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SUBROUTINE CGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
* * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX A( LDA, * ), WORK( * ) * .. * * Purpose * ======= * * CGETRI computes the inverse of a matrix using the LU factorization * computed by CGETRF. * * 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 array, dimension (LDA,N) * On entry, the factors L and U from the factorization * A = P*L*U as computed by CGETRF. * 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 CGETRF; for 1<=i<=N, row i of the * matrix was interchanged with row IPIV(i). * * WORK (workspace/output) COMPLEX 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 ZERO, ONE PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ), $ ONE = ( 1.0E+0, 0.0E+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 CGEMM, CGEMV, CSWAP, CTRSM, CTRTRI, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NB = ILAENV( 1, 'CGETRI', ' ', 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( 'CGETRI', -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 CTRTRI, then U is singular, * and the inverse is not computed. * CALL CTRTRI( '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, 'CGETRI', ' ', 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 CGEMV( '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 CGEMM( '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 CTRSM( '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 CSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) 60 CONTINUE * WORK( 1 ) = IWS RETURN * * End of CGETRI * END |