trtri(3)

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version 3.12.1 · 9 versions
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🌸 NAME 🌸

trtri — trtri: triangular inverse

okay so bestie, welcome to trtri(3), straight out of the Library Functions Manual. This page is the group chat for four triangular-inverse routines, and yes, they are all lowkey iconic. 💅

✨ SYNOPSIS ✨

Functions

There are four function signatures, one for each precision/flavor. Here they are, exactly as the page lists them:

subroutine ctrtri (uplo, diag, n, a, lda, info)
    CTRTRI
subroutine dtrtri (uplo, diag, n, a, lda, info)
    DTRTRI
subroutine strtri (uplo, diag, n, a, lda, info)
    STRTRI
subroutine ztrtri (uplo, diag, n, a, lda, info)
    ZTRTRI

💅 Detailed Description 💅

This section is the runway, not the runway show — the actual function-by-function tea is right below in Function Documentation. No extra lore here.

🔥 Function Documentation 🔥

okay bestie, this is the main character section. Four routines, same parameter lineup, different data types. Keep your eyes on the types and the UPLO/DIAG flags. 💖

subroutine ctrtri (character uplo, character diag, integer n, complex, dimension( lda, * ) a, integer lda, integer info)

CTRTRI

Purpose: CTRTRI computes the inverse of a complex upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

Parameters

  • UPLO — CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular.
  • DIAG — CHARACTER*1. = 'N': A is non-unit triangular; = 'U': A is unit triangular.
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX array, dimension (LDA,N). On entry, this is the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • INFO — 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.

Definition at line 108 of file ctrtri.f.

subroutine dtrtri (character uplo, character diag, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)

DTRTRI

Purpose: DTRTRI computes the inverse of a real upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

Parameters

  • UPLO — CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular.
  • DIAG — CHARACTER*1. = 'N': A is non-unit triangular; = 'U': A is unit triangular.
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — DOUBLE PRECISION array, dimension (LDA,N). On entry, this is the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • INFO — 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.

Definition at line 108 of file dtrtri.f.

subroutine strtri (character uplo, character diag, integer n, real, dimension( lda, * ) a, integer lda, integer info)

STRTRI

Purpose: STRTRI computes the inverse of a real upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

Parameters

  • UPLO — CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular.
  • DIAG — CHARACTER*1. = 'N': A is non-unit triangular; = 'U': A is unit triangular.
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — REAL array, dimension (LDA,N). On entry, this is the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • INFO — 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.

Definition at line 108 of file strtri.f.

subroutine ztrtri (character uplo, character diag, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

ZTRTRI

Purpose: ZTRTRI computes the inverse of a complex upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

Parameters

  • UPLO — CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular.
  • DIAG — CHARACTER*1. = 'N': A is non-unit triangular; = 'U': A is unit triangular.
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, this is the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • INFO — 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.

Definition at line 108 of file ztrtri.f.

🫶 Author 🫶

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