zgetri.f

          SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDA, LWORK, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX*16         A( LDA, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZGETRI computes the inverse of a matrix using the LU factorization
    *  computed by ZGETRF.
    *
    *  This method inverts U and then computes inv(A) by solving the system
    *  inv(A)*L = inv(U) for inv(A).
    *
    *  Arguments
    *  =========
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
    *          On entry, the factors L and U from the factorization
    *          A = P*L*U as computed by ZGETRF.
    *          On exit, if INFO = 0, the inverse of the original matrix A.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  IPIV    (input) INTEGER array, dimension (N)
    *          The pivot indices from ZGETRF; for 1<=i<=N, row i of the
    *          matrix was interchanged with row IPIV(i).
    *
    *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
    *          On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) 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.
    *
    *  INFO    (output) 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.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX*16         ZERO, ONE
          PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
         $                   ONE = ( 1.0D+0, 0.0D+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           XERBLA, ZGEMM, ZGEMV, ZSWAP, ZTRSM, ZTRTRI
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          NB = ILAENV( 1, 'ZGETRI', ' ', 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( 'ZGETRI', -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 ZTRTRI, then U is singular,
    *     and the inverse is not computed.
    *
          CALL ZTRTRI( '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, 'ZGETRI', ' ', 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 ZGEMV( '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 ZGEMM( '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 ZTRSM( '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 ZSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
       60 CONTINUE
    *
          WORK( 1 ) = IWS
          RETURN
    *
    *     End of ZGETRI
    *
          END