potrf(3)

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version 3.12.1 · 9 versions
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potrf(3) — triangular factor 🌸

okay so bestie, this is the Library Functions Manual page for potrf(3), and it is literally all about the Cholesky triangular factor. no cap, we are covering every flag, every author line, and every "Definition at line 106" moment. 💅✨

✨ NAME ✨

potrf — potrf: triangular factor (that is the whole name section and yes she ate 💅).

💅 SYNOPSIS 💅

🎀 Functions 🎀

  • subroutine cpotrf (uplo, n, a, lda, info) — CPOTRF
  • subroutine dpotrf (uplo, n, a, lda, info) — DPOTRF
  • subroutine spotrf (uplo, n, a, lda, info) — SPOTRF
  • subroutine zpotrf (uplo, n, a, lda, info) — ZPOTRF

🌈 Detailed Description 🌈

okay so this heading is literally just vibing here — the actual detailed docs are in the next section, and that is where all the function tea is. 🫖✨

🔥 Function Documentation 🔥

🧚 subroutine cpotrf (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer info)

CPOTRF — this one is the complex Hermitian icon of the group. 💜

🌸 Purpose

okay so CPOTRF computes the Cholesky factorization of a complex 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 block version of the algorithm, calling Level 3 BLAS. slay. 💅

🎀 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, it is 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 principal minor of order i is not positive, and the factorization could not be completed.

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🦋 Definition

Definition at line 106 of file cpotrf.f.

🧚 subroutine dpotrf (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)

DPOTRF — this one is the real symmetric double precision bestie. 💖

🌸 Purpose

okay so 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 block version of the algorithm, calling Level 3 BLAS. iconic. ✨

🎀 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, it is 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 principal minor of order i is not positive, and the factorization could not be completed.

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🦋 Definition

Definition at line 106 of file dpotrf.f.

🧚 subroutine spotrf (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer info)

SPOTRF — this one is the real symmetric single precision moment. 🍓

🌸 Purpose

okay so 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 block version of the algorithm, calling Level 3 BLAS. periodt. 💅

🎀 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, it is 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 principal minor of order i is not positive, and the factorization could not be completed.

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🦋 Definition

Definition at line 106 of file spotrf.f.

🧚 subroutine zpotrf (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

ZPOTRF — this one is the complex Hermitian double precision main character. 🌟

🌸 Purpose

okay so ZPOTRF computes the Cholesky factorization of a complex 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 block version of the algorithm, calling Level 3 BLAS. obsessed. 🔥

🎀 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, it is 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 principal minor of order i is not positive, and the factorization could not be completed.

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🦋 Definition

Definition at line 106 of file zpotrf.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, that is the literal line 🫶)

🎀 okay that is the whole potrf(3) page — source/version: LAPACK Version 3.12.0; page: potrf(3); date: the footer did not list one, so no cap, that is the sign-off. periodt ✨💖

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