Man page - pbtrs(3)

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Manual

pbtrs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cpbtrs (character uplo, integer n, integer kd, integer nrhs,complex, dimension( ldab, * ) ab, integer ldab, complex, dimension(ldb, * ) b, integer ldb, integer info)
subroutine dpbtrs (character uplo, integer n, integer kd, integer nrhs,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( ldb, * ) b, integer ldb, integer info)
subroutine spbtrs (character uplo, integer n, integer kd, integer nrhs,real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * )b, integer ldb, integer info)
subroutine zpbtrs (character uplo, integer n, integer kd, integer nrhs,complex*16, dimension( ldab, * ) ab, integer ldab, complex*16,dimension( ldb, * ) b, integer ldb, integer info)
Author

NAME

pbtrs - pbtrs: triangular solve using factor

SYNOPSIS

Functions

subroutine cpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
CPBTRS
subroutine dpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
DPBTRS
subroutine spbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
SPBTRS
subroutine zpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
ZPBTRS

Detailed Description

Function Documentation

subroutine cpbtrs (character uplo, integer n, integer kd, integer nrhs,complex, dimension( ldab, * ) ab, integer ldab, complex, dimension(ldb, * ) b, integer ldb, integer info)

CPBTRS

Purpose:

CPBTRS solves a system of linear equations A*X = B with a Hermitian
positive definite band matrix A using the Cholesky factorization
A = U**H*U or A = L*L**H computed by CPBTRF.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: Lower triangular factor stored in AB.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A, stored in the
first KD+1 rows of the array. The j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).

LDAB

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

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dpbtrs (character uplo, integer n, integer kd, integer nrhs,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( ldb, * ) b, integer ldb, integer info)

DPBTRS

Purpose:

DPBTRS solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization
A = U**T*U or A = L*L**T computed by DPBTRF.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: Lower triangular factor stored in AB.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T of the band matrix A, stored in the
first KD+1 rows of the array. The j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).

LDAB

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

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine spbtrs (character uplo, integer n, integer kd, integer nrhs,real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * )b, integer ldb, integer info)

SPBTRS

Purpose:

SPBTRS solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization
A = U**T*U or A = L*L**T computed by SPBTRF.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: Lower triangular factor stored in AB.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AB

AB is REAL array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T of the band matrix A, stored in the
first KD+1 rows of the array. The j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).

LDAB

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

B

B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zpbtrs (character uplo, integer n, integer kd, integer nrhs,complex*16, dimension( ldab, * ) ab, integer ldab, complex*16,dimension( ldb, * ) b, integer ldb, integer info)

ZPBTRS

Purpose:

ZPBTRS solves a system of linear equations A*X = B with a Hermitian
positive definite band matrix A using the Cholesky factorization
A = U**H *U or A = L*L**H computed by ZPBTRF.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: Lower triangular factor stored in AB.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H *U or A = L*L**H of the band matrix A, stored in the
first KD+1 rows of the array. The j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).

LDAB

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

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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