SSYCON_3(3)

🦋 SSYCON_3(3) — Library Functions Manual 🦋

bestie, this is the Library Functions Manual page for SSYCON_3(3), also chilling at /home/abui.../ssycon_3.f(3). Let's get into it.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssycon_3.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine SSYCON_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, iwork, info)

SSYCON_3 — yes queen, that's the subroutine.

💅 Function/Subroutine Documentation 💅

subroutine SSYCON_3 (character uplo, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real
    anorm, real rcond, real, dimension( * ) work, integer, dimension( * )
    iwork, integer info)

SSYCON_3

🎯 Purpose 🎯

okay so SSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization computed by DSYTRF_RK or DSYTRF_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 SSYTRS_3.

🌈 Parameters 🌈

These are the deets, no cap.

💖 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 REAL array, dimension (LDA,N). It holds the diagonal of the block diagonal matrix D and factors U or L as computed by SSYTRF_RK and SSYTRF_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 REAL 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 SSYTRF_RK or SSYTRF_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 REAL array, dimension (2*N).

🌸 IWORK 🌸

IWORK is INTEGER array, dimension (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 📌

Definition at line 169 of file ssycon_3.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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