gbtf2(3)

NAME
gbtf2 - gbtf2: triangular factor, level 2

SYNOPSIS

  Functions

subroutine cgbtf2 (m, n, kl, ku, ab, ldab, ipiv, info)
CGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
subroutine dgbtf2 (m, n, kl, ku, ab, ldab, ipiv, info)
DGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
subroutine sgbtf2 (m, n, kl, ku, ab, ldab, ipiv, info)
SGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
subroutine zgbtf2 (m, n, kl, ku, ab, ldab, ipiv, info)
ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

Detailed Description

Function Documentation

  subroutine cgbtf2 (integer m, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)

CGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

Purpose:

    !>
    !> CGBTF2 computes an LU factorization of a complex m-by-n band matrix
    !> A using partial pivoting with row interchanges.
    !>
    !> This is the unblocked version of the algorithm, calling Level 2 BLAS.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows KL+1 to
    !>          2*KL+KU+1; rows 1 to KL of the array need not be set.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, details of the factorization: U is stored as an
    !>          upper triangular band matrix with KL+KU superdiagonals in
    !>          rows 1 to KL+KU+1, and the multipliers used during the
    !>          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
    !>          See below for further details.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    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.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  M = N = 6, KL = 2, KU = 1:
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *    *    +    +    +       *    *    *   u14  u25  u36
    !>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
    !>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
    !>
    !>  Array elements marked * are not used by the routine; elements marked
    !>  + need not be set on entry, but are required by the routine to store
    !>  elements of U, because of fill-in resulting from the row
    !>  interchanges.
    !>

  subroutine dgbtf2 (integer m, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)

DGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

Purpose:

    !>
    !> DGBTF2 computes an LU factorization of a real m-by-n band matrix A
    !> using partial pivoting with row interchanges.
    !>
    !> This is the unblocked version of the algorithm, calling Level 2 BLAS.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows KL+1 to
    !>          2*KL+KU+1; rows 1 to KL of the array need not be set.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, details of the factorization: U is stored as an
    !>          upper triangular band matrix with KL+KU superdiagonals in
    !>          rows 1 to KL+KU+1, and the multipliers used during the
    !>          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
    !>          See below for further details.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    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.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  M = N = 6, KL = 2, KU = 1:
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *    *    +    +    +       *    *    *   u14  u25  u36
    !>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
    !>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
    !>
    !>  Array elements marked * are not used by the routine; elements marked
    !>  + need not be set on entry, but are required by the routine to store
    !>  elements of U, because of fill-in resulting from the row
    !>  interchanges.
    !>

  subroutine sgbtf2 (integer m, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)

SGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

Purpose:

    !>
    !> SGBTF2 computes an LU factorization of a real m-by-n band matrix A
    !> using partial pivoting with row interchanges.
    !>
    !> This is the unblocked version of the algorithm, calling Level 2 BLAS.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is REAL array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows KL+1 to
    !>          2*KL+KU+1; rows 1 to KL of the array need not be set.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, details of the factorization: U is stored as an
    !>          upper triangular band matrix with KL+KU superdiagonals in
    !>          rows 1 to KL+KU+1, and the multipliers used during the
    !>          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
    !>          See below for further details.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    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.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  M = N = 6, KL = 2, KU = 1:
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *    *    +    +    +       *    *    *   u14  u25  u36
    !>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
    !>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
    !>
    !>  Array elements marked * are not used by the routine; elements marked
    !>  + need not be set on entry, but are required by the routine to store
    !>  elements of U, because of fill-in resulting from the row
    !>  interchanges.
    !>

  subroutine zgbtf2 (integer m, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)

ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

Purpose:

    !>
    !> ZGBTF2 computes an LU factorization of a complex m-by-n band matrix
    !> A using partial pivoting with row interchanges.
    !>
    !> This is the unblocked version of the algorithm, calling Level 2 BLAS.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX*16 array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows KL+1 to
    !>          2*KL+KU+1; rows 1 to KL of the array need not be set.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, details of the factorization: U is stored as an
    !>          upper triangular band matrix with KL+KU superdiagonals in
    !>          rows 1 to KL+KU+1, and the multipliers used during the
    !>          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
    !>          See below for further details.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    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.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  M = N = 6, KL = 2, KU = 1:
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *    *    +    +    +       *    *    *   u14  u25  u36
    !>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
    !>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
    !>
    !>  Array elements marked * are not used by the routine; elements marked
    !>  + need not be set on entry, but are required by the routine to store
    !>  elements of U, because of fill-in resulting from the row
    !>  interchanges.
    !>

Author

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