1DGETRI(1)                LAPACK routine (version 3.1)                DGETRI(1)
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NAME

6       DGETRI - the inverse of a matrix using the LU factorization computed by
7       DGETRF
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SYNOPSIS

10       SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
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12           INTEGER        INFO, LDA, LWORK, N
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14           INTEGER        IPIV( * )
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16           DOUBLE         PRECISION A( LDA, * ), WORK( * )
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PURPOSE

19       DGETRI computes the inverse of a matrix using the LU factorization com‐
20       puted by DGETRF.
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22       This  method  inverts  U and then computes inv(A) by solving the system
23       inv(A)*L = inv(U) for inv(A).
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ARGUMENTS

27       N       (input) INTEGER
28               The order of the matrix A.  N >= 0.
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30       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
31               On entry, the factors L and U from the factorization A =  P*L*U
32               as  computed  by  DGETRF.  On exit, if INFO = 0, the inverse of
33               the original matrix A.
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35       LDA     (input) INTEGER
36               The leading dimension of the array A.  LDA >= max(1,N).
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38       IPIV    (input) INTEGER array, dimension (N)
39               The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix
40               was interchanged with row IPIV(i).
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42       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
43       (MAX(1,LWORK))
44               On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
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46       LWORK   (input) INTEGER
47               The dimension of the array WORK.  LWORK >= max(1,N).  For opti‐
48               mal  performance  LWORK >= N*NB, where NB is the optimal block‐
49               size returned by ILAENV.
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51               If LWORK = -1, then a workspace query is assumed;  the  routine
52               only  calculates  the  optimal  size of the WORK array, returns
53               this value as the first entry of the WORK array, and  no  error
54               message related to LWORK is issued by XERBLA.
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56       INFO    (output) INTEGER
57               = 0:  successful exit
58               < 0:  if INFO = -i, the i-th argument had an illegal value
59               > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is singu‐
60               lar and its inverse could not be computed.
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64 LAPACK routine (version 3.1)    November 2006                       DGETRI(1)
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