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gbtf2(3) Library Functions Manual 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.
!>

Definition at line 144 of file cgbtf2.f.

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.
!>

Definition at line 144 of file dgbtf2.f.

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.
!>

Definition at line 144 of file sgbtf2.f.

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.
!>

Definition at line 144 of file zgbtf2.f.

Author

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