SRC/zsycon_3.f(3)

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🎀 NAME

SRC/zsycon_3.f

✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine zsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)

ZSYCON_3

🫶 Function/Subroutine Documentation

okay so here’s the full signature, exactly as it appears, no cap:

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

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.

🌸 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).

It 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).

🧚 E

E is COMPLEX*16 array, dimension (N).

On entry, it 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

👑 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 zsycon_3.f.

👑 Author

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