SRC/dtptri.f(3)

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💖 SRC/dtptri.f(3) 💖

Hii bestie, welcome to the Library Functions Manual page for SRC/dtptri.f(3) — aka the DTPTRI zone. It’s giving linear algebra realness, and we’re gonna read every single detail together. 🫶✨

🌸 NAME 🌸

SRC/dtptri.f — home of dtptri, aka DTPTRI. That’s the name section, and it ate. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine dtptri (uplo, diag, n, ap, info) — DTPTRI

🦋 Function/Subroutine Documentation 🦋

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

DTPTRI — yes bestie, same iconic subroutine, now with the full signature glowing. ⭐

🎀 Purpose: 🎀

Okay so DTPTRI computes the inverse of a real upper or lower triangular matrix A stored in packed format. No cap, it’s literally out here inverting triangular matrices in packed storage. 🔥

💅 Parameters 💅

  • 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)

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.

  • INFO — INFO is INTEGER
    • = 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.

👑 Author 👑

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

🌈 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

🧚 Definition 🧚

Definition at line 116 of file dtptri.f.

🍓 Author 🍓

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Okay bestie, that’s the whole page 🫶. Footer vibes: this is SRC/dtptri.f(3) from LAPACK Version 3.12.0, and the footer doesn’t print a date, so no invented date here — periodt 💜.

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