SRC/strtrs.f(3)

💖 NAME 💖

SRC/strtrs.f

okay so this is SRC/strtrs.f(3) from the Library Functions Manual — bestie, we're in Fortran linear algebra land and the vibes are immaculate. ✨

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine strtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) — STRTRS

🎀 Function/Subroutine Documentation 🎀

subroutine strtrs

subroutine strtrs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)

STRTRS

Purpose

okay so STRTRS solves a triangular system of the form

A * X = B  or  A**T * X = B,

where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine.

bestie, this is the important part: it catches exact singularity only. Tiny diagonal elements can slip by without an error, so if near-singular precision is a worry, do your own tolerance check before calling. 💅

Parameters

• UPLO — UPLO is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• TRANS — TRANS is CHARACTER*1
  • Specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• 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.
• NRHS — NRHS is INTEGER
  • The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — A is REAL array, dimension (LDA,N)
  • 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.
• LDA — LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).
• B — B is REAL array, dimension (LDB,NRHS)
  • On entry, the right hand side matrix B.
  • On exit, if INFO = 0, the solution matrix X.
• LDB — LDB is INTEGER
  • The leading dimension of the array B. LDB >= max(1,N).
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

Author

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

Definition at line 144 of file strtrs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. Cute sign-off time: this is LAPACK Version 3.12.0, and we're closing out SRC/strtrs.f(3) — go solve those triangular systems responsibly. 💖✨