sgetri(3S)

NAME
     SGETRI - compute the inverse of a matrix using the LU factorization
     computed by SGETRF

SYNOPSIS
     SUBROUTINE SGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )

         INTEGER        INFO, LDA, LWORK, N

         INTEGER        IPIV( * )

         REAL           A( LDA, * ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     SGETRI computes the inverse of a matrix using the LU factorization
     computed by SGETRF. 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) REAL array, dimension (LDA,N)
             On entry, the factors L and U from the factorization A = P*L*U as
             computed by SGETRF.  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 SGETRF; for 1<=i<=N, row i of the matrix
             was interchanged with row IPIV(i).

     WORK    (workspace/output) REAL array, dimension (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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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