## table of contents

variantsPOcomputational(3) | LAPACK | variantsPOcomputational(3) |

# NAME¶

variantsPOcomputational

# 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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

**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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

## 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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

**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*

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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

## 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*

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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

**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*

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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

## 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*

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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

**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*

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 California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date**

# Author¶

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