ZSYCON_3(3)

💅 ZSYCON_3(3) — bestie, it's a Library Functions Manual moment

okay so. before we even start, you need to know this page lives at /home/abui.../zsycon_3.f(3) and it's part of the Library Functions Manual. that's the vibe. now let's get into it 💖

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zsycon_3.f

like, that's literally the whole name. she's a file path and she's serving. 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine ZSYCON_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)

ZSYCON_3 — that's her. that's the girl. 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine ZSYCON_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)

ZSYCON_3 💫

🫶 Purpose 🫶

bestie. ZSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:

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

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric 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 ZSYTRS_3. 🔥

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💜 Parameters 💜

• UPLO — UPLO is CHARACTER*1. it 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**T)*(P**T);
  • = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).
• N — N is INTEGER. the order of the matrix A. N >= 0. ✨
• A — A is COMPLEX*16 array, dimension (LDA,N). she holds the diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK:
  • a) ONLY diagonal elements of the symmetric 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). no cap 📏
• E — E is COMPLEX*16 array, dimension (N). on entry, contains the superdiagonal (or subdiagonal) elements of the symmetric 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 ZSYTRF_RK or ZSYTRF_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 💀

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👑 Author 👑

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

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🌈 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

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⭐ Definition at line 164 of file zsycon_3.f. ⭐

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. (yes, a robot wrote the vibes. we're just translating. 🙈)

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🍓 and that's the whole page, bestie! every flag, every formula, every contributor — nothing dropped, nothing invented. iykyk 💅

LAPACK Version 3.12.0 — she's iconic, she's automatic, and she lives at /home/abui.../zsycon_3.f(3). mwah 💋 periodt. 💖✨🎀