CHECON_3(3)

🎀 NAME 🎀

okay bestie, this is the <pink>Library Functions Manual</pink> page for /home/abui.../checon_3.f(3), and the main character is CHECON_3. The source path is exactly:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/checon_3.f

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🛠️ SYNOPSIS 🛠️

   Functions/Subroutines
       subroutine CHECON_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
           CHECON_3

💅 Function/Subroutine Documentation 💅

Here's the full signature, no cap:

subroutine CHECON_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)
    CHECON_3

🎯 Purpose 🎯

CHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A using the factorization computed by CHETRF_RK or CHETRF_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 CHETRS_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**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 array, dimension (LDA,N)

Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_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 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 CHETRF_RK or CHETRF_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)

⭐ 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 checon_3.f.

📝 Author (auto-generated note) 📝

Generated automatically by Doxygen for LAPACK from the source code.

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