Module: LUSolve
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Extension / Inclusion / Inheritance Descendants | |
Included In:
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Defined in: | ext/bigdecimal/lib/bigdecimal/ludcmp.rb |
Overview
Solves a*x = b for x, using LU decomposition.
Class Method Summary
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.ludecomp(a, n, zero = 0, one = 1)
mod_func
Performs LU decomposition of the n by n matrix a.
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.lusolve(a, b, ps, zero = 0.0)
mod_func
Solves a*x = b for x, using LU decomposition.
Class Method Details
.ludecomp(a, n, zero = 0, one = 1) (mod_func)
Performs LU decomposition of the n by n matrix a.
# File 'ext/bigdecimal/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
.lusolve(a, b, ps, zero = 0.0) (mod_func)
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 'ext/bigdecimal/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