SRC/clansp.f(3)

🎀 SRC/clansp.f(3) 🎀

okay so bestie, welcome to the Library Functions Manual page for SRC/clansp.f — yes, the whole page is literally just this one function and it is so worth your time 💖

---

✨ SYNOPSIS ✨

Functions/Subroutines

• real function clansp (norm, uplo, n, ap, work) — CLANSP 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. that's the whole vibe ✨

---

💅 Function/Subroutine Documentation 💅

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

okay so what does she do? CLANSP 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. lowkey iconic 🫶

Purpose:

!>
!> CLANSP  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> complex symmetric matrix A,  supplied in packed form.
!>

like, she just knows how big your matrix is. no cap 💀

Returns

CLANSP — and here's exactly what she hands back, fr fr:

!>
!>    CLANSP = ( 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.
!>

⚠️ bestie, please read that last line again: max(abs(A(i,j))) is not a consistent matrix norm. she said what she said 🙈

Parameters

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANSP as described above. so like, pick your norm queen 👑
• UPLO — UPLO is CHARACTER*1. 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, CLANSP is set to zero. (zero matrix? zero norm. math said balance ✨)
• AP — AP is COMPLEX 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.

(yes the indexing is giving main character energy, copy it exactly, do not freestyle 💅)

• 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 doing those norms, WORK is literally just sitting there, not invited to the function 🪑😭

Author

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

Definition at line 114 of file clansp.f.

---

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just vibes 🧚)

---

🌈 and that's the whole page bestie! source & version check: this is LAPACK, Version 3.12.0, filed under SRC/clansp.f(3) — go forth and compute your norms responsibly, ily, bye 💜🦋🌸