SRC/dppcon.f(3)

💖 SRC/dppcon.f(3) — Library Functions Manual 💖

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✨ NAME ✨

SRC/dppcon.f

🌸 SYNOPSIS 🌸

💫 Functions/Subroutines

• subroutine dppcon (uplo, n, ap, anorm, rcond, work, iwork, info) — DPPCON

🦋 Function/Subroutine Documentation 🦋

💫 subroutine dppcon signature

subroutine dppcon (character uplo, integer n, double precision, dimension( *
       ) ap, double precision anorm, double precision rcond, double precision,
       dimension( * ) work, integer, dimension( * ) iwork, integer info)

DPPCON

💡 Purpose:

okay so DPPCON is lowkey the condition-number girlie here: it estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF. ✨

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

💅 Parameters

here’s the parameter tea, bestie 🍓

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER The order of the matrix A. N >= 0.
• AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
• ANORM — ANORM is DOUBLE PRECISION The 1-norm (or infinity-norm) of the symmetric 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 DOUBLE PRECISION array, dimension (3*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

shoutout to the author besties:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 117 of file dppcon.f.

👑 Author 👑

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