SRC/slantr.f(3)

hey bestie 💖 this is the SRC/slantr.f(3) page from the Library Functions Manual, and it’s all about one little function that does norm vibes on trapezoidal or triangular matrices. lowkey iconic.

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🌸 NAME 🌸

SRC/slantr.f — that’s the whole name, no cap. This page is the manual for the slantr function/subroutine in that file. 🎀

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• real function slantr (norm, uplo, diag, m, n, a, lda, work) — SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. periodt.

🦋 Function/Subroutine Documentation 🦋

🎀 real function slantr (character norm, character uplo, character diag, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work) 🎀

real function slantr (character norm, character uplo, character diag,
     integer m, integer n, real, dimension( lda, * ) a, integer lda, real,
     dimension( * ) work)

okay so the signature is exactly that ^^ and the function is SLANTR, which returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. iykyk ✨

💜 Purpose 💜

the purpose is literally: SLANTR returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. that’s it, that’s the vibe.

🌈 Returns 🌈

ngl the return value mapping is giving choose-your-own-norm:

• SLANTR = max(abs(A(i,j))) when NORM = 'M' or 'm'
• SLANTR = norm1(A) when NORM = '1', 'O', or 'o'
• SLANTR = normI(A) when NORM = 'I' or 'i'
• SLANTR = normF(A) when NORM = 'F', 'f', 'E', or 'e'

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum), and normF denotes the Frobenius norm of a matrix (square root of sum of squares).

heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. no cap, it’s in the docs.

🫶 Parameters 🫶

• NORM — CHARACTER*1. Specifies the value to be returned in SLANTR as described above. pick your fighter.
• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower trapezoidal.
  • = 'U': Upper trapezoidal
  • = 'L': Lower trapezoidal
  • Note that A is triangular instead of trapezoidal if M = N.
• DIAG — CHARACTER*1. Specifies whether or not the matrix A has unit diagonal.
  • = 'N': Non-unit diagonal
  • = 'U': Unit diagonal
• M — INTEGER. The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, SLANTR is set to zero. zero era.
• N — INTEGER. The number of columns of the matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, SLANTR is set to zero. also zero era.
• A — REAL array, dimension (LDA,N). The trapezoidal matrix A (A is triangular if M = N). If UPLO = 'U', the leading m by n upper trapezoidal part of the array A contains the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading m by n lower trapezoidal part of the array A contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be one. don’t touch the unreferenced parts, bestie.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• WORK — REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. only the infinity-norm girlies need it.

👑 Author 👑

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

Definition at line 139 of file slantr.f.

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💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code. slay.

okay that’s the whole page, bestie 🫶 — footer check says LAPACK Version 3.12.0 and SRC/slantr.f(3), and there’s no date line in the footer so I’m not gonna invent one. bye 💖