---
name: "variantsPOcomputational"
section: "3"
platform: "linux"
package: "liblapack-doc"
version: "3.11.0-2"
release: "Debian 12 (Bookworm)"
platforms: ["linux"]
url: "https://new.carta.tech/variantsPOcomputational"
---

# variantsPOcomputational(3)

Variants Computational routines

## 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

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

### 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*

```
          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

### 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

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*

```
          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

### 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

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*

```
          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

## Author

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