SRC/csycon_3.f(3)

💖 NAME

SRC/csycon_3.f — okay bestie, this is the file page for SRC/csycon_3.f(3) in the Library Functions Manual, and the main character is csycon_3. She's a LAPACK subroutine and she's here to estimate condition numbers. Slay. ✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine csycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
    CSYCON_3

👑 Function/Subroutine Documentation

   subroutine csycon_3 (character uplo, integer n, complex, dimension( lda, * )
       a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv,
       real anorm, real rcond, complex, dimension( * ) work, integer info)
       CSYCON_3

🎯 Purpose

okay so CSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by CSYTRF_RK or CSYTRF_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 CSYTRS_3.

🌸 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**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 array, dimension (LDA,N) — diagonal of the block diagonal matrix D and factors U or L as computed by CSYTRF_RK and CSYTRF_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).

E

• E is COMPLEX 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 CSYTRF_RK or CSYTRF_BK.

ANORM

• ANORM is REAL — the 1-norm of the original matrix A.

RCOND

• RCOND is REAL — 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 array, dimension (2*N) — that's the workspace, periodt. 💅

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

Definition at line 164 of file csycon_3.f.

📜 Author

Generated automatically by Doxygen for LAPACK from the source code.

later, bestie 💖 — this was LAPACK Version 3.12.0, from SRC/csycon_3.f(3), generated automatically by Doxygen for LAPACK from the source code. byeeee! 💅