DTPTRI(3)

💖 DTPTRI(3) 💖

okay so bestie, this one lives in the Library Functions Manual and it's literally the glow-up arc for a triangular matrix 💅 the file is:

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

yes the path is a whole paragraph, we don't talk about it 🙈

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✨ SYNOPSIS ✨

Functions/Subroutines 🫶

subroutine DTPTRI (uplo, diag, n, ap, info)
    DTPTRI

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🌸 Function/Subroutine Documentation 🌸

subroutine DTPTRI (character uplo, character diag, integer n, double
    precision, dimension( * ) ap, integer info)
    DTPTRI

🎀 Purpose 🎀

!> !> DTPTRI computes the inverse of a real upper or lower triangular !> matrix A stored in packed format. !>

like, it takes your triangular matrix, keeps it in its cute little packed box, and hands you back the inverse. main character energy fr 🔥

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💜 Parameters 💜

• UPLO — ok so this is a CHARACTER*1 and it tells us which triangle we're dealing with:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — also CHARACTER*1, the vibe check on the diagonal:
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — this one's an INTEGER, it's the order of the matrix A. and listen: N >= 0. non-negotiable bestie ✨
• AP — DOUBLE PRECISION array, dimension (N*(N+1)/2). this is the icon of the whole page so pay attention 👑
  • On entry, the upper or lower triangular matrix A, stored 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)*((2*n-j)/2) = A(i,j) for j<=i<=n.
  • See below for further details.
  • On exit, the (triangular) inverse of the original matrix, in the same packed storage format. she left the house as A and came back as A⁻¹, we love a transformation 💫
• INFO — INTEGER, the receipts:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 😭
  • > 0: if INFO = i, A(i,i) is exactly zero. the triangular matrix is singular and its inverse can not be computed. no inverse for you, she's singular 💀

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🌈 Author 🌈

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

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🦋 Further Details: 🦋

!> !> A triangular matrix A can be transferred to packed storage using one !> of the following program segments: !> !> UPLO = 'U': UPLO = 'L': !> !> JC = 1 JC = 1 !> DO 2 J = 1, N DO 2 J = 1, N !> DO 1 I = 1, J DO 1 I = J, N !> AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) !> 1 CONTINUE 1 CONTINUE !> JC = JC + J JC = JC + N - J + 1 !> 2 CONTINUE 2 CONTINUE !>

two little snippets side by side, pick your triangle, copy the loop, slay 💅

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⭐ Note ⭐

Definition at line 116 of file dtptri.f.

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🍓 Author 🍓

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page bestie, you ate 🫶

LAPACK — Version 3.12.0 — dated /home/abui...RC/dtptri.f(3) — mwah, see you at the next manpage 💖✨🎀