DLANSP(3)

🌸 DLANSP(3) — bestie edition 🌸

okay so this page is for dlansp.f(3), a little file living at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlansp.f — yes that's the whole path, we don't gatekeep 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlansp.f

like, that's it. that's the name. it's giving "my parents named me after the street they lived on" 🎀

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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.

she does one thing and she does it iconically, no cap 👑

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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 for real: 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. that's the whole personality. main character energy fr fr 🌈

🌸 Purpose 🌸

!>
!> 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.
!>

literally just read the comment block, it's serving the whole point 🫶

⭐ Returns ⭐

DLANSP

!>
!>    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.
!>

look at that cute little selector, it's a choose-your-own-norm adventure 🎀

⚠️ and yes bestie, the fine print matters: max(abs(A(i,j))) is not a consistent matrix norm. that's not me being dramatic, that's literally in the docs. know the difference iykyk 💀

🧚 Parameters 🧚

NORM

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in DLANSP as described
!>          above.
!>

it's a CHARACTER*1 and it decides which vibe you get back. see the "as described above" selector, that's the menu, pick your fave ✨

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
!>

• 'U' — upper triangular part of A is supplied 💖
• 'L' — lower triangular part of A is supplied 💜

pick one, bestie, and commit. it's a CHARACTER*1, it's not that deep 🌸

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, DLANSP is
!>          set to zero.
!>

INTEGER, the order of the matrix A, and it must satisfy N >= 0. oh and when N = 0, DLANSP is set to zero — small but mighty, she still shows up 🥺

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.
!>

• AP is a DOUBLE PRECISION 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

those index formulas are the whole entire point, do not eyeball them, copy them exactly 😭 the packing is real and the packing is unforgiving 🦋

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.
!>

WORK is a DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'. otherwise? WORK is not referenced. she's off duty, she's not even invited 🙈

👑 Author 👑

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

the whole group project got credit, and honestly? deserved 🌟

⭐ Definition at line 113 of file dlansp.f. ⭐

line 113, file dlansp.f. noted, bookmarked, screenshotted 💅

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💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

like, no human typed this, a robot did, and she ate 🔥

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and that's the whole page bestie 🫶 — with all the love in the world from the LAPACK crew, LAPACK Version 3.12.0, generated automatically by Doxygen for LAPACK from the source code. now go forth and norm your symmetric packed matrices, mwah 💖✨🎀