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# dpbtrs

```
NAME
DPBTRS - solve 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

SYNOPSIS
SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO
)

CHARACTER      UPLO

INTEGER        INFO, KD, LDAB, LDB, N, NRHS

DOUBLE         PRECISION AB( LDAB, * ), B( LDB, * )

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.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangular factor stored in AB;
= 'L':  Lower triangular factor stored in AB.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

KD      (input) INTEGER
The number of superdiagonals of the matrix A if UPLO
= 'U', or the number of subdiagonals if UPLO = 'L'.
KD >= 0.

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

AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky fac-
torization 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
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    (input) INTEGER
The leading dimension of the array AB.  LDAB >=
KD+1.

(LDB,NRHS)

B       (input/output) DOUBLE PRECISION array, dimension
On entry, the right hand side matrix B.  On exit,
the solution matrix X.

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

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
```