# dpbtrs.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dpbtrs (character UPLO, integer N, integer KD, integer NRHS, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, 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 = '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

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 123 of file dpbtrs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dpbtrs(3) is an alias of dpbtrs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK