# DPBTRS (3) - Linux Manuals

dpbtrs.f -

## SYNOPSIS

### Functions/Subroutines

subroutine dpbtrs (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
DPBTRS

## Function/Subroutine Documentation

### subroutine dpbtrs (characterUPLO, integerN, integerKD, integerNRHS, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldb, * )B, integerLDB, integerINFO)

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
= '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 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 ='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 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