LU decomposition

Write a routine that computes the LU decomposition of a matrix with partial pivoting.

Input arguments:

• , a square matrix.

Output arguments:

• , containing the compact storage of and ; the input value of is overwritten.
• , an integer dimensional vector, containing the pivot positions (i.e. the permutations).
• , an integer, indicating the column where a zero pivot was found (which means that the matrix is singular). if no zero pivots were found (nonsingular matrix).

The header and the declarations of this routine should be

subroutine LU_Fact(A,Pivot,Ierr)
implicit none
! The input matrix, at exit
! will hold the LU factorization
real, dimension(:,:), intent(inout) :: A
! Vector of permutations
integer, dimension(:), intent(out)   :: Pivot
! Singularity indicator, = 0 if A nonsingular,
! and = column number j if the first zero
! pivot was detected in column j
integer, intent(out)   :: Ierr
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