getri(3)

NAME
getri - getri: triangular inverse

SYNOPSIS

  Functions

subroutine cgetri (n, a, lda, ipiv, work, lwork, info)
CGETRI
subroutine dgetri (n, a, lda, ipiv, work, lwork, info)
DGETRI
subroutine sgetri (n, a, lda, ipiv, work, lwork, info)
SGETRI
subroutine zgetri (n, a, lda, ipiv, work, lwork, info)
ZGETRI

Detailed Description

Function Documentation

  subroutine cgetri (integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CGETRI

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).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is 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

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          IPIV is 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

    !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          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.
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dgetri (integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info)

DGETRI

Purpose:

    !>
    !> 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).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          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).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          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.
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sgetri (integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)

SGETRI

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).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is 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

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          IPIV is 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

    !>          WORK is REAL array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          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.
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zgetri (integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

ZGETRI

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).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is 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

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          IPIV is 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

    !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          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.
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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