SRC/zpstf2.f(3)

💅 SRC/zpstf2.f(3) — Library Functions Manual, bestie ✨

🌸 NAME

SRC/zpstf2.f — that's the file, and this whole page is its moment. 🫶

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✨ SYNOPSIS

🎀 Functions/Subroutines

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.

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💖 Function/Subroutine Documentation

Okay so here's the full signature, no cap:

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 linear algebra main character energy, honestly. 🔥

🧚 Purpose

ZPSTF2 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*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 — 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 141 of file zpstf2.f

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Cute sign-off, bestie: LAPACK Version 3.12.0 — SRC/zpstf2.f(3) — that's the footer, periodt. 🫶✨