本文共 4767 字，大约阅读时间需要 15 分钟。
backsolve(r, x, k = ncol(r), upper.tri = TRUE, transpose = FALSE) forwardsolve(l, x, k = ncol(l), upper.tri = FALSE, transpose = FALSE)
> A=matrix(1:9,3,3)> A [,1] [,2] [,3][1,] 1 4 7[2,] 2 5 8[3,] 3 6 9> x=c(1,2,3)> x[1] 1 2 3> B=A> upper.tri(B) [,1] [,2] [,3][1,] FALSE TRUE TRUE[2,] FALSE FALSE TRUE[3,] FALSE FALSE FALSE> B[upper.tri(B)]=0 # 使用upper.tri将上三角设置为0> B [,1] [,2] [,3][1,] 1 0 0[2,] 2 5 0[3,] 3 6 9> C=A> lower.tri(C) [,1] [,2] [,3][1,] FALSE FALSE FALSE[2,] TRUE FALSE FALSE[3,] TRUE TRUE FALSE> C[lower.tri(C)]=0 # 使用lower.tri将下三角设置为0> C [,1] [,2] [,3][1,] 1 4 7[2,] 0 5 8[3,] 0 0 9> backsolve(A,x,upper.tri=T,transpose=T) # 参数upper.tri=T表示保留上三角, 即下三角为0[1] 1.00000000 -0.40000000 -0.08888889 # transpose=T 表示对"执行上三角值保留后的值"进行行列转换结果和solve(t(C),x)一致.> solve(t(C),x)[1] 1.00000000 -0.40000000 -0.08888889> backsolve(A,x,upper.tri=T,transpose=F) # 参数upper.tri=T表示保留上三角, 即下三角为0[1] -0.8000000 -0.1333333 0.3333333 # transpose=F 表示对"执行上三角值保留后的值"不进行行列转换结果和solve(C,x)一致.> solve(C,x)[1] -0.8000000 -0.1333333 0.3333333> backsolve(A,x,upper.tri=F,transpose=T) # 参数upper.tri=F表示不保留上三角, 即上三角为0[1] 1.111307e-17 2.220446e-17 3.333333e-01> solve(t(B),x)[1] 1.110223e-17 2.220446e-17 3.333333e-01> backsolve(A,x,upper.tri=F,transpose=F) # 参数upper.tri=F表示不保留上三角, 即上三角为0[1] 1 0 0> solve(B,x)[1] 1.000000e+00 -1.540744e-33 -1.850372e-17
> A [,1] [,2] [,3][1,] 1 4 7[2,] 2 5 8[3,] 3 6 9> B [,1] [,2] [,3][1,] 1 0 0[2,] 2 5 0[3,] 3 6 9> C [,1] [,2] [,3][1,] 1 4 7[2,] 0 5 8[3,] 0 0 9> x[1] 1 2 3> forwardsolve(A,x,upper.tri=T,transpose=T)[1] 1.00000000 -0.40000000 -0.08888889> solve(t(C),x)[1] 1.00000000 -0.40000000 -0.08888889> forwardsolve(A,x,upper.tri=T,transpose=F)[1] -0.8000000 -0.1333333 0.3333333> solve(C,x)[1] -0.8000000 -0.1333333 0.3333333> forwardsolve(A,x,upper.tri=F,transpose=T)[1] 1.111307e-17 2.220446e-17 3.333333e-01> solve(t(B),x)[1] 1.110223e-17 2.220446e-17 3.333333e-01> forwardsolve(A,x,upper.tri=F,transpose=F)[1] 1 0 0> solve(B,x)[1] 1.000000e+00 -1.540744e-33 -1.850372e-17
backsolve package:base R DocumentationSolve an Upper or Lower Triangular SystemDescription: Solves a triangular system of linear equations.Usage: backsolve(r, x, k = ncol(r), upper.tri = TRUE, transpose = FALSE) forwardsolve(l, x, k = ncol(l), upper.tri = FALSE, transpose = FALSE) Arguments: r, l: an upper (or lower) triangular matrix giving the coefficients for the system to be solved. Values below (above) the diagonal are ignored. x: a matrix whose columns give the right-hand sides for the equations. k: The number of columns of ‘r’ and rows of ‘x’ to use.upper.tri: logical; if ‘TRUE’ (default), the _upper_ _tri_angular part of ‘r’ is used. Otherwise, the lower one.transpose: logical; if ‘TRUE’, solve r' * y = x for y, i.e., ‘t(r) %*% y == x’.Details: Solves a system of linear equations where the coefficient matrix is upper (or ‘right’, ‘R’) or lower (‘left’, ‘L’) triangular. ‘x <- backsolve (R, b)’ solves R x = b, and ‘x <- forwardsolve(L, b)’ solves L x = b, respectively. The ‘r’/‘l’ must have at least ‘k’ rows and columns, and ‘x’ must have at least ‘k’ rows. This is a wrapper for the level-3 BLAS routine ‘dtrsm’.Value: The solution of the triangular system. The result will be a vector if ‘x’ is a vector and a matrix if ‘x’ is a matrix.References: Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) _The New S Language_. Wadsworth & Brooks/Cole. Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W. (1978) _LINPACK Users Guide_. Philadelphia: SIAM Publications.See Also: ‘chol’, ‘qr’, ‘solve’.Examples: ## upper triangular matrix 'r': r <- rbind(c(1,2,3), c(0,1,1), c(0,0,2)) ( y <- backsolve(r, x <- c(8,4,2)) ) # -1 3 1 r %*% y # == x = (8,4,2) backsolve(r, x, transpose = TRUE) # 8 -12 -5
转载地址：http://unbva.baihongyu.com/