Merge pull request #1 from prashantsinalkar/masterHEADmaster

Added R TBC

1 files changed, 67 insertions, 0 deletions

diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.4.2/Ex3.4_2.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.4.2/Ex3.4_2.r
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+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.4.2/Ex3.4_2.r
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+# Packages used  : pracma
+# To install pracma,type following in command line while connected to internet
+# install.packages("pracma") 
+# package can be included by command " library(pracma) "
+# for more information about pracma visit https://cran.r-project.org/web/packages/pracma/index.html
+
+# Example : 2   Chapter : 3.4     Page No: 158
+# Find the particular solution and special solution of the given system
+
+library(pracma)
+nullspacebasis <- function(A){
+  R<-rref(A)
+  m<-nrow(A)
+  n<-ncol(A)
+  pivotcol<-c() #vector to store the column numbers of pivot columns
+  freecol<-c()  #vector to store the column numbers of free columns
+  i<-1
+  j<-1
+  
+  # to find which columns are pivot and which are free
+  while(i<=m & j<=n){
+    if(R[i,j]==1){
+      pivotcol<-c(pivotcol,j)
+      i<-i+1
+      j<-j+1
+    }
+    else{
+      j<-j+1
+    }
+  }
+  y<-length(pivotcol)
+  freecol<-c(1:n)
+  freecol<-freecol[!freecol%in%pivotcol]
+  x<-length(freecol)
+  N<-c()
+  #find the basis for null space based on Row reduced echelon form of given matrix
+  if(y==n){
+    return(N)
+  }
+  for(i in 1:x){
+    temp<-c(1:n)
+    for(j in 1:x){
+      temp[freecol[j]]<-0
+    }
+    temp[freecol[i]]<-1
+    temp[freecol[i]]
+    for(j in 1:y){
+      temp[pivotcol[j]]<-R[j,freecol[i]]*-1
+    }
+    N<-c(N,temp)
+  }
+  N<-matrix(N,nrow=n,ncol=x)
+  #Basis for the nullspace of given matrix
+  return(N)
+}
+A<-matrix(c(1,1,1,2,1,-1),nrow=2)
+b<-c(3,4)
+s<-nullspacebasis(A)
+Ab<-cbind(A,b)
+Rd<-rref(Ab)
+p<-Rd[,4]
+p<-c(p,0)
+print("Particualar solution is")
+print(p)
+print("special solution is ")
+print(s)
+print("The complete solution = particular solution + special solution")