hptri(3)

📦
version 3.12.1 · 9 versions
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🦋 hptri(3) — {hp,sp}tri: triangular inverse 💅

okay so bestie, welcome to the hptri(3) page ✨ this is the whole family — {hp,sp}tri — and yes she's giving "triangular inverse", no cap. Six routines, one job, absolute main character energy 👑

🌸 NAME

hptri — {hp,sp}tri: triangular inverse 🎀

✨ SYNOPSIS

🫶 Functions

  • chptri — subroutine chptri (uplo, n, ap, ipiv, work, info) — CHPTRI
  • csptri — subroutine csptri (uplo, n, ap, ipiv, work, info) — CSPTRI
  • dsptri — subroutine dsptri (uplo, n, ap, ipiv, work, info) — DSPTRI
  • ssptri — subroutine ssptri (uplo, n, ap, ipiv, work, info) — SSPTRI
  • zhptri — subroutine zhptri (uplo, n, ap, ipiv, work, info) — ZHPTRI
  • zsptri — subroutine zsptri (uplo, n, ap, ipiv, work, info) — ZSPTRI

💀 Detailed Description

so the vibe of this section in the source is basically "see below" — the real tea is all in Function Documentation, where each of the six icons gets her own little spotlight. keep scrolling, bestie 💖

👑 Function Documentation

💜 chptri — the complex Hermitian one, single precision

subroutine chptri (character uplo, integer n, complex, dimension( * ) ap,
    integer, dimension( * ) ipiv, complex, dimension( * ) work, integer
    info)

CHPTRI 🦋

Purpose — CHPTRI computes the inverse of a complex Hermitian indefinite matrix A in packed storage, using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF. like, she takes the factorization CHPTRF already did and flips it into a full inverse. periodt.

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**H;
    • = 'L': Lower triangular, form is A = L*D*L**H.
  • 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHPTRF, stored as a packed triangular matrix.
    • On exit, if INFO = 0: the (Hermitian) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows:
      • if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
      • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHPTRF. 🎀
  • 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 108 of file chptri.f.

🍓 csptri — the complex symmetric one, single precision

subroutine csptri (character uplo, integer n, complex, dimension( * ) ap,
    integer, dimension( * ) ipiv, complex, dimension( * ) work, integer
    info)

CSPTRI 🌸

Purpose — CSPTRI computes the inverse of a complex symmetric indefinite matrix A in packed storage, using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF. note the **T bestie, not **H — symmetric, not Hermitian, 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.
  • AP — AP is COMPLEX array, dimension (N*(N+1)/2).
    • On entry: the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSPTRF, stored as a packed triangular matrix.
    • On exit, if INFO = 0: the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows:
      • if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
      • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSPTRF.
  • 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 108 of file csptri.f.

🧚 dsptri — the real symmetric one, double precision

subroutine dsptri (character uplo, integer n, double precision, dimension( *
    ) ap, integer, dimension( * ) ipiv, double precision, dimension( * )
    work, integer info)

DSPTRI 🔥

Purpose — DSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage, using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF. double the precision, double the slay 🎀

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.
  • AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2).
    • On entry: the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSPTRF, stored as a packed triangular matrix.
    • On exit, if INFO = 0: the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows:
      • if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
      • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSPTRF.
  • 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 108 of file dsptri.f.

🌈 ssptri — the real symmetric one, single precision

subroutine ssptri (character uplo, integer n, real, dimension( * ) ap,
    integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)

SSPTRI ⭐

Purpose — SSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage, using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF. lowkey the workhorse of the whole friend group ngl 🫶

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.
  • AP — AP is REAL array, dimension (N*(N+1)/2).
    • On entry: the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSPTRF, stored as a packed triangular matrix.
    • On exit, if INFO = 0: the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows:
      • if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
      • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSPTRF.
  • 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 108 of file ssptri.f.

🦋 zhptri — the complex Hermitian one, double precision

subroutine zhptri (character uplo, integer n, complex*16, dimension( * ) ap,
    integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer
    info)

ZHPTRI 🧚

Purpose — ZHPTRI computes the inverse of a complex Hermitian indefinite matrix A in packed storage, using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. big complex*16 energy, the way she ate 💅

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**H;
    • = 'L': Lower triangular, form is A = L*D*L**H.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — okay bestie the source page literally cuts off right here mid-parameter 😭 hold that thought — the rest of ZHPTRI lives in the next part 🫶

AP — okay so this one is a COMPLEX*16 array, dimension (N*(N+1)/2). On entry, it's holding the block diagonal matrix D plus the multipliers that were used to get the factor U or L as computed by ZHPTRF, all stored as a packed triangular matrix. 💅

On exit, if INFO = 0, you get the (Hermitian) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) lives in AP like this:

if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
   AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV — a INTEGER array, dimension (N), carrying the details of the interchanges and the block structure of D exactly as determined by ZHPTRF. 🫶

WORK — a COMPLEX*16 array, dimension (N). That's it, that's the whole vibe.

INFO — an INTEGER, and it's giving status report:

  • = 0: successful exit, we love a clean run ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value (rude)
  • > 0: if INFO = i, then D(i,i) = 0; the matrix is singular and its inverse could not be computed. 💀 no inverse for you.

👑 Author

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

📍 Definition

Definition at line 108 of file zhptri.f.

🌀 subroutine zsptri (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)

ZSPTRI

🎯 Purpose

ZSPTRI computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF. 🧚✨

🌸 Parameters

UPLO — a 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 — an INTEGER. The order of the matrix A. N >= 0. periodt.

AP — a COMPLEX*16 array, dimension (N*(N+1)/2). On entry, it's the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSPTRF, stored as a packed triangular matrix. 👑

On exit, if INFO = 0, you get the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in AP like this:

if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
   AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV — an INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSPTRF. 🔥

WORK — a COMPLEX*16 array, dimension (N). Same energy as before.

INFO — an INTEGER:

  • = 0: successful exit, we slay ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, then D(i,i) = 0; the matrix is singular and its inverse could not be computed. 😭 singular behaviour, literally cannot.

👑 Author

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

📍 Definition

Definition at line 108 of file zsptri.f.

📜 Author

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