pstf2(3)

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pstf2(3) 🎀 — Library Functions Manual

okay so bestie, welcome to pstf2(3) from the Library Functions Manual. This is literally the triangular factor, with pivoting panel, level 2 situation, and we’re in part 1, so buckle up. ✨

NAME

pstf2 — pstf2: triangular factor, with pivoting panel, level 2

SYNOPSIS

Functions

  • subroutine cpstf2 (uplo, n, a, lda, piv, rank, tol, work, info) — CPSTF2 computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix. 💜
  • subroutine dpstf2 (uplo, n, a, lda, piv, rank, tol, work, info) — DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. 💖
  • subroutine spstf2 (uplo, n, a, lda, piv, rank, tol, work, info) — SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. 🌸
  • subroutine zpstf2 (uplo, n, a, lda, piv, rank, tol, work, info) — ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix. 🦋

Detailed Description

okay so this is the bit where the page gives you a Detailed Description heading and then immediately dives into the function docs. iconic, honestly. 🫶

Function Documentation

subroutine cpstf2

subroutine cpstf2 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, real tol, real, dimension( 2*n ) work, integer info)

CPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix. 💅

Purpose:

Bestie, CPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A.

The factorization has the form:

P**T * A * P = U**H * U ,  if UPLO = 'U',
P**T * A * P = L  * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV.

This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS.

Parameters

  • UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — 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 as above.

  • PIV — INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
  • RANK — INTEGER. The rank of A given by the number of steps the algorithm completed.
  • TOL — REAL. User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • WORK — REAL array, dimension (2*N). Work space.
  • INFO — INTEGER.
    • < 0: If INFO = -K, the K-th argument had an illegal value,
    • = 0: algorithm completed successfully, and
    • > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information.

Author

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

Definition at line 141 of file cpstf2.f.

subroutine dpstf2

subroutine dpstf2 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, double precision tol, double precision, dimension( 2*n ) work, integer info)

DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. 💖

Purpose:

DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A.

The factorization has the form:

P**T * A * P = U**T * U ,  if UPLO = 'U',
P**T * A * P = L  * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV.

This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS.

Parameters

  • UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — 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 as above.

  • PIV — INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
  • RANK — INTEGER. The rank of A given by the number of steps the algorithm completed.
  • TOL — DOUBLE PRECISION. User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • WORK — DOUBLE PRECISION array, dimension (2*N). Work space.
  • INFO — INTEGER.
    • < 0: If INFO = -K, the K-th argument had an illegal value,
    • = 0: algorithm completed successfully, and
    • > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information.

Author

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

Definition at line 140 of file dpstf2.f.

subroutine spstf2

subroutine spstf2 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, real tol, real, dimension( 2*n ) work, integer info)

SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. 🌸

Purpose:

SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A.

The factorization has the form:

P**T * A * P = U**T * U ,  if UPLO = 'U',
P**T * A * P = L  * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV.

This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS.

Parameters

  • UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — 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 as above.

  • PIV — INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
  • RANK — INTEGER. The rank of A given by the number of steps the algorithm completed.
  • TOL — REAL. User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • WORK — REAL array, dimension (2*N). Work space.

INFO

  • INFO — INFO is INTEGER. Here's the vibe check: if INFO < 0 and INFO = -K, the K-th argument had an illegal value (not it being messy 💀). If INFO = 0, the algorithm completed successfully, slay ✨. If INFO > 0, the matrix A is either rank deficient with computed rank as returned in RANK, or it's not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information. No cap.

👑 Author 👑

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

Definition at line 140 of file spstf2.f.

🦋 subroutine zpstf2 🦋

   subroutine zpstf2 (character uplo, integer n, complex*16, dimension( lda, *
       ) a, integer lda, integer, dimension( n ) piv, integer rank, double
       precision tol, double precision, dimension( 2*n ) work, integer info)

ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix. It's giving main character energy for sure. 💅

🎯 Purpose 🎯

ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A. Obsessed.

The factorization has the form:

P**T * A * P = U**H * U ,  if UPLO = 'U',
P**T * A * P = L  * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV. Iconic.

This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS. Just so you know, bestie. 🫶

📋 Parameters 📋

  • UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular. = 'L': Lower triangular.
  • 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 as above.
  • PIV — PIV is INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
  • RANK — RANK is INTEGER. The rank of A given by the number of steps the algorithm completed.
  • TOL — TOL is DOUBLE PRECISION. User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • WORK — WORK is DOUBLE PRECISION array, dimension (2*N). Work space. Just doing its thing. 🛠️
  • INFO — INFO is INTEGER. < 0: If INFO = -K, the K-th argument had an illegal value, = 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information.

👑 Author 👑

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

Definition at line 141 of file zpstf2.f.

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