dgetri.f

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*> \brief \b DGETRI
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, LWORK, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGETRI computes the inverse of a matrix using the LU factorization
*> computed by DGETRF.
*>
*> This method inverts U and then computes inv(A) by solving the system
*> inv(A)*L = inv(U) for inv(A).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          On entry, the factors L and U from the factorization
*>          A = P*L*U as computed by DGETRF.
*>          On exit, if INFO = 0, the inverse of the original matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          The pivot indices from DGETRF; for 1<=i<=N, row i of the
*>          matrix was interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*>          On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK.  LWORK >= max(1,N).
*>          For optimal performance LWORK >= N*NB, where NB is
*>          the optimal blocksize returned by ILAENV.
*>
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          only calculates the optimal size of the WORK array, returns
*>          this value as the first entry of the WORK array, and no error
*>          message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*>          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is
*>                singular and its inverse could not be computed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleGEcomputational
*
*  =====================================================================
      SUBROUTINE dgetri( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
     $                   NBMIN, NN
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemm, dgemv, dswap, dtrsm, dtrtri, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      nb = ilaenv( 1, 'DGETRI', ' ', n, -1, -1, -1 )
      lwkopt = n*nb
      work( 1 ) = lwkopt
      lquery = ( lwork.EQ.-1 )
      IF( n.LT.0 ) THEN
         info = -1
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -3
      ELSE IF( lwork.LT.max( 1, n ) .AND. .NOT.lquery ) THEN
         info = -6
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DGETRI', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Form inv(U).  If INFO > 0 from DTRTRI, then U is singular,
*     and the inverse is not computed.
*
      CALL dtrtri( 'Upper', 'Non-unit', n, a, lda, info )
      IF( info.GT.0 )
     $   RETURN
*
      nbmin = 2
      ldwork = n
      IF( nb.GT.1 .AND. nb.LT.n ) THEN
         iws = max( ldwork*nb, 1 )
         IF( lwork.LT.iws ) THEN
            nb = lwork / ldwork
            nbmin = max( 2, ilaenv( 2, 'DGETRI', ' ', n, -1, -1, -1 ) )
         END IF
      ELSE
         iws = n
      END IF
*
*     Solve the equation inv(A)*L = inv(U) for inv(A).
*
      IF( nb.LT.nbmin .OR. nb.GE.n ) THEN
*
*        Use unblocked code.
*
         DO 20 j = n, 1, -1
*
*           Copy current column of L to WORK and replace with zeros.
*
            DO 10 i = j + 1, n
               work( i ) = a( i, j )
               a( i, j ) = zero
   10       CONTINUE
*
*           Compute current column of inv(A).
*
            IF( j.LT.n )
     $         CALL dgemv( 'No transpose', n, n-j, -one, a( 1, j+1 ),
     $                     lda, work( j+1 ), 1, one, a( 1, j ), 1 )
   20    CONTINUE
      ELSE
*
*        Use blocked code.
*
         nn = ( ( n-1 ) / nb )*nb + 1
         DO 50 j = nn, 1, -nb
            jb = min( nb, n-j+1 )
*
*           Copy current block column of L to WORK and replace with
*           zeros.
*
            DO 40 jj = j, j + jb - 1
               DO 30 i = jj + 1, n
                  work( i+( jj-j )*ldwork ) = a( i, jj )
                  a( i, jj ) = zero
   30          CONTINUE
   40       CONTINUE
*
*           Compute current block column of inv(A).
*
            IF( j+jb.LE.n )
     $         CALL dgemm( 'No transpose', 'No transpose', n, jb,
     $                     n-j-jb+1, -one, a( 1, j+jb ), lda,
     $                     work( j+jb ), ldwork, one, a( 1, j ), lda )
            CALL dtrsm( 'Right', 'Lower', 'No transpose', 'Unit', n, jb,
     $                  one, work( j ), ldwork, a( 1, j ), lda )
   50    CONTINUE
      END IF
*
*     Apply column interchanges.
*
      DO 60 j = n - 1, 1, -1
         jp = ipiv( j )
         IF( jp.NE.j )
     $      CALL dswap( n, a( 1, j ), 1, a( 1, jp ), 1 )
   60 CONTINUE
*
      work( 1 ) = iws
      RETURN
*
*     End of DGETRI
*
      END