SRC/slansp.f(3)

okay so bestie, welcome to SRC/slansp.f(3) — it's from the Library Functions Manual, and it's literally the glow-up of a Fortran routine named slansp ✨

🌸 NAME 🌸

SRC/slansp.f — that's the name, no cap 💅

✨ 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.

🦋 Function/Subroutine Documentation 🦋

🫶 real function slansp (character norm, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) 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. That's the whole main-character assignment 💖

🎯 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. Periodt 🌟

💖 Returns

SLANSP

The source comment spells it out like this — yes, with the Doxygen !> markers and all, bestie:

!>
!>    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 like: SLANSP gives you max(abs(A(i,j))) when NORM = 'M' or 'm'; norm1(A) when NORM = '1', 'O' or 'o'; normI(A) when NORM = 'I' or 'i'; and normF(A) when NORM = 'F', 'f', 'E' or 'e' 🔥

And just so we're clear: norm1 is the one norm (maximum column sum), normI is the infinity norm (maximum row sum), and normF is the Frobenius norm (square root of sum of squares). ⚠️ Also, max(abs(A(i,j))) is not a consistent matrix norm — the source says it, so we say it, fr fr 💀

🧾 Parameters

• NORM — NORM is CHARACTER*1; it specifies the value to be returned in SLANSP as described above.
• 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, SLANSP is set to zero.
• AP — AP is REAL 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.

• WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; 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 slansp.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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byeee 💖 — this page's footer is literally LAPACK Version 3.12.0 + SRC/slansp.f(3). No extra date on this one, just the version and source, and that's the whole footer, bestie. mwah 💋✨