| #------------------------------------------------------------- |
| # |
| # Licensed to the Apache Software Foundation (ASF) under one |
| # or more contributor license agreements. See the NOTICE file |
| # distributed with this work for additional information |
| # regarding copyright ownership. The ASF licenses this file |
| # to you under the Apache License, Version 2.0 (the |
| # "License"); you may not use this file except in compliance |
| # with the License. You may obtain a copy of the License at |
| # |
| # http://www.apache.org/licenses/LICENSE-2.0 |
| # |
| # Unless required by applicable law or agreed to in writing, |
| # software distributed under the License is distributed on an |
| # "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY |
| # KIND, either express or implied. See the License for the |
| # specific language governing permissions and limitations |
| # under the License. |
| # |
| #------------------------------------------------------------- |
| |
| # Lanczos algorithm to compute eigen vectors and eigen values of a square matrix |
| |
| A = read($1); # input data, must be a square matrix |
| |
| m = nrow(A); |
| v0 = matrix(0, m, 1); |
| v1 = Rand(rows=m, cols=1); |
| v1 = sqrt(v1/sum(v1)); # vector with norm 1 |
| |
| T = matrix(0, m, m); |
| TV = matrix(0, m, m); |
| |
| # Lanczos iterations to compute Tri-Diagonal Matrix |
| beta = 0; |
| for(i in seq(1,m)) { |
| if (i == m) { |
| w1 = A %*% v1; |
| alpha = sum(w1*v1); |
| T[m, m] = alpha; |
| } else { |
| w1 = A %*% v1; |
| alpha = sum(w1*v1); |
| w1 = w1 - alpha*v1 - beta*v0; |
| beta = sqrt(sum(w1^2)); |
| v0 = v1; |
| v1 = w1/beta |
| |
| T[i, i] = alpha; |
| T[i+1, i] = beta; |
| T[i, i+1] = beta; |
| } |
| TV[,i] = v1; |
| } |
| # compute eigen vectors of Tri-diagonal matrix |
| [eval, tevec] = eigen(T) |
| # compute eigen vectors of Tri-diagonal matrix |
| evec = TV %*% tevec; |
| |
| # output data |
| write(eval, $2); |
| write(evec, $3); |