SLANSP(3)

🌟 NAME 🌟

okay so this page is SLANSP(3) — the Library Functions Manual one — and the header path is /home/abui...RC/slansp.f(3). yes, the raw header echoes that same /home/abui...RC/slansp.f(3) path twice, because headers love drama 💅

✨ SYNOPSIS ✨

Functions/Subroutines

real function SLANSP (norm, uplo, n, ap, work)

SLANSP 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. periodt 💖

🦋 Function/Subroutine Documentation 🦋

real function SLANSP (character norm, character uplo, integer n, real,
    dimension( * ) ap, real, dimension( * ) work)

and yep, the docs say it again: SLANSP 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. iconic behavior, no notes 👑

🌸 Purpose

SLANSP 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 the whole assignment, bestie ✨

🎀 Returns

Returns SLANSP, and the literal formula situation is:

!>
!>    SLANSP = ( 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.
!>

so norm1 = one norm of a matrix (maximum column sum), normI = infinity norm of a matrix (maximum row sum), and normF = Frobenius norm of a matrix (square root of sum of squares). also important: max(abs(A(i,j))) is not a consistent matrix norm. noted, respected, remembered 🫶

💜 Parameters

• NORM — NORM is CHARACTER*1. it specifies the value to be returned in SLANSP as described above. (the Returns section is the “above,” iykyk)
• UPLO — UPLO is CHARACTER*1. it says 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. it's the order of the matrix A. N >= 0. when N = 0, SLANSP is set to zero. short king behavior 💀
• AP — AP is REAL array, dimension (N*(N+1)/2). it holds 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.
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. so if you're not in that norm club, she's literally just vibing 🦋

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📌 Definition at line 113 of file slansp.f.

👑 Author

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