Man page - pbtrf(3)

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Manual

pbtrf

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cpbtrf (character uplo, integer n, integer kd, complex,dimension( ldab, * ) ab, integer ldab, integer info)
subroutine dpbtrf (character uplo, integer n, integer kd, double precision,dimension( ldab, * ) ab, integer ldab, integer info)
subroutine spbtrf (character uplo, integer n, integer kd, real, dimension(ldab, * ) ab, integer ldab, integer info)
subroutine zpbtrf (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, integer info)
Author

NAME

pbtrf - pbtrf: triangular factor

SYNOPSIS

Functions

subroutine cpbtrf (uplo, n, kd, ab, ldab, info)
CPBTRF
subroutine dpbtrf (uplo, n, kd, ab, ldab, info)
DPBTRF
subroutine spbtrf (uplo, n, kd, ab, ldab, info)
SPBTRF
subroutine zpbtrf (uplo, n, kd, ab, ldab, info)
ZPBTRF

Detailed Description

Function Documentation

subroutine cpbtrf (character uplo, integer n, integer kd, complex,dimension( ldab, * ) ab, integer ldab, integer info)

CPBTRF

Purpose:

CPBTRF computes the Cholesky factorization of a complex Hermitian
positive definite band matrix A.

The factorization has the form
A = U**H * U, if UPLO = ā€™Uā€™, or
A = L * L**H, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is lower triangular.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

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

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H*U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.

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
N = 6, KD = 2, and UPLO = ā€™Uā€™:

On entry: On exit:

* * a13 a24 a35 a46 * * 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

Similarly, if UPLO = ā€™Lā€™ the format of A is as follows:

On entry: On exit:

a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
a31 a42 a53 a64 * * l31 l42 l53 l64 * *

Array elements marked * are not used by the routine.

Contributors:

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

subroutine dpbtrf (character uplo, integer n, integer kd, double precision,dimension( ldab, * ) ab, integer ldab, integer info)

DPBTRF

Purpose:

DPBTRF computes the Cholesky factorization of a real symmetric
positive definite band matrix A.

The factorization has the form
A = U**T * U, if UPLO = ā€™Uā€™, or
A = L * L**T, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is lower triangular.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

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

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.

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
N = 6, KD = 2, and UPLO = ā€™Uā€™:

On entry: On exit:

* * a13 a24 a35 a46 * * 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

Similarly, if UPLO = ā€™Lā€™ the format of A is as follows:

On entry: On exit:

a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
a31 a42 a53 a64 * * l31 l42 l53 l64 * *

Array elements marked * are not used by the routine.

Contributors:

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

subroutine spbtrf (character uplo, integer n, integer kd, real, dimension(ldab, * ) ab, integer ldab, integer info)

SPBTRF

Purpose:

SPBTRF computes the Cholesky factorization of a real symmetric
positive definite band matrix A.

The factorization has the form
A = U**T * U, if UPLO = ā€™Uā€™, or
A = L * L**T, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is lower triangular.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

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

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.

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
N = 6, KD = 2, and UPLO = ā€™Uā€™:

On entry: On exit:

* * a13 a24 a35 a46 * * 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

Similarly, if UPLO = ā€™Lā€™ the format of A is as follows:

On entry: On exit:

a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
a31 a42 a53 a64 * * l31 l42 l53 l64 * *

Array elements marked * are not used by the routine.

Contributors:

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

subroutine zpbtrf (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, integer info)

ZPBTRF

Purpose:

ZPBTRF computes the Cholesky factorization of a complex Hermitian
positive definite band matrix A.

The factorization has the form
A = U**H * U, if UPLO = ā€™Uā€™, or
A = L * L**H, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is lower triangular.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

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

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H*U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.

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
N = 6, KD = 2, and UPLO = ā€™Uā€™:

On entry: On exit:

* * a13 a24 a35 a46 * * 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

Similarly, if UPLO = ā€™Lā€™ the format of A is as follows:

On entry: On exit:

a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
a31 a42 a53 a64 * * l31 l42 l53 l64 * *

Array elements marked * are not used by the routine.

Contributors:

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

Author

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