SRC/dsycon_3.f(3)

🦋 NAME 🦋

Okay bestie, this page is for SRC/dsycon_3.f, straight from the Library Functions Manual. It's the home of the DSYCON_3 subroutine, and we are gonna get you comfy with it. No cap. ✨

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

       subroutine dsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work,
           iwork, info)
           DSYCON_3

📚 Function/Subroutine Documentation 📚

Full signature time, literally:

   subroutine dsycon_3 (character uplo, integer n, double precision, dimension(
       lda, * ) a, integer lda, double precision, dimension( * ) e, integer,
       dimension( * ) ipiv, double precision anorm, double precision rcond,
       double precision, dimension( * ) work, integer, dimension( * ) iwork,
       integer info)
       DSYCON_3

🎯 Purpose 🎯

DSYCON_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 DSYTRS_3.

🧸 Parameters 🧸

• UPLO — 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 — INTEGER. The order of the matrix A. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by DSYTRF_RK and DSYTRF_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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• E — DOUBLE PRECISION 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 — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSYTRF_RK or DSYTRF_BK.
• ANORM — DOUBLE PRECISION. The 1-norm of the original matrix A.
• RCOND — 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 — DOUBLE PRECISION array, dimension (2*N).
• IWORK — INTEGER array, dimension (N).
• INFO — 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 169 of file dsycon_3.f.

🖋️ Author 🖋️

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