tptri(3)

📦
version 3.12.1 · 9 versions
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💖 NAME 💖

tptri — tptri: triangular inverse. Bestie, this is the manual page for tptri(3), and it is literally the LAPACK glow-up for computing the inverse of a triangular matrix stored in packed format. 💅✨

✨ SYNOPSIS ✨

🌸 Functions 🌸

  • subroutine ctptri (uplo, diag, n, ap, info) — CTPTRI
  • subroutine dtptri (uplo, diag, n, ap, info) — DTPTRI
  • subroutine stptri (uplo, diag, n, ap, info) — STPTRI
  • subroutine ztptri (uplo, diag, n, ap, info) — ZTPTRI

🦋 Detailed Description 🦋

Okay so this page is the group chat for four LAPACK subroutines: ctptri, dtptri, stptri, and ztptri. They all do the triangular-inverse thing, just with different type/precision vibes. Scroll down for the full purpose, parameters, author, further details, and definition line for each one. No skipped tea. 🫶

👑 Function Documentation 👑

💜 ctptri — CTPTRI 💜

subroutine ctptri (character uplo, character diag, integer n, complex,
       dimension( * ) ap, integer info)

CTPTRI

💖 Purpose 💖

CTPTRI computes the inverse of a complex upper or lower triangular matrix A stored in packed format.

🌸 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. No cap.
  • AP — AP is COMPLEX 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:

!>
!>  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 at line 116 of file ctptri.f.

💙 dtptri — DTPTRI 💙

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

DTPTRI

💖 Purpose 💖

DTPTRI computes the inverse of a real upper or lower triangular matrix A stored in packed format.

🌸 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. No cap.
  • 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:

!>
!>  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 at line 116 of file dtptri.f.

💚 stptri — STPTRI 💚

subroutine stptri (character uplo, character diag, integer n, real,
       dimension( * ) ap, integer info)

STPTRI

💖 Purpose 💖

STPTRI computes the inverse of a real upper or lower triangular matrix A stored in packed format.

🌸 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. No cap.
  • AP — AP is REAL 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:

!>
!>  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 at line 116 of file stptri.f.

💜 ztptri — ZTPTRI 💜

subroutine ztptri (character uplo, character diag, integer n, complex*16,
       dimension( * ) ap, integer info)

ZTPTRI

💖 Purpose 💖

ZTPTRI computes the inverse of a complex upper or lower triangular matrix A stored in packed format.

🌸 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. No cap.
  • AP — AP is COMPLEX*16 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:

!>
!>  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 at line 116 of file ztptri.f.

🌟 Author 🌟

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okay bestie, that’s the whole tptri(3) vibe 💅 — the footer stamps this as LAPACK Version 3.12.0, page tptri(3). No date is shown on this footer, so I’m not gonna invent one, periodt 🎀. Bye! ✨

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