# module LUSolve

Solves a*x = b for x, using LU decomposition.

### Public Instance Methods

ludecomp(a,n,zero=0,one=1) click to toggle source

Performs LU decomposition of the n by n matrix a.

    # File lib/bigdecimal/ludcmp.rb, line 11
      def ludecomp(a,n,zero=0,one=1)
        prec = BigDecimal.limit(nil)
        ps     = []
        scales = []
        for i in 0...n do  # pick up largest(abs. val.) element in each row.
          ps <<= i
          nrmrow  = zero
          ixn = i*n
          for j in 0...n do
            biggst = a[ixn+j].abs
            nrmrow = biggst if biggst>nrmrow
          end
          if nrmrow>zero then
            scales <<= one.div(nrmrow,prec)
          else
            raise "Singular matrix"
          end
        end
        n1          = n - 1
        for k in 0...n1 do # Gaussian elimination with partial pivoting.
          biggst  = zero;
          for i in k...n do
            size = a[ps[i]*n+k].abs*scales[ps[i]]
            if size>biggst then
              biggst = size
              pividx  = i
            end
          end
          raise "Singular matrix" if biggst<=zero
          if pividx!=k then
            j = ps[k]
            ps[k] = ps[pividx]
            ps[pividx] = j
          end
          pivot   = a[ps[k]*n+k]
          for i in (k+1)...n do
            psin = ps[i]*n
            a[psin+k] = mult = a[psin+k].div(pivot,prec)
            if mult!=zero then
              pskn = ps[k]*n
              for j in (k+1)...n do
                a[psin+j] -= mult.mult(a[pskn+j],prec)
              end
            end
          end
        end
        raise "Singular matrix" if a[ps[n1]*n+n1] == zero
        ps
      end

      # Solves a*x = b for x, using LU decomposition.
      #
      # a is a matrix, b is a constant vector, x is the solution vector.
      #
      # ps is the pivot, a vector which indicates the permutation of rows performed
      # during LU decomposition.
      def lusolve(a,b,ps,zero=0.0)
        prec = BigDecimal.limit(nil)
        n = ps.size
        x = []
        for i in 0...n do
          dot = zero
          psin = ps[i]*n
          for j in 0...i do
            dot = a[psin+j].mult(x[j],prec) + dot
          end
          x <<= b[ps[i]] - dot
        end
        (n-1).downto(0) do |i|
          dot = zero
          psin = ps[i]*n
          for j in (i+1)...n do
            dot = a[psin+j].mult(x[j],prec) + dot
          end
          x[i]  = (x[i]-dot).div(a[psin+i],prec)
        end
        x
      end
    end

lusolve(a,b,ps,zero=0.0) click to toggle source

Solves a*x = b for x, using LU decomposition.

a is a matrix, b is a constant vector, x is the solution vector.

ps is the pivot, a vector which indicates the permutation of rows performed during LU decomposition.

    # File lib/bigdecimal/ludcmp.rb, line 67
      def lusolve(a,b,ps,zero=0.0)
        prec = BigDecimal.limit(nil)
        n = ps.size
        x = []
        for i in 0...n do
          dot = zero
          psin = ps[i]*n
          for j in 0...i do
            dot = a[psin+j].mult(x[j],prec) + dot
          end
          x <<= b[ps[i]] - dot
        end
        (n-1).downto(0) do |i|
          dot = zero
          psin = ps[i]*n
          for j in (i+1)...n do
            dot = a[psin+j].mult(x[j],prec) + dot
          end
          x[i]  = (x[i]-dot).div(a[psin+i],prec)
        end
        x
      end
    end