Man page - gbtrf(3)

Packages contains this manual

Manual

gbtrf

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgbtrf (integer m, integer n, integer kl, integer ku, complex,dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv,integer info)
subroutine dgbtrf (integer m, integer n, integer kl, integer ku, doubleprecision, dimension( ldab, * ) ab, integer ldab, integer, dimension( *) ipiv, integer info)
subroutine sgbtrf (integer m, integer n, integer kl, integer ku, real,dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv,integer info)
subroutine zgbtrf (integer m, integer n, integer kl, integer ku,complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension(* ) ipiv, integer info)
Author

NAME

gbtrf - gbtrf: triangular factor

SYNOPSIS

Functions

subroutine cgbtrf (m, n, kl, ku, ab, ldab, ipiv, info)
CGBTRF
subroutine dgbtrf (m, n, kl, ku, ab, ldab, ipiv, info)
DGBTRF
subroutine sgbtrf (m, n, kl, ku, ab, ldab, ipiv, info)
SGBTRF
subroutine zgbtrf (m, n, kl, ku, ab, ldab, ipiv, info)
ZGBTRF

Detailed Description

Function Documentation

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

CGBTRF

Purpose:

CGBTRF computes an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 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 dgbtrf (integer m, integer n, integer kl, integer ku, doubleprecision, dimension( ldab, * ) ab, integer ldab, integer, dimension( *) ipiv, integer info)

DGBTRF

Purpose:

DGBTRF computes an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 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 sgbtrf (integer m, integer n, integer kl, integer ku, real,dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv,integer info)

SGBTRF

Purpose:

SGBTRF computes an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 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 zgbtrf (integer m, integer n, integer kl, integer ku,complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension(* ) ipiv, integer info)

ZGBTRF

Purpose:

ZGBTRF computes an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 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

Generated automatically by Doxygen for LAPACK from the source code.