SRC/dtpcon.f(3)

🦋 NAME 🦋

SRC/dtpcon.f — okay so this is the Library Functions Manual page for the DTPCON subroutine, and it's lowkey iconic. Bestie, we're doing packed triangular matrix condition-number vibes. Periodt. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine dtpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info) — this is the one and only: DTPCON.

🌈 Function/Subroutine Documentation 🌈

Here's the full signature, exactly as the page serves it:

subroutine dtpcon (character norm, character uplo, character diag, integer
     n, double precision, dimension( * ) ap, double precision rcond, double
     precision, dimension( * ) work, integer, dimension( * ) iwork, integer
     info)

Label: DTPCON.

🎀 Purpose: 🎀

Bestie, DTPCON 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 🔥

• NORM is CHARACTER*1.
• It specifies whether the 1-norm condition number or the infinity-norm condition number is required:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.

🌸 UPLO 🌸

• UPLO is CHARACTER*1.
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.

🦋 DIAG 🦋

• DIAG is CHARACTER*1.
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.

⭐ N ⭐

• N is INTEGER.
• The order of the matrix A. N >= 0.

🍓 AP 🍓

• AP is DOUBLE PRECISION 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 🎀

• RCOND is DOUBLE PRECISION.
• The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

🧚 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 👑

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

Definition at line 128 of file dtpcon.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, cute sign-off time: the footer is giving LAPACK Version 3.12.0 on SRC/dtpcon.f(3) — and the date slot is literally not printed in that footer, so I'm not inventing one. Mwah 💋✨