Version: develop

# 稀疏矩阵

Sparse matrices are frequently involved in solving linear systems in science and engineering. Taichi provides useful APIs for sparse matrices on the CPU and CUDA backends.

To use sparse matrices in Taichi programs, follow these three steps:

1. Create a `builder` using `ti.linalg.SparseMatrixBuilder()`.
2. Call `ti.kernel` to fill the `builder` with your matrices' data.
3. Build sparse matrices from the `builder`.
##### WARNING

The sparse matrix feature is still under development. 以下是一些限制：

• The sparse matrix data type on the CPU backend only supports `f32` and `f64`.
• The sparse matrix data type on the CUDA backend only supports `f32`.
``import taichi as tiarch = ti.cpu # or ti.cudati.init(arch=arch)n = 4# step 1: create sparse matrix builderK = ti.linalg.SparseMatrixBuilder(n, n, max_num_triplets=100)@ti.kerneldef fill(A: ti.types.sparse_matrix_builder()):    for i in range(n):        A[i, i] += 1  # Only +=  and -= operators are supported for now.# step 2: 填充 builderfill(K)print(">>>> K.print_triplets()")K.print_triplets()# outputs:# >>>> K.print_triplets()# n=4, m=4, num_triplets=4 (max=100)(0, 0) val=1.0(1, 1) val=1.0(2, 2) val=1.0(3, 3) val=1.0# step 3: 由builder创建稀疏矩阵.A = K.build()print(">>>> A = K.build()")print(A)# outputs:# >>>> A = K.build()# [1, 0, 0, 0]# [0, 1, 0, 0]# [0, 0, 1, 0]# [0, 0, 0, 1]``

``print(">>>> Summation: C = A + A")C = A + Aprint(C)# outputs:# >>>> Summation: C = A + A# [2, 0, 0, 0]# [0, 2, 0, 0]# [0, 0, 2, 0]# [0, 0, 0, 2]print(">>>> Subtraction: D = A - A")D = A - Aprint(D)# outputs:# >>>> Subtraction: D = A - A# [0, 0, 0, 0]# [0, 0, 0, 0]# [0, 0, 0, 0]# [0, 0, 0, 0]print(">>>> Multiplication with a scalar on the right: E = A * 3.0")E = A * 3.0print(E)# outputs:# >>>> Multiplication with a scalar on the right: E = A * 3.0# [3, 0, 0, 0]# [0, 3, 0, 0]# [0, 0, 3, 0]# [0, 0, 0, 3]print(">>>> Multiplication with a scalar on the left: E = 3.0 * A")E = 3.0 * Aprint(E)# outputs:# >>>> Multiplication with a scalar on the left: E = 3.0 * A# [3, 0, 0, 0]# [0, 3, 0, 0]# [0, 0, 3, 0]# [0, 0, 0, 3]print(">>>> Transpose: F = A.transpose()")F = A.transpose()print(F)# outputs:# >>>> Transpose: F = A.transpose()# [1, 0, 0, 0]# [0, 1, 0, 0]# [0, 0, 1, 0]# [0, 0, 0, 1]print(">>>> Matrix multiplication: G = E @ A")G = E @ Aprint(G)# outputs:# >>>> Matrix multiplication: G = E @ A# [3, 0, 0, 0]# [0, 3, 0, 0]# [0, 0, 3, 0]# [0, 0, 0, 3]print(">>>> Element-wise multiplication: H = E * A")H = E * Aprint(H)# outputs:# >>>> Element-wise multiplication: H = E * A# [3, 0, 0, 0]# [0, 3, 0, 0]# [0, 0, 3, 0]# [0, 0, 0, 3]print(f">>>> Element Access: A[0,0] = {A[0,0]}")# outputs:# >>>> Element Access: A[0,0] = 1.0``