SRC/zhecon_3.f(3)

💖 NAME 💖

SRC/zhecon_3.f — okay bestie, this is the LAPACK Library Functions Manual page for the zhecon_3 subroutine (yep, the SRC/zhecon_3.f(3) one, iykyk). It’s giving “estimate the reciprocal condition number of a complex Hermitian matrix” energy, and honestly? iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zhecon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info) — the main character, aka ZHECON_3. Slay.

🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, bestie — keep it exactly as-is, no cap:

       subroutine zhecon_3 (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
       ) ipiv, double precision anorm, double precision rcond, complex*16,
       dimension( * ) work, integer info)

ZHECON_3 — that’s the name, periodt. 🎀

🎀 Purpose 🎀

ZHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver ZHETRS_3. Obsessed with the efficiency, honestly. ✨

🌸 Parameters 🌸

• UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
  • 'U': Upper triangular, form is A = P*U*D*(U**H)*(P**T);
  • 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T).
• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK:
  • a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
  • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• E — E is COMPLEX*16 array, dimension (N). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where:
  • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
  • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.

• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.
• ANORM — ANORM is DOUBLE PRECISION. The 1-norm of the original matrix A.
• RCOND — RCOND is DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
• WORK — WORK is COMPLEX*16 array, dimension (2*N).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

💜 Author 💜

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

🫶 Contributors 🫶

• June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

⭐ Definition at line 164 of file zhecon_3.f. ⭐

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that’s the whole page 💖 — from the LAPACK manual, Version 3.12.0, and the footer-y bit is SRC/zhecon_3.f(3). Periodt. 🎀