hetri(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💜 hetri(3) 💜

okay so real talk: this is from the Library Functions Manual, and it's the manual page for hetri — the {he,sy}tri girlies, aka the triangular inverse squad. Six whole subroutines live here and every single one of them is about undoing a factorization that somebody else already did. no cap, it's giving "inverse era" 🦋

✨ NAME ✨

hetri — {he,sy}tri: triangular inverse. that's the whole name, bestie, she's concise 👑

🌸 SYNOPSIS 🌸

🎀 Functions

  • subroutine chetri (uplo, n, a, lda, ipiv, work, info) — CHETRI
  • subroutine csytri (uplo, n, a, lda, ipiv, work, info) — CSYTRI
  • subroutine dsytri (uplo, n, a, lda, ipiv, work, info) — DSYTRI
  • subroutine ssytri (uplo, n, a, lda, ipiv, work, info) — SSYTRI
  • subroutine zhetri (uplo, n, a, lda, ipiv, work, info) — ZHETRI
  • subroutine zsytri (uplo, n, a, lda, ipiv, work, info) — ZSYTRI

🦋 Detailed Description 🦋

this is where it gets juicy — the function documentation, one baddie at a time 💅

🔥 Function Documentation 🔥

⭐ subroutine chetri (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)

💖 CHETRI

Purpose:

CHETRI computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF. it's giving "you did CHETRF, now let me finish the job" ✨

Parameters

  • UPLO — UPLO is CHARACTER*1. it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': upper triangular, form is A = U*D*U**H;
    • = 'L': lower triangular, form is A = L*D*L**H.
  • N — N is INTEGER. the order of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N).
    • On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF.
    • On exit, if INFO = 0, the (Hermitian) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by CHETRF.
  • WORK — WORK is COMPLEX array, dimension (N).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file chetri.f.

⭐ subroutine csytri (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)

💖 CSYTRI

Purpose:

CSYTRI computes the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF. symmetric this time, not Hermitian — note the **T, bestie, the transpose is doing the work 🙈

Parameters

  • UPLO — UPLO is CHARACTER*1. it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': upper triangular, form is A = U*D*U**T;
    • = 'L': lower triangular, form is A = L*D*L**T.
  • N — N is INTEGER. the order of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N).
    • On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.
    • On exit, if INFO = 0, the (symmetric) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by CSYTRF.
  • WORK — WORK is COMPLEX array, dimension (2*N). ⚠️ yes bestie, 2*N — this one's hungrier than her sisters, do not skimp on the workspace.
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file csytri.f.

⭐ subroutine dsytri (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer info)

💖 DSYTRI

Purpose:

DSYTRI computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF. double precision, real symmetric, absolutely ate 🔥

Parameters

  • UPLO — UPLO is CHARACTER*1. it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': upper triangular, form is A = U*D*U**T;
    • = 'L': lower triangular, form is A = L*D*L**T.
  • N — N is INTEGER. the order of the matrix A. N >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N).
    • On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF.
    • On exit, if INFO = 0, the (symmetric) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by DSYTRF.
  • WORK — WORK is DOUBLE PRECISION array, dimension (N).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file dsytri.f.

⭐ subroutine ssytri (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)

💖 SSYTRI

Purpose:

SSYTRI computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF. single precision version, same energy, smaller floats 🍓

Parameters

  • UPLO — UPLO is CHARACTER*1. it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': upper triangular, form is A = U*D*U**T;
    • = 'L': lower triangular, form is A = L*D*L**T.
  • N — N is INTEGER. the order of the matrix A. N >= 0.
  • A — A is REAL array, dimension (LDA,N).
    • On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF.
    • On exit, if INFO = 0, the (symmetric) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by SSYTRF.
  • WORK — WORK is REAL array, dimension (N).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file ssytri.f.

⭐ subroutine zhetri (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)

💖 ZHETRI

Purpose:

ZHETRI computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF. the double-complex Hermitian main character, she's literally the blueprint 💅

Parameters

🌈 UPLO

and this is where part one of the page runs out, bestie — UPLO is only just getting introduced... the rest of her parameters are in part two 🫶

✨ UPLO ✨

  • UPLO is CHARACTER*1
  • Tells us whether the deets of the factorization got stored as an upper or lower triangular matrix, bestie:
    • = 'U': upper triangular, form is A = U*D*U**H;
    • = 'L': lower triangular, form is A = L*D*L**H.

🌸 N 🌸

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

🦋 A 🦋

  • A is COMPLEX*16 array, dimension (LDA,N)
  • On entry: the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF.
  • On exit, if INFO = 0, the (Hermitian) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced. So yeah, half of it is literally just vibing, unread 💅

🎀 LDA 🎀

  • LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).

⭐ IPIV ⭐

  • IPIV is INTEGER array, dimension (N)
  • All the details of the interchanges and the block structure of D, as determined by ZHETRF.

🍓 WORK 🍓

  • WORK is COMPLEX*16 array, dimension (N)

💀 INFO 💀

  • INFO is INTEGER
  • = 0: successful exit — slay 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. Not me showing up to invert a singular matrix 🙈

💖 Author 💖

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

Definition at line 113 of file zhetri.f.

🦋 okay now the next one — ZSYTRI 🦋

subroutine zsytri (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)

🫶 Purpose 🫶

ZSYTRI computes the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF.

Note the energy shift: this one's symmetric with a plain **T transpose, not Hermitian with **H. Know the difference, iykyk 😌

✨ Parameters ✨

✨ UPLO ✨

  • UPLO is CHARACTER*1
  • Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
    • = 'U': upper triangular, form is A = U*D*U**T;
    • = 'L': lower triangular, form is A = L*D*L**T.

🌈 N 🌈

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

🧚 A 🧚

  • A is COMPLEX*16 array, dimension (LDA,N)
  • On entry: the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF.
  • On exit, if INFO = 0, the (symmetric) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced. Same deal — the other half of the array is not even looked at 👑

💜 LDA 💜

  • LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).

🔥 IPIV 🔥

  • IPIV is INTEGER array, dimension (N)
  • Details of the interchanges and the block structure of D, as determined by ZSYTRF.

😭 WORK 😭

  • WORK is COMPLEX*16 array, dimension (2*N)
Real talk: it's (2*N) here, not (N) like in ZHETRI. Do not reuse the same workspace sizing and then act surprised. That's not the vibe.

🐚 INFO 🐚

  • INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. Singular matrix found dead in a ditch 💀

💖 Author 💖

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

Definition at line 113 of file zsytri.f.

📜 Author 📜

This whole page was generated automatically by Doxygen for LAPACK from the source code — nobody hand-typed this, it's giving ✨ automation ✨.

and that's the whole page, bestie, you made it to the end 🫶 This was hetri(3) from LAPACK, Version 3.12.0 — go forth and invert responsibly, and remember: INFO never lies 💅✨

📦 where this page comes from