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+*DECK ALPINV
+ SUBROUTINE ALPINV(M,N,A,AINV)
+*
+*-----------------------------------------------------------------------
+*
+*Purpose:
+* pseudo inversion of a non singular matrix using Gaussian elimination
+* with partial pivoting. Real version.
+*
+*Copyright:
+* Copyright (C) 2015 Ecole Polytechnique de Montreal
+* This library is free software; you can redistribute it and/or
+* modify it under the terms of the GNU Lesser General Public
+* License as published by the Free Software Foundation; either
+* version 2.1 of the License, or (at your option) any later version.
+*
+*Author(s): A. Hebert
+*
+*Parameters: input
+* M first dimension of matrix A.
+* N second dimension of matrix A.
+* A coefficient matrix to be inverted.
+*
+*Parameters: output
+* AINV pseudo inverted matrix.
+*
+*-----------------------------------------------------------------------
+*
+*----
+* SUBROUTINE ARGUMENTS
+*----
+ INTEGER M,N
+ REAL A(M,N),AINV(N,M)
+*----
+* LOCAL VARIABLES
+*----
+ REAL, DIMENSION(:,:), ALLOCATABLE :: B
+*
+ ALLOCATE(B(N,N))
+ B=MATMUL(TRANSPOSE(A),A)
+ CALL ALINV(N, B, N, IER)
+ IF(IER.NE.0) CALL XABORT('ALPINV: PSEUDO INVERSION FAILURE.')
+ AINV=MATMUL(B, TRANSPOSE(A))
+ DEALLOCATE(B)
+ RETURN
+ END