variantsPOcomputational(3)

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variantsPOcomputational(3) — Variants Computational routines 💖

okay bestie, welcome to the LAPACK manual page for variantsPOcomputational — yes the name is giving "someone's dissertation filename" but stay with me, it's actually so good. 🫶

🌸 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. periodt. 👑

🎀 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

(to be continued in part 2 bestie, this page is LONG and we are only just getting started 💀)

LDA

LDA is INTEGER, bestie — it's the leading dimension of the array A, and the rule is LDA >= max(1,N). No cap. 💅

INFO

INFO is INTEGER and it's giving exit-status realness:

  • = 0: successful exit, slay ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value, not iconic 💀
  • > 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. Periodt.

✨ Parameters ✨

UPLO

UPLO is CHARACTER*1 and it picks your triangle:

  • = '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 🦋

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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And that's the whole vibe, bestie! This page is LAPACK version 3.11.0, dated Sun Nov 27 2022, and it's variantsPOcomputational(3). Stay slaying those Cholesky factorizations! 💅✨

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