SRC/slatrs3.f(3)

✨ SRC/slatrs3.f ✨

okay so this page is straight out of the Library Functions Manual, and it's all about slatrs3 — the BLAS-3 bestie who solves triangular systems with scaling so nothing overflows. 💖

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine slatrs3 — SLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

subroutine slatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx,
    scale, cnorm, work, lwork, info)

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💅 Function/Subroutine Documentation 💅

subroutine slatrs3

subroutine slatrs3 (character uplo, character trans, character diag,
    character normin, integer n, integer nrhs, real, dimension( lda, * ) a,
    integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension(
    * ) scale, real, dimension( * ) cnorm, real, dimension( * ) work,
    integer lwork, integer info)

SLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow. No cap. 🫶

🎯 Purpose

okay so SLATRS3 solves one of these triangular systems:

A * X = B * diag(scale)  or  A**T * X = B * diag(scale)

with scaling to prevent overflow. Here A is an upper or lower triangular matrix, and A**T denotes the transpose of A. X and B are n by nrhs matrices, and scale is an nrhs element vector of scaling factors. A scaling factor scale(j) is usually less than or equal to 1, chosen such that X(:,j) is less than the overflow threshold. If the matrix A is singular (A(j,j) = 0 for some j), then a non-trivial solution to A*X = 0 is returned. If the system is so badly scaled that the solution cannot be represented as (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.

This is a BLAS-3 version of LATRS for solving several right hand sides simultaneously. Literally iconic behavior. 👑

🧸 Parameters

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — CHARACTER*1. Specifies the operation applied to A.
  • = 'N': Solve A * x = s*b (No transpose)
  • = 'T': Solve A**T* x = s*b (Transpose)
  • = 'C': Solve A**T* x = s*b (Conjugate transpose = Transpose)
• DIAG — CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• NORMIN — CHARACTER*1. Specifies whether CNORM has been set or not.
  • = 'Y': CNORM contains the column norms on entry
  • = 'N': CNORM is not set on entry. On exit, the norms will be computed and stored in CNORM.
• N — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of columns of X. NRHS >= 0.
• A — 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 — INTEGER. The leading dimension of the array A. LDA >= max (1,N).
• X — REAL array, dimension (LDX,NRHS). On entry, the right hand side B of the triangular system. On exit, X is overwritten by the solution matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max (1,N).
• SCALE — REAL array, dimension (NRHS). The scaling factor s(k) is for the triangular system A * x(:,k) = s(k)*b(:,k) or A**T* x(:,k) = s(k)*b(:,k). If SCALE = 0, the matrix A is singular or badly scaled. If A(j,j) = 0 is encountered, a non-trivial vector x(:,k) that is an exact or approximate solution to A*x(:,k) = 0 is returned. If the system so badly scaled that solution cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0 is returned.
• CNORM — REAL array, dimension (N). If NORMIN = 'Y', CNORM is an input argument and CNORM(j) contains the norm of the off-diagonal part of the j-th column of A. If TRANS = 'N', CNORM(j) must be greater than or equal to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) must be greater than or equal to the 1-norm. If NORMIN = 'N', CNORM is an output argument and CNORM(j) returns the 1-norm of the offdiagonal part of the j-th column of A.
• WORK — REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. The dimension of the array WORK. If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where NBA = (N + NB - 1)/NB and NB is the optimal block size.

Heads up: If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal dimensions of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• INFO — INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -k, the k-th argument had an illegal value

👑 Author

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

🔍 Further Details:

(no extra details were listed here — just the heading, bestie 💫)

📍 Definition at line 231 of file slatrs3.f.

Definition at line 231 of file slatrs3.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole SRC/slatrs3.f(3) page 💖 The footer stamp says LAPACK Version 3.12.0 and the page is SRC/slatrs3.f(3). No extra date was shown on the page, so we're not inventing one — periodt. 🌈✨