hetri2x(3)

📦
version 3.12.1 · 9 versions
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💖 NAME 💖

hetri2x — {he,sy}tri2x: inverse

This is hetri2x(3) from the Library Functions Manual — bestie, it’s the inverse routine family, and it’s giving serious linear-algebra main character energy ✨

✨ SYNOPSIS ✨

Functions

  • subroutine chetri2x (uplo, n, a, lda, ipiv, work, nb, info) — CHETRI2X
  • subroutine csytri2x (uplo, n, a, lda, ipiv, work, nb, info) — CSYTRI2X
  • subroutine dsytri2x (uplo, n, a, lda, ipiv, work, nb, info) — DSYTRI2X
  • subroutine ssytri2x (uplo, n, a, lda, ipiv, work, nb, info) — SSYTRI2X
  • subroutine zhetri2x (uplo, n, a, lda, ipiv, work, nb, info) — ZHETRI2X
  • subroutine zsytri2x (uplo, n, a, lda, ipiv, work, nb, info) — ZSYTRI2X

🦋 Detailed Description 🦋

This section is just the doorway into the function docs below — no extra body text lives here in the original, so we’re rolling straight into it 🫶

🛠️ Function Documentation 🛠️

chetri2x

subroutine chetri2x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( n+nb+1,* ) work, integer nb, integer info)

CHETRI2X

Purpose

CHETRI2X 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.

Parameters

  • UPLO — 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**H;
    • = 'L': Lower triangular, form is A = L*D*L**H.
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX array, dimension (LDA,N).
    • On entry, the NNB diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF.
    • 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the NNB structure of D as determined by CHETRF.
  • WORK — COMPLEX array, dimension (N+NB+1,NB+3).
  • NB — INTEGER. Block size.
  • INFO — 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 119 of file chetri2x.f.

csytri2x

subroutine csytri2x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( n+nb+1,* ) work, integer nb, integer info)

CSYTRI2X

Purpose

CSYTRI2X 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 CSYTRF.

Parameters

  • UPLO — 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 — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX array, dimension (LDA,N).
    • On entry, the NNB 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the NNB structure of D as determined by CSYTRF.
  • WORK — COMPLEX array, dimension (N+NB+1,NB+3).
  • NB — INTEGER. Block size.
  • INFO — 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 119 of file csytri2x.f.

dsytri2x

subroutine dsytri2x (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( n+nb+1,* ) work, integer nb, integer info)

DSYTRI2X

Purpose

DSYTRI2X 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.

Parameters

  • UPLO — 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 — INTEGER. The order of the matrix A. N >= 0.
  • A — DOUBLE PRECISION array, dimension (LDA,N).
    • On entry, the NNB 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the NNB structure of D as determined by DSYTRF.
  • WORK — DOUBLE PRECISION array, dimension (N+NB+1,NB+3).
  • NB — INTEGER. Block size.
  • INFO — 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 119 of file dsytri2x.f.

ssytri2x

subroutine ssytri2x (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( n+nb+1,* ) work, integer nb, integer info)

SSYTRI2X

Purpose

SSYTRI2X 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.

Parameters

  • UPLO — 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 — INTEGER. The order of the matrix A. N >= 0.
  • A — REAL array, dimension (LDA,N).
    • On entry, the NNB 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the NNB structure of D as determined by SSYTRF.
  • WORK — REAL array, dimension (N+NB+1,NB+3).
  • NB — INTEGER. Block size.
  • INFO — 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 119 of file ssytri2x.f.

🫶 zhetri2x — the Hermitian inverse bestie

   subroutine zhetri2x (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(
       n+nb+1,* ) work, integer nb, integer info)
       ZHETRI2X

💅 Purpose

Okay so ZHETRI2X computes the inverse of a COMPLEX*16 Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF. That’s the whole main-character job. ✨

✨ Parameters (yes, all of them)

  • UPLO — CHARACTER*1. Tells you 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 — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, the NNB diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF.

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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the NNB structure of D as determined by ZHETRF.
  • WORK — COMPLEX*16 array, dimension (N+NB+1,NB+3).
  • NB — INTEGER. Block size.
  • INFO — 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

Definition at line 119 of file zhetri2x.f.

🫶 zsytri2x — the symmetric inverse bestie

   subroutine zsytri2x (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(
       n+nb+1,* ) work, integer nb, integer info)
       ZSYTRI2X

💅 Purpose

ZSYTRI2X 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. Different factorization, same “bestie, invert this” energy. 🦋

✨ Parameters (yes, all of them too)

  • UPLO — 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 — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, the NNB 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.

  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the NNB structure of D as determined by ZSYTRF.
  • WORK — COMPLEX*16 array, dimension (N+NB+1,NB+3).
  • NB — INTEGER. Block size.
  • INFO — 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

Definition at line 119 of file zsytri2x.f.

🎀 Author (the meta one)

This whole page was generated automatically by Doxygen for LAPACK from the source code. Cute, right? 💖

Okay bye bestie, this iconic footer is from LAPACK, Version 3.12.0, and it’s the hetri2x(3) page. The date slot is literally not listed on the footer, so I’m not inventing one. Periodt. 💅✨

📦 where this page comes from