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Systems and methods for a combined matrix-vector and matrix transpose vector multiply for a block-sparse matrix
Systems and methods for a combined matrix-vector and matrix transpose vector multiply for a block-sparse matrix
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机译：用于块稀疏矩阵的组合矩阵向量和矩阵转置向量相乘的系统和方法
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摘要
Systems and methods for combined matrix-vector and matrix-transpose vector multiply for block sparse matrices. Exemplary embodiments include a method of updating a simulation of physical objects in an interactive computer, including generating a set of representations of objects in the interactive computer environment, partitioning the set of representations into a plurality of subsets such that objects in any given set interact only with other objects in that set, generating a vector b describing an expected position of each object at the end of a time interval h, applying a biconjugate gradient algorithm to solve A*Δv=b for the vector Δv of position and velocity changes to be applied to each object wherein the q=Ap and qt=AT(pt) calculations are combined so that A only has to be read once, integrating the updated motion vectors to determine a next state of the simulated objects, and converting the simulated objects to a visual.
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机译：用于块稀疏矩阵的组合矩阵矢量和矩阵转置矢量相乘的系统和方法。示例性实施例包括一种更新交互式计算机中的物理对象的仿真的方法，该方法包括在交互式计算机环境中生成对象的表示集，将该表示集划分为多个子集，使得任何给定集合中的对象仅进行交互与该集合中的其他对象一起，生成描述每个对象在时间间隔h末尾的预期位置的向量b，应用双共轭梯度算法对位置和速度变化的向量Δv求解A *Δv= b应用于每个对象，其中q = Ap和qt = A T （pt）计算被组合，使得A仅需读取一次，对更新后的运动矢量进行积分即可确定模拟的下一个状态对象，并将模拟对象转换为视觉对象。
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