PROGRAM GRAM_SCHMIDT
      IMPLICIT NONE
      INTEGER, PARAMETER :: N = 3
      DOUBLE PRECISION :: A(N,N), Q(N,N), R(N,N)
      INTEGER :: I, J, K
 
      ! Initialize the given vectors a1, a2, a3
      DATA A /1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0/
 
      ! Gram-Schmidt process
      DO K = 1, N
          Q(:,K) = A(:,K)
          DO I = 1, K-1
              R(I,K) = DOT_PRODUCT(Q(:,I), A(:,K))
              Q(:,K) = Q(:,K) - R(I,K) * Q(:,I)
          END DO
          R(K,K) = SQRT(DOT_PRODUCT(Q(:,K), Q(:,K)))
          Q(:,K) = Q(:,K) / R(K,K)
      END DO
 
      ! Output the orthonormal vectors
      PRINT *, 'Orthonormal vectors:'
      DO I = 1, N
          PRINT *, 'q', I, ':', Q(:,I)
      END DO
 
      END PROGRAM GRAM_SCHMIDT 

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