 1] *= norm
Q[2, 1] *= norm
Q[0, 2] = Q[1, 0] * Q[2, 1] - Q[2, 0] * Q[1, 1]
Q[1, 2] = Q[2, 0] * Q[0, 1] - Q[0, 0] * Q[2, 1]
Q[2, 2] = Q[0, 0] * Q[1, 1] - Q[1, 0] * Q[0, 1]
return eigenvalues, Q
def __getitem__(self, key):
self._initialize_host_accessors()
key = self.g2r_field[key]
key = self._pad_key(key)
return Matrix(self._host_access(key), is_ref=True)
def decl_matrix_arg(matrixtype):
return Matrix(
[[decl_scalar_arg(matrixtype.dtype) for _ in range(matrixtype.m)]
for _ in range(matrixtype.n)])
def func__(*args):
assert len(args) == len(
self.argument_annotations
), f'{len(self.argument_annotations)} arguments needed but {len(args)} provided'
tmps = []
callbacks = []
has_external_arrays = False
has_torch = has_pytorch()
actual_argument_slot = 0
launch_ctx = t_kernel.make_launch_context()
for i, v in enumerate(args):
needed = self.argument_annotations[i]
if isinstance(needed, template):
continue
provided = type(v)
# Note: do not use sth like "needed == f32". That would be slow.
if id(needed) in primitive_types.real_type_ids:
if not isinstance(v, (float, int)):
raise TaichiRuntimeTypeError.get(
i, needed.to_string(), provided)
launch_ctx.set_arg_float(actual_argument_slot, float(v))
elif id(needed) in primitive_types.integer_type_ids:
if not isinstance(v, int):
raise TaichiRuntimeTypeError.get(
i, needed.to_string(), provided)
launch_ctx.set_arg_int(actual_argument_slot, int(v))
elif isinstance(needed, sparse_matrix_builder):
# Pass only the base pointer of the ti.types.sparse_matrix_builder() argument
launch_ctx.set_arg_int(actual_argument_slot, v._get_addr())
elif isinstance(needed,
ndarray_type.NdarrayType) and isinstance(
v, taichi.lang._ndarray.Ndarray):
has_external_arrays = True
v = v.arr
launch_ctx.set_arg_ndarray(actual_argument_slot, v)
elif isinstance(
needed,
ndarray_type.NdarrayType) and (self.match_ext_arr(v)):
has_external_arrays = True
is_numpy = isinstance(v, np.ndarray)
if is_numpy:
tmp = np.ascontiguousarray(v)
# Purpose: DO NOT GC |tmp|!
tmps.append(tmp)
launch_ctx.set_arg_external_array_with_shape(
actual_argument_slot, int(tmp.ctypes.data),
tmp.nbytes, v.shape)
else:
is_ndarray = False
tmp, torch_callbacks = self.get_torch_callbacks(
v, has_torch, is_ndarray)
callbacks += torch_callbacks
launch_ctx.set_arg_external_array_with_shape(
actual_argument_slot, int(tmp.data_ptr()),
tmp.element_size() * tmp.nelement(), v.shape)
elif isinstance(needed, MatrixType):
if id(needed.dtype) in primitive_types.real_type_ids:
for a in range(needed.n):
for b in range(needed.m):
if not isinstance(v[a, b], (int, float)):
raise TaichiRuntimeTypeError.get(
i, needed.dtype.to_string(),
type(v[a, b]))
launch_ctx.set_arg_float(
actual_argument_slot, float(v[a, b]))
actual_argument_slot += 1
elif id(needed.dtype) in primitive_types.integer_type_ids:
for a in range(needed.n):
for b in range(needed.m):
if not isinstance(v[a, b], int):
raise TaichiRuntimeTypeError.get(
i, needed.dtype.to_string(),
type(v[a, b]))
launch_ctx.set_arg_int(actual_argument_slot,
int(v[a, b]))
actual_argument_slot += 1
else:
raise ValueError(
f'Matrix dtype {needed.dtype} is not integer type or real type.'
)
continue
else:
raise ValueError(
f'Argument type mismatch. Expecting {needed}, got {type(v)}.'
)
actual_argument_slot += 1
# Both the class kernels and the plain-function kernels are unified now.
# In both cases, |self.grad| is another Kernel instance that computes the
# gradient. For class kernels, args[0] is always the kernel owner.
if not self.is_grad and self.runtime.target_tape and not self.runtime.grad_replaced:
self.runtime.target_tape.insert(self, args)
if actual_argument_slot > 8 and (
impl.current_cfg().arch == _ti_core.opengl
or impl.current_cfg().arch == _ti_core.cc):
raise TaichiRuntimeError(
f"The number of elements in kernel arguments is too big! Do not exceed 8 on {_ti_core.arch_name(impl.current_cfg().arch)} backend."
)
if actual_argument_slot > 64 and (
(impl.current_cfg().arch != _ti_core.opengl
and impl.current_cfg().arch != _ti_core.cc)):
raise TaichiRuntimeError(
f"The number of elements in kernel arguments is too big! Do not exceed 64 on {_ti_core.arch_name(impl.current_cfg().arch)} backend."
)
try:
t_kernel(launch_ctx)
except Exception as e:
e = handle_exception_from_cpp(e)
raise e from None
ret = None
ret_dt = self.return_type
has_ret = ret_dt is not None
if has_ret or (impl.current_cfg().async_mode
and has_external_arrays):
runtime_ops.sync()
if has_ret:
if id(ret_dt) in primitive_types.integer_type_ids:
ret = t_kernel.get_ret_int(0)
elif id(ret_dt) in primitive_types.real_type_ids:
ret = t_kernel.get_ret_float(0)
elif id(ret_dt.dtype) in primitive_types.integer_type_ids:
it = iter(t_kernel.get_ret_int_tensor(0))
ret = Matrix([[next(it) for _ in range(ret_dt.m)]
for _ in range(ret_dt.n)])
else:
it = iter(t_kernel.get_ret_float_tensor(0))
ret = Matrix([[next(it) for _ in range(ret_dt.m)]
for _ in range(ret_dt.n)])
if callbacks:
for c in callbacks:
c()
return ret