---
name: "spbtrs"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/spbtrs/3lapack"
---

# spbtrs(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE SPBTRS(

  UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, KD, LDAB, LDB, N, NRHS

- REAL

  AB( LDAB, \* ), B( LDB, \* )

## 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.

## 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) 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 (input) INTEGER

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

- B (input/output) REAL array, dimension (LDB,NRHS)

  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