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

# spotrf(3lapack)

computes the Cholesky factorization of a real symmetric positive definite matrix A

## NAME

SPOTRF - computes the Cholesky factorization of a real symmetric positive definite matrix A

## SYNOPSIS

- SUBROUTINE SPOTRF(

  UPLO, N, A, LDA, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, LDA, N

- REAL

  A( LDA, \* )

## PURPOSE

SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. The factorization has the form\
\
    A = U\*\*T \* U,  if UPLO = 'U', or\
\
    A = L  \* L\*\*T,  if UPLO = 'L',\
 where U is an upper triangular matrix and L is lower triangular. This is the block version of the algorithm, calling Level 3 BLAS.

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangle of A is stored;\
   \= 'L':  Lower triangle of A is stored.

- N (input) INTEGER

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

- A (input/output) REAL array, dimension (LDA,N)

  On entry, the symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U\*\*T\*U or A = L\*L\*\*T.

- LDA (input) INTEGER

  The leading dimension of the array A.  LDA \>= 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 factorization could not be completed.