getrf(3)

NAME
getrf - getrf: triangular factor

SYNOPSIS

  Functions

subroutine cgetrf (m, n, a, lda, ipiv, info)
CGETRF
subroutine dgetrf (m, n, a, lda, ipiv, info)
DGETRF
subroutine sgetrf (m, n, a, lda, ipiv, info)
SGETRF
subroutine zgetrf (m, n, a, lda, ipiv, info)
ZGETRF

Detailed Description

Function Documentation

  subroutine cgetrf (integer m, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

CGETRF

Purpose:

    !>
    !> CGETRF computes an LU factorization of a general M-by-N matrix A
    !> using partial pivoting with row interchanges.
    !>
    !> The factorization has the form
    !>    A = P * L * U
    !> where P is a permutation matrix, L is lower triangular with unit
    !> diagonal elements (lower trapezoidal if m > n), and U is upper
    !> triangular (upper trapezoidal if m < n).
    !>
    !> This is the right-looking Level 3 BLAS version of the algorithm.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix to be factored.
    !>          On exit, the factors L and U from the factorization
    !>          A = P*L*U; the unit diagonal elements of L are not stored.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (min(M,N))
    !>          The pivot indices; for 1 <= i <= min(M,N), row i of the
    !>          matrix was interchanged with row IPIV(i).
    !>

    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 factorization
    !>                has been completed, but the factor U is exactly
    !>                singular, and division by zero will occur if it is used
    !>                to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dgetrf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

DGETRF

Purpose:

    !>
    !> DGETRF computes an LU factorization of a general M-by-N matrix A
    !> using partial pivoting with row interchanges.
    !>
    !> The factorization has the form
    !>    A = P * L * U
    !> where P is a permutation matrix, L is lower triangular with unit
    !> diagonal elements (lower trapezoidal if m > n), and U is upper
    !> triangular (upper trapezoidal if m < n).
    !>
    !> This is the right-looking Level 3 BLAS version of the algorithm.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

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

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix to be factored.
    !>          On exit, the factors L and U from the factorization
    !>          A = P*L*U; the unit diagonal elements of L are not stored.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (min(M,N))
    !>          The pivot indices; for 1 <= i <= min(M,N), row i of the
    !>          matrix was interchanged with row IPIV(i).
    !>

    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 factorization
    !>                has been completed, but the factor U is exactly
    !>                singular, and division by zero will occur if it is used
    !>                to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sgetrf (integer m, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

SGETRF

Purpose:

    !>
    !> SGETRF computes an LU factorization of a general M-by-N matrix A
    !> using partial pivoting with row interchanges.
    !>
    !> The factorization has the form
    !>    A = P * L * U
    !> where P is a permutation matrix, L is lower triangular with unit
    !> diagonal elements (lower trapezoidal if m > n), and U is upper
    !> triangular (upper trapezoidal if m < n).
    !>
    !> This is the right-looking Level 3 BLAS version of the algorithm.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

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

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix to be factored.
    !>          On exit, the factors L and U from the factorization
    !>          A = P*L*U; the unit diagonal elements of L are not stored.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (min(M,N))
    !>          The pivot indices; for 1 <= i <= min(M,N), row i of the
    !>          matrix was interchanged with row IPIV(i).
    !>

    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 factorization
    !>                has been completed, but the factor U is exactly
    !>                singular, and division by zero will occur if it is used
    !>                to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zgetrf (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

ZGETRF

Purpose:

    !>
    !> ZGETRF computes an LU factorization of a general M-by-N matrix A
    !> using partial pivoting with row interchanges.
    !>
    !> The factorization has the form
    !>    A = P * L * U
    !> where P is a permutation matrix, L is lower triangular with unit
    !> diagonal elements (lower trapezoidal if m > n), and U is upper
    !> triangular (upper trapezoidal if m < n).
    !>
    !> This is the right-looking Level 3 BLAS version of the algorithm.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix to be factored.
    !>          On exit, the factors L and U from the factorization
    !>          A = P*L*U; the unit diagonal elements of L are not stored.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (min(M,N))
    !>          The pivot indices; for 1 <= i <= min(M,N), row i of the
    !>          matrix was interchanged with row IPIV(i).
    !>

    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 factorization
    !>                has been completed, but the factor U is exactly
    !>                singular, and division by zero will occur if it is used
    !>                to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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