# spbtrs(3) [debian man page]

```spbtrs.f(3)							      LAPACK							       spbtrs.f(3)

NAME
spbtrs.f -

SYNOPSIS
Functions/Subroutines
subroutine spbtrs (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
SPBTRS

Function/Subroutine Documentation
subroutine spbtrs (characterUPLO, integerN, integerKD, integerNRHS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldb, * )B,
integerLDB, integerINFO)
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
= 'U':  Upper triangular factor stored in AB;
= 'L':  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 = 'U',
or the number of subdiagonals if UPLO = 'L'.  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 ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', 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

NAG Ltd.

Date:
November 2011

Definition at line 122 of file spbtrs.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       spbtrs.f(3)```

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```spbtrs.f(3)							      LAPACK							       spbtrs.f(3)

NAME
spbtrs.f -

SYNOPSIS
Functions/Subroutines
subroutine spbtrs (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
SPBTRS

Function/Subroutine Documentation
subroutine spbtrs (characterUPLO, integerN, integerKD, integerNRHS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldb, * )B,
integerLDB, integerINFO)
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
= 'U':  Upper triangular factor stored in AB;
= 'L':  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 = 'U',
or the number of subdiagonals if UPLO = 'L'.  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 ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', 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

NAG Ltd.

Date:
November 2011

Definition at line 122 of file spbtrs.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       spbtrs.f(3)```
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