# spotrf2.f - Man Page

## Synopsis

### Functions/Subroutines

recursive subroutine **spotrf2** (UPLO, **N**, A, **LDA**, INFO)**SPOTRF2**

## Function/Subroutine Documentation

### recursive subroutine spotrf2 (character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, integer INFO)

**SPOTRF2**

**Purpose:**

SPOTRF2 computes the Cholesky factorization of a real symmetric positive definite matrix A using the recursive algorithm. 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 recursive version of the algorithm. It divides the matrix into four submatrices: [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 A = [ -----|----- ] with n1 = n/2 [ A21 | A22 ] n2 = n-n1 The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then call itself to factor A22.

**Parameters:***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*INFO*INFO is 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.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**November 2017

Definition at line 108 of file spotrf2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page spotrf2(3) is an alias of spotrf2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK