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 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