# variantsPOcomputational - Man Page

Variants Computational routines

## Synopsis

### Functions

subroutine **cpotrf** (UPLO, **N**, A, **LDA**, INFO)**CPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.

subroutine **dpotrf** (UPLO, **N**, A, **LDA**, INFO)**DPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.

subroutine **spotrf** (UPLO, **N**, A, **LDA**, INFO)**SPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.

subroutine **zpotrf** (UPLO, **N**, A, **LDA**, INFO)**ZPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.

## Detailed Description

This is the group of Variants Computational routines

## Function Documentation

### subroutine cpotrf (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer INFO)

**CPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. **CPOTRF** VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

**Purpose:**

CPOTRF computes the Cholesky factorization of a real Hermitian positive definite matrix A. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the right looking block version of the algorithm, calling Level 3 BLAS.

**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 COMPLEX array, dimension (LDA,N) On entry, the Hermitian 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**H*U or A = L*L**H.

*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**December 2016

**Purpose:**

CPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the top-looking block version of the algorithm, calling Level 3 BLAS.

**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 COMPLEX 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**H*U or A = L*L**H.

*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**December 2016

Definition at line 101 of file VARIANTS/cholesky/RL/cpotrf.f.

### subroutine dpotrf (character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, integer INFO)

**DPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. **DPOTRF** VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

**Purpose:**

DPOTRF 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 right looking block version of the algorithm, calling Level 3 BLAS.

**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 DOUBLE PRECISION 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**December 2016

**Purpose:**

DPOTRF 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 top-looking block version of the algorithm, calling Level 3 BLAS.

**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 DOUBLE PRECISION 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***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**December 2016

Definition at line 101 of file VARIANTS/cholesky/RL/dpotrf.f.

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

**SPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. **SPOTRF** VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

**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 right looking block version of the algorithm, calling Level 3 BLAS.

**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***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**December 2016

**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 top-looking block version of the algorithm, calling Level 3 BLAS.

**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***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**December 2016

Definition at line 101 of file VARIANTS/cholesky/RL/spotrf.f.

### subroutine zpotrf (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer INFO)

**ZPOTRF** VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. **ZPOTRF** VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

**Purpose:**

ZPOTRF computes the Cholesky factorization of a real Hermitian positive definite matrix A. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the right looking block version of the algorithm, calling Level 3 BLAS.

**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 COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian 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**H*U or A = L*L**H.

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

*INFO***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**December 2016

**Purpose:**

ZPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the top-looking block version of the algorithm, calling Level 3 BLAS.

**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 COMPLEX*16 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**H*U or A = L*L**H.

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

*INFO***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**December 2016

Definition at line 101 of file VARIANTS/cholesky/RL/zpotrf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man pages cpotrf(3), dpotrf(3), spotrf(3) and zpotrf(3) are aliases of variantsPOcomputational(3).