CPSTF2(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 CPSTF2(3) 💅

okay so bestie, this is the CPSTF2(3) page from the Library Functions Manual. It’s giving “complex Hermitian positive semidefinite Cholesky with complete pivoting” and honestly it ate. Let’s get into it. ✨

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cpstf2.f

This is the path, bestie. 💖

✨ SYNOPSIS ✨

Functions/Subroutines

       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.

📚 Function/Subroutine Documentation 📚

   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 complex Hermitian positive semidefinite matrix.

🎯 Purpose 🎯

okay so 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

UPLO is CHARACTER*1. It 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 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 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

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).

WORK

WORK is REAL array, dimension (2*N). Work space.

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 cpstf2.f.

🫶 Author 🫶

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xoxo bestie 💖 this page is from LAPACK, Version 3.12.0, source path /home/abui...RC/cpstf2.f(3). Slay and stay safe. 🫶

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