ZTPCON(3)

💖 ZTPCON(3) — Library Functions Manual 💖

okay so bestie, this is the ZTPCON(3) page from the Library Functions Manual, and it's literally all about a Fortran subroutine that estimates condition numbers. No cap, it's giving numerical linear algebra main character energy 🔥

🌈 NAME 🌈

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

That's the file path the original NAME section gives us, periodt 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine ZTPCON (norm, uplo, diag, n, ap, rcond, work, rwork, info)

ZTPCON

🦋 Function/Subroutine Documentation 🦋

subroutine ZTPCON (character norm, character uplo, character diag, integer n, complex*16, dimension( * ) ap, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZTPCON

💜 Purpose 💜

Bestie, here's the vibe: ZTPCON estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as:

RCOND = 1 / ( norm(A) * norm(inv(A)) ).

🌸 Parameters 🌸

• NORM — CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• UPLO — CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — CHARACTER*1
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — INTEGER. The order of the matrix A. N >= 0.
• AP — COMPLEX*16 array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• RCOND — DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — COMPLEX*16 array, dimension (2*N)
• RWORK — DOUBLE PRECISION 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.

Definition at line 128 of file ztpcon.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off bestie: LAPACK Version 3.12.0 • /home/abui...RC/ztpcon.f(3) • date: not printed in the original footer, so we're keeping it honest 🫶💖✨