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

# sptsv(3lapack)

computes the solution to a real system of linear equations A\*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices

## NAME

SPTSV - computes the solution to a real system of linear equations A\*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices

## SYNOPSIS

- SUBROUTINE SPTSV(

  N, NRHS, D, E, B, LDB, INFO )

- INTEGER

  INFO, LDB, N, NRHS

- REAL

  B( LDB, \* ), D( \* ), E( \* )

## PURPOSE

SPTSV computes the solution to a real system of linear equations A\*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. A is factored as A = L\*D\*L\*\*T, and the factored form of A is then used to solve the system of equations.\

## ARGUMENTS

- N (input) INTEGER

  The order of the matrix A.  N \>= 0.

- NRHS (input) INTEGER

  The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS \>= 0.

- D (input/output) REAL array, dimension (N)

  On entry, the n diagonal elements of the tridiagonal matrix A.  On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L\*D\*L\*\*T.

- E (input/output) REAL array, dimension (N-1)

  On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A.  On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L\*D\*L\*\*T factorization of A.  (E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U\*\*T\*D\*U factorization of A.)

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

  On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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\
   \> 0:  if INFO = i, the leading minor of order i is not positive definite, and the solution has not been computed.  The factorization has not been completed unless i = N.