variantsPOcomputational(3) LAPACK variantsPOcomputational(3)

# NAME¶

variantsPOcomputational - 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

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

NAG Ltd.

Date

December 2016

## 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

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

```
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

NAG Ltd.

Date

December 2016

## 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 Tennessee

Univ. of California Berkeley

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

```
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

NAG Ltd.

Date

December 2016

## 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 Tennessee

Univ. of California Berkeley

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

```
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