Summary

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	File:     lu.icn

	Subject:  Procedures for LU manipulation

	Author:   Ralph E. Griswold

	Date:     August 14, 1996

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   This file is in the public domain.

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  lu_decomp(M, I) performs LU decomposition on the square matrix M
  using the vector I.  Both M and I are modified in the process.  The
  value returned is +1 or -1 depending on whether the number of row
  interchanges is even or odd.  lu_decomp() is used in combination with
  lu_back_sub() to solve linear equations or invert matrices.

  lu_decomp() fails if the matrix is singular.

  lu_back_sub(M, I, B) solves the set of linear equations M x X = B.  M
  is the matrix as modified by lu_decomp().  I is the index vector
  produced by lu_decomp().  B is the right-hand side vector and return
  with the solution vector. M and I are not modified by lu_back_sub()
  and can be used in successive calls of lu_back_sub() with different
  Bs.

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  Acknowledgement:  These procedures are based on algorithms given in
  "Numerical Recipes; The Art of Scientific Computing"; William H. Press,
  Brian P. Flannery, Saul A. Teukolsky. and William T. Vetterling;
  Cambridge University Press, 1986.

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This file is part of the (main) package.

lu_back_sub(M, I, B)

lu_decomp(M, I)