SRC/dlansp.f(3)

💖 SRC/dlansp.f 💖

okay so bestie, this one is from the Library Functions Manual, and it's literally all about dlansp — the icon that measures a packed symmetric matrix. no cap, it's giving math girlie main character energy. 💅✨

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🌸 NAME 🌸

SRC/dlansp.f — that's the file, and inside it lives the dlansp function. periodt.

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🎀 SYNOPSIS 🎀

🫶 Functions/Subroutines 🫶

• double precision function dlansp (norm, uplo, n, ap, work) — DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.

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🦋 Function/Subroutine Documentation 🦋

double precision function dlansp (character norm, character uplo, integer n,
     double precision, dimension( * ) ap, double precision, dimension( * )
     work)

okay so DLANSP 💖 returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form. it's literally the vibe check for your matrix. 🔥

✨ Purpose ✨

bestie, the whole point is this: DLANSP 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 symmetric matrix A, supplied in packed form. that's it, that's the purpose. 💅

🌈 Returns 🌈

here's the full menu of what DLANSP can hand back — no guessing, this is the exact formula:

!>
!>    DLANSP = ( 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'
!>
!> 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).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
!>

⚠️ heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. the original said it and I'm saying it again, fr fr.

🧚 Parameters 🧚

NORM — NORM is CHARACTER*1. It specifies the value to be returned in DLANSP as described above (yes, the menu right up there ☝️💖).

UPLO — UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the symmetric matrix A is supplied.

• = 'U': Upper triangular part of A is supplied
• = 'L': Lower triangular part of A is supplied

N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANSP is set to zero. slay, zero is still valid. 🫶

AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2). The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

like, that's the packing tea. 🍓

WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. so if your norm isn't one of those, WORK literally gets ignored. not me being extra, that's just the rule. 💀

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👑 Author 👑

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

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Definition at line 113 of file dlansp.f.

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Author: Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page — catch you later! the footer says LAPACK Version 3.12.0 and the source page is SRC/dlansp.f(3). stay packed and symmetric 💜🦋✨