SRC/dlange.f(3)

🌸 NAME 🌸

SRC/dlange.f — this is the manual page for the DLANGE routine, from the Library Functions Manual. The page title is SRC/dlange.f(3), and we are folding that in right here like a good bestie. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• double precision function dlange (norm, m, n, a, lda, work) — DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. She ate, no cap.

🦋 Function/Subroutine Documentation 🦋

double precision function dlange (character norm, integer m, integer n,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( * ) work)

DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. That's the assignment, bestie. 💅

💖 Purpose 💖

okay so DLANGE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A. That's it. That's the whole vibe. ✨

🌈 Returns 🌈

The return value is DLANGE, and here's the iconic little mapping:

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

Here's what those mean:

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

⚠️ okay important: max(abs(A(i,j))) is not a consistent matrix norm. The original says it, I'm saying it, we're all saying it. Don't forget it. 💀

💜 Parameters 💜

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANGE as described above. She's got range, literally. 🦋
• M — M is INTEGER. The number of rows of the matrix A. M >= 0. When M = 0, DLANGE is set to zero.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0. When N = 0, DLANGE is set to zero.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The m by n matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. 🫶

👑 Author 👑

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

Definition at line 113 of file dlange.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. Yes, another Author section — the original does that, so we do that. Periodt. 💅

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okay bye bestie! stay hydrated, norm responsibly, and remember this page is SRC/dlange.f(3) from LAPACK Version 3.12.0 — date? the original footer doesn't list one, so I'm not inventing one. 🫶✨🎀