def inverse(self):
assert self.n == self.m, 'Only square matrices are invertible'
if self.n == 1:
return Matrix([1 / self(0, 0)])
elif self.n == 2:
inv_det = impl.expr_init(1.0 / self.determinant(self))
return inv_det * Matrix([[self(1, 1), -self(0, 1)],
[-self(1, 0), self(0, 0)]])
elif self.n == 3:
n = 3
import taichi as ti
inv_determinant = ti.expr_init(1.0 / ti.determinant(self))
entries = [[0] * n for _ in range(n)]
def E(x, y):
return self(x % n, y % n)
for i in range(n):
for j in range(n):
entries[j][i] = ti.expr_init(
inv_determinant * (E(i + 1, j + 1) * E(i + 2, j + 2) -
E(i + 2, j + 1) * E(i + 1, j + 2)))
return Matrix(entries)
else:
raise Exception(
"Inversions of matrices with sizes >= 4 are not supported")
def build_assign_annotated(ctx, target, value, is_static_assign,
annotation):
"""Build an annotated assginment like this: target: annotation = value.
Args:
ctx (ast_builder_utils.BuilderContext): The builder context.
target (ast.Name): A variable name. `target.id` holds the name as
a string.
annotation: A type we hope to assign to the target
value: A node representing the value.
is_static_assign: A boolean value indicating whether this is a static assignment
"""
is_local = isinstance(target, ast.Name)
anno = ti.expr_init(annotation)
if is_static_assign:
raise TaichiSyntaxError(
"Static assign cannot be used on annotated assignment")
if is_local and not ctx.is_var_declared(target.id):
var = ti.cast(value, anno)
var = ti.expr_init(var)
ctx.create_variable(target.id, var)
else:
var = target.ptr
if var.ptr.get_ret_type() != anno:
raise TaichiSyntaxError(
"Static assign cannot have type overloading")
var.assign(value)
return var
def build_grouped_ndrange_for(ctx, node):
with ctx.variable_scope_guard():
ndrange_var = ti.expr_init(build_stmt(ctx, node.iter.args[0]).ptr)
ndrange_begin = ti.cast(ti.Expr(0), ti.i32)
ndrange_end = ti.cast(
ti.Expr(ti.subscript(ndrange_var.acc_dimensions, 0)), ti.i32)
ndrange_loop_var = ti.Expr(ti.core.make_id_expr(''))
ti.core.begin_frontend_range_for(ndrange_loop_var.ptr,
ndrange_begin.ptr,
ndrange_end.ptr)
targets = IRBuilder.get_for_loop_targets(node)
if len(targets) != 1:
raise TaichiSyntaxError(
f"Group for should have 1 loop target, found {len(targets)}"
)
target = targets[0]
target_var = ti.expr_init(
ti.Vector([0] * len(ndrange_var.dimensions), dt=ti.i32))
ctx.create_variable(target, target_var)
I = ti.expr_init(ndrange_loop_var)
for i in range(len(ndrange_var.dimensions)):
if i + 1 < len(ndrange_var.dimensions):
target_tmp = I // ndrange_var.acc_dimensions[i + 1]
else:
target_tmp = I
ti.subscript(target_var,
i).assign(target_tmp + ndrange_var.bounds[i][0])
if i + 1 < len(ndrange_var.dimensions):
I.assign(I -
target_tmp * ndrange_var.acc_dimensions[i + 1])
node.body = build_stmts(ctx, node.body)
ti.core.end_frontend_range_for()
return node
def build_ndrange_for(ctx, node):
with ctx.variable_scope_guard():
ndrange_var = ti.expr_init(build_stmt(ctx, node.iter).ptr)
ndrange_begin = ti.cast(ti.Expr(0), ti.i32)
ndrange_end = ti.cast(
ti.Expr(ti.subscript(ndrange_var.acc_dimensions, 0)), ti.i32)
ndrange_loop_var = ti.Expr(ti.core.make_id_expr(''))
ti.core.begin_frontend_range_for(ndrange_loop_var.ptr,
ndrange_begin.ptr,
ndrange_end.ptr)
I = ti.expr_init(ndrange_loop_var)
targets = IRBuilder.get_for_loop_targets(node)
for i, target in enumerate(targets):
if i + 1 < len(targets):
target_tmp = ti.expr_init(
I // ndrange_var.acc_dimensions[i + 1])
else:
target_tmp = ti.expr_init(I)
ctx.create_variable(
target,
ti.expr_init(
target_tmp +
ti.subscript(ti.subscript(ndrange_var.bounds, i), 0)))
if i + 1 < len(targets):
I.assign(I -
target_tmp * ndrange_var.acc_dimensions[i + 1])
node.body = build_stmts(ctx, node.body)
ti.core.end_frontend_range_for()
return node
def svd3d(A, dt, iters=None):
assert A.n == 3 and A.m == 3
inputs = tuple([e.ptr for e in A.entries])
assert dt in [ti.f32, ti.f64]
if iters is None:
if dt == ti.f32:
iters = 5
else:
iters = 8
if dt == ti.f32:
rets = ti.core.sifakis_svd_f32(*inputs, iters)
else:
rets = ti.core.sifakis_svd_f64(*inputs, iters)
assert len(rets) == 21
U_entries = rets[:9]
V_entries = rets[9:18]
sig_entries = rets[18:]
U = ti.expr_init(ti.Matrix.zero(dt, 3, 3))
V = ti.expr_init(ti.Matrix.zero(dt, 3, 3))
sigma = ti.expr_init(ti.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 pow(self, power):
import taichi as ti
if not isinstance(power, int):
return raw_pow(self, power)
if power == 0:
# TODO: remove the hack, use {Expr,Matrix}.dup().fill(1)
# also note that this can be solved by #940
return self * 0 + Expr(1)
negative = power < 0
# Why not simply use `power = abs(power)`?
# Because `abs` is overrided by the `ti.abs` above.
if negative:
power = -power
tmp = self
ret = None
while power:
if power & 1:
if ret is None:
ret = tmp
else:
ret = ti.expr_init(ret * tmp)
tmp = ti.expr_init(tmp * tmp)
power >>= 1
if negative:
return 1 / ret
else:
return ret
def inverse(self):
assert self.n == self.m, 'Only square matrices are invertible'
if self.n == 1:
return Matrix([1 / self(0, 0)])
elif self.n == 2:
inv_det = impl.expr_init(1.0 / self.determinant())
# Discussion: https://github.com/taichi-dev/taichi/pull/943#issuecomment-626344323
return inv_det * Matrix([[self(1, 1), -self(0, 1)],
[-self(1, 0), self(0, 0)]]).variable()
elif self.n == 3:
n = 3
import taichi as ti
inv_determinant = ti.expr_init(1.0 / self.determinant())
entries = [[0] * n for _ in range(n)]
def E(x, y):
return self(x % n, y % n)
for i in range(n):
for j in range(n):
entries[j][i] = ti.expr_init(
inv_determinant * (E(i + 1, j + 1) * E(i + 2, j + 2) -
E(i + 2, j + 1) * E(i + 1, j + 2)))
return Matrix(entries)
elif self.n == 4:
n = 4
import taichi as ti
inv_determinant = ti.expr_init(1.0 / self.determinant())
entries = [[0] * n for _ in range(n)]
def E(x, y):
return self(x % n, y % n)
for i in range(n):
for j in range(n):
entries[j][i] = ti.expr_init(
inv_determinant * (-1)**(i + j) *
((E(i + 1, j + 1) *
(E(i + 2, j + 2) * E(i + 3, j + 3) -
E(i + 3, j + 2) * E(i + 2, j + 3)) -
E(i + 2, j + 1) *
(E(i + 1, j + 2) * E(i + 3, j + 3) -
E(i + 3, j + 2) * E(i + 1, j + 3)) +
E(i + 3, j + 1) *
(E(i + 1, j + 2) * E(i + 2, j + 3) -
E(i + 2, j + 2) * E(i + 1, j + 3)))))
return Matrix(entries)
else:
raise Exception(
"Inversions of matrices with sizes >= 5 are not supported")
def build_IfExp(ctx, node):
node.test = build_stmt(ctx, node.test)
node.body = build_stmt(ctx, node.body)
node.orelse = build_stmt(ctx, node.orelse)
if ti.is_taichi_class(node.test.ptr) or ti.is_taichi_class(
node.body.ptr) or ti.is_taichi_class(node.orelse.ptr):
node.ptr = ti.select(node.test.ptr, node.body.ptr, node.orelse.ptr)
return node
is_static_if = (IRBuilder.get_decorator(ctx, node.test) == "static")
if is_static_if:
if node.test.ptr:
node.body = build_stmt(ctx, node.body)
node.ptr = node.body.ptr
else:
node.orelse = build_stmt(ctx, node.orelse)
node.ptr = node.orelse.ptr
return node
val = ti.expr_init(None)
ti.begin_frontend_if(node.test.ptr)
ti.core.begin_frontend_if_true()
val.assign(node.body.ptr)
ti.core.pop_scope()
ti.core.begin_frontend_if_false()
val.assign(node.orelse.ptr)
ti.core.pop_scope()
node.ptr = val
return node
def build_IfExp(ctx, node):
build_stmt(ctx, node.test)
build_stmt(ctx, node.body)
build_stmt(ctx, node.orelse)
if ti.is_taichi_class(node.test.ptr) or ti.is_taichi_class(
node.body.ptr) or ti.is_taichi_class(node.orelse.ptr):
node.ptr = ti.select(node.test.ptr, node.body.ptr, node.orelse.ptr)
return node.ptr
is_static_if = (ASTTransformer.get_decorator(ctx,
node.test) == "static")
if is_static_if:
if node.test.ptr:
node.ptr = build_stmt(ctx, node.body)
else:
node.ptr = build_stmt(ctx, node.orelse)
return node.ptr
val = ti.expr_init(None)
ti.begin_frontend_if(node.test.ptr)
_ti_core.begin_frontend_if_true()
val.assign(node.body.ptr)
_ti_core.pop_scope()
_ti_core.begin_frontend_if_false()
val.assign(node.orelse.ptr)
_ti_core.pop_scope()
node.ptr = val
return node.ptr
def _vector_getattr(self, key):
ret = []
stk = []
for k in key:
sgn = 0
i = 0
if k != '_':
sgn = 1
i = 'xyzw'.find(k)
if i == -1:
sgn = -1
i = 'XYZW'.find(k)
if i == -1:
break
stk.append((i, sgn))
else:
for i, sgn in stk:
if ti.inside_kernel():
t = self.subscript(i) * sgn
ret.append(ti.expr_init(t))
else:
t = self[i] * sgn
ret.append(t)
return ti.Vector(ret)
_taichi_skip_traceback = 1
raise AttributeError(f"'Matrix' object has no attribute {key}")
def determinant(a):
if a.n == 2 and a.m == 2:
return a(0, 0) * a(1, 1) - a(0, 1) * a(1, 0)
elif a.n == 3 and a.m == 3:
return a(0, 0) * (a(1, 1) * a(2, 2) - a(2, 1) * a(1, 2)) - a(
1, 0) * (a(0, 1) * a(2, 2) - a(2, 1) * a(0, 2)) + a(
2, 0) * (a(0, 1) * a(1, 2) - a(1, 1) * a(0, 2))
elif a.n == 4 and a.m == 4:
import taichi as ti
n = 4
def E(x, y):
return a(x % n, y % n)
det = ti.expr_init(0.0)
for i in range(4):
det = det + (-1.0)**i * (
a(i, 0) *
(E(i + 1, 1) *
(E(i + 2, 2) * E(i + 3, 3) - E(i + 3, 2) * E(i + 2, 3)) -
E(i + 2, 1) *
(E(i + 1, 2) * E(i + 3, 3) - E(i + 3, 2) * E(i + 1, 3)) +
E(i + 3, 1) *
(E(i + 1, 2) * E(i + 2, 3) - E(i + 2, 2) * E(i + 1, 3))))
return det
else:
raise Exception(
"Determinants of matrices with sizes >= 5 are not supported")
def __pow__(self, power, modulo=None):
import taichi as ti
if not isinstance(power, int) or abs(power) > 100:
return Expr(taichi_lang_core.expr_pow(self.ptr, Expr(power).ptr))
if power == 0:
return Expr(1)
negative = power < 0
power = abs(power)
tmp = self
ret = None
while power:
if power & 1:
if ret is None:
ret = tmp
else:
ret = ti.expr_init(ret * tmp)
tmp = ti.expr_init(tmp * tmp)
power >>= 1
if negative:
return 1 / ret
else:
return ret
def __pow__(self, power, modulo=None):
import taichi as ti
if ti.is_taichi_class(power):
return power.element_wise_binary(lambda x, y: pow(y, x), self)
if not isinstance(power, int) or abs(power) > 100:
return Expr(taichi_lang_core.expr_pow(self.ptr, Expr(power).ptr))
if power == 0:
return Expr(1)
negative = power < 0
power = abs(power)
tmp = self
ret = None
while power:
if power & 1:
if ret is None:
ret = tmp
else:
ret = ti.expr_init(ret * tmp)
tmp = ti.expr_init(tmp * tmp)
power >>= 1
if negative:
return 1 / ret
else:
return ret
def build_assign_basic(ctx, target, value):
"""Build basic assginment like this: target = value.
Args:
ctx (ast_builder_utils.BuilderContext): The builder context.
target (ast.Name): A variable name. `target.id` holds the name as
a string.
value: A node representing the value.
"""
is_local = isinstance(target, ast.Name)
if is_local and not ctx.is_var_declared(target.id):
ctx.create_variable(target.id, ti.expr_init(value))
else:
var = target.ptr
var.assign(value)
def polygonise(self, triangles: ti.template()):
numOftriangle = 0;
cubeIndex = 0;
vertlist = [ti.expr_init(ti.Vector.zero(float, 3)) for t in range(12)] # 保存等值面与立方体各边相交的坐标
# 确定那个顶点位于等值面内部
if (grid.val[0] < 1): cubeIndex |= 1;
if (grid.val[1] < 1): cubeIndex |= 2;
if (grid.val[2] < 1): cubeIndex |= 4;
if (grid.val[3] < 1): cubeIndex |= 8;
if (grid.val[4] < 1): cubeIndex |= 16;
if (grid.val[5] < 1): cubeIndex |= 32;
if (grid.val[6] < 1): cubeIndex |= 64;
if (grid.val[7] < 1): cubeIndex |= 128;
# 异常：立方体所有顶点都在或者都不在等值面内部
if (self.edgeTable[cubeIndex] != 0):
# 确定等值面与立方体交点坐标
if (edgeTable[cubeIndex] & 1):
vertlist[0] = self.vertex_interp(grid.p[0],grid.p[1],grid.val[0],grid.val[1]);
if (edgeTable[cubeIndex] & 2):
vertlist[1] = self.vertex_interp(grid.p[1],grid.p[2],grid.val[1],grid.val[2]);
if (edgeTable[cubeIndex] & 4):
vertlist[2] = self.vertex_interp(grid.p[2],grid.p[3],grid.val[2],grid.val[3]);
if (edgeTable[cubeIndex] & 8):
vertlist[3] = self.vertex_interp(grid.p[3],grid.p[0],grid.val[3],grid.val[0]);
if (edgeTable[cubeIndex] & 16):
vertlist[4] = self.vertex_interp(grid.p[4],grid.p[5],grid.val[4],grid.val[5]);
if (edgeTable[cubeIndex] & 32):
vertlist[5] = self.vertex_interp(grid.p[5],grid.p[6],grid.val[5],grid.val[6]);
if (edgeTable[cubeIndex] & 64):
vertlist[6] = self.vertex_interp(grid.p[6],grid.p[7],grid.val[6],grid.val[7]);
if (edgeTable[cubeIndex] & 128):
vertlist[7] = self.vertex_interp(grid.p[7],grid.p[4],grid.val[7],grid.val[4]);
if (edgeTable[cubeIndex] & 256):
vertlist[8] = self.vertex_interp(grid.p[0],grid.p[4],grid.val[0],grid.val[4]);
if (edgeTable[cubeIndex] & 512):
vertlist[9] = self.vertex_interp(grid.p[1],grid.p[5],grid.val[1],grid.val[5]);
if (edgeTable[cubeIndex] & 1024):
vertlist[10] = self.vertex_interp(grid.p[2],grid.p[6],grid.val[2],grid.val[6]);
if (edgeTable[cubeIndex] & 2048):
vertlist[11] = self.vertex_interp(grid.p[3],grid.p[7],grid.val[3],grid.val[7]);
//根据交点坐标确定三角形面片，并进行保存
for (int i=0; triTable[cubeIndex][i] != -1; i+=3):
tri[numOftriangle].p[0] = vertlist[ triTable[cubeIndex][i ] ];
tri[numOftriangle].p[1] = vertlist[ triTable[cubeIndex][i+1] ];
tri[numOftriangle].p[2] = vertlist[ triTable[cubeIndex][i+2] ];
numOftriangle++;
def build_short_circuit_or(operands):
if len(operands) == 1:
return operands[0].ptr
val = ti.expr_init(None)
lhs = operands[0].ptr
ti.begin_frontend_if(lhs)
_ti_core.begin_frontend_if_true()
val.assign(1)
_ti_core.pop_scope()
_ti_core.begin_frontend_if_false()
rhs = ASTTransformer.build_short_circuit_or(operands[1:])
val.assign(rhs)
_ti_core.pop_scope()
return val
def build_assign_basic(ctx, target, value, is_static_assign):
"""Build basic assginment like this: target = value.
Args:
ctx (ast_builder_utils.BuilderContext): The builder context.
target (ast.Name): A variable name. `target.id` holds the name as
a string.
value: A node representing the value.
is_static_assign: A boolean value indicating whether this is a static assignment
"""
is_local = isinstance(target, ast.Name)
if is_static_assign:
if not is_local:
raise TaichiSyntaxError(
"Static assign cannot be used on elements in arrays")
ctx.create_variable(target.id, value)
var = value
elif is_local and not ctx.is_var_declared(target.id):
var = ti.expr_init(value)
ctx.create_variable(target.id, var)
else:
var = target.ptr
var.assign(value)
return var
def atomic_add(self, other): import taichi as ti other_ptr = ti.wrap_scalar(other).ptr return ti.expr_init(taichi_lang_core.expr_atomic_add(self.ptr, other_ptr))
def shuffle(a, *ks):
ret = []
for k in ks:
t = a.subscript(k)
ret.append(ti.expr_init(t))
return ti.Vector(ret)
def all(self):
import taichi as ti
ret = self.entries[0] != ti.expr_init(0)
for i in range(1, len(self.entries)):
ret = ret + (self.entries[i] != ti.expr_init(0))
return -(ret == ti.expr_init(-len(self.entries)))
def append(l, indices, val):
import taichi as ti
a = ti.expr_init(
ti_core.insert_append(l.snode.ptr, make_expr_group(indices),
Expr(val).ptr))
return a
def variable(self):
return self.__class__(*(ti.expr_init(e) for e in self.entries))
def __init__(self):
self.p = [ti.expr_init(ti.Vector.zero(int, 3)) for t in range(8)]
self.val = [ti.expr_init(0.0) for t in range(8)]
def assign(self, value):
self.parent[self.name] = ti.expr_init(value)
def __isub__(self, other): # TODO: add atomic_sub() import taichi as ti ti.expr_init(taichi_lang_core.expr_atomic_sub(self.ptr, other.ptr))
def __init__(self, **kwargs):
res = dict()
for k, v in kwargs.items():
res[k] = ti.expr_init(v)
super().__init__(res)