pptri(3)

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version 3.12.1 · 9 versions
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✨ pptri(3) ✨ — the triangular inverse girlies

okay so bestie, this is the manual page for pptri, living in section 3 of the Library Functions Manual 🎀. it's the LAPACK crew that inverts your positive definite matrices after you've already done the Cholesky glow-up. four flavors, one vibe. let's go 💅

🌸 NAME 🌸

pptri — pptri: triangular inverse

💅 SYNOPSIS 💅

📋 Functions

  • subroutine cpptri (uplo, n, ap, info) — CPPTRI
  • subroutine dpptri (uplo, n, ap, info) — DPPTRI
  • subroutine spptri (uplo, n, ap, info) — SPPTRI
  • subroutine zpptri (uplo, n, ap, info) — ZPPTRI

🦋 Detailed Description 🦋

(yes babe, the heading is literally "Detailed Description" and there's nothing under it in the source — it's giving mysterious main character energy. the real tea is in the function docs below 👇)

🎀 Function Documentation 🎀

🧚 subroutine cpptri (character uplo, integer n, complex, dimension( * ) ap, integer info) 🧚

CPPTRI

⭐ Purpose

CPPTRI computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF. literally the inverse, handed to you on a platter ✨

🔥 Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangular factor is stored in AP;
    • = 'L': Lower triangular factor is stored in AP.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — AP is COMPLEX array, dimension (N*(N+1)/2).

On entry, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise as 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.

On exit, the upper or lower triangle of the (Hermitian) inverse of A, overwriting the input factor U or L. she ate and left no crumbs 💀

  • INFO — INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the (i,i) element of the factor U or L is
      zero, and the inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 92 of file cpptri.f.

🍓 subroutine dpptri (character uplo, integer n, double precision, dimension( * ) ap, integer info) 🍓

DPPTRI

⭐ Purpose

DPPTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF.

🔥 Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangular factor is stored in AP;
    • = 'L': Lower triangular factor is stored in AP.
  • 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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise as 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.

On exit, the upper or lower triangle of the (symmetric) inverse of A, overwriting the input factor U or L.

  • INFO — INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the (i,i) element of the factor U or L is
      zero, and the inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 92 of file dpptri.f.

🌈 subroutine spptri (character uplo, integer n, real, dimension( * ) ap, integer info) 🌈

SPPTRI

⭐ Purpose

SPPTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF.

🔥 Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangular factor is stored in AP;
    • = 'L': Lower triangular factor is stored in AP.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — AP is REAL array, dimension (N*(N+1)/2).

On entry, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise as 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.

On exit, the upper or lower triangle of the (symmetric) inverse of A, overwriting the input factor U or L.

  • INFO — INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the (i,i) element of the factor U or L is
      zero, and the inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 92 of file spptri.f.

💜 subroutine zpptri (character uplo, integer n, complex*16, dimension( * ) ap, integer info) 💜

ZPPTRI

⭐ Purpose

ZPPTRI computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF.

🔥 Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangular factor is stored in AP;
    • = 'L': Lower triangular factor is stored in AP.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2).

On entry, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise as 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.

On exit, the upper or lower triangle of the (Hermitian) inverse of A, overwriting the input factor U or L. no cap, the input gets fully replaced 🫶

  • INFO — INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the (i,i) element of the factor U or L is
      zero, and the inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 92 of file zpptri.f.

💀 real talk: if INFO > 0, that (i,i) element of your factor U or L is literally zero and the inverse could not be computed. that's not a vibe, that's a singular situation. and if INFO < 0, you passed a bad argument — INFO = -i tells you exactly which one. check yourself bestie 🙈

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

and that's the whole page, bestie 🌸 the source is LAPACK, Version 3.12.0, and this cutie is pptri(3) — go invert something iconic 👑✨

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