SRC/dlantp.f(3)

💖 NAME 💖

Okay bestie, welcome to the SRC/dlantp.f(3) page from the Library Functions Manual — this is the moment for SRC/dlantp.f, and it's all about the dlantp function. No cap, she's here to compute triangular matrix norms in packed form. 💅✨

---

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

• double precision function dlantp (norm, uplo, diag, n, ap, work) — DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. That's the whole assignment, and she ate. 🍓

---

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, copy-paste exact, because we do not play with function declarations:

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

And what does she do? DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. Literally her only job. Iconic. 💖

🎯 Purpose

DLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form. That's the purpose, bestie — no side quests. 🫶

🌈 Returns

DLANTP returns this whole mood:

!>
!>    DLANTP = ( 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(A) is the one norm (maximum column sum), normI(A) is the infinity norm (maximum row sum), and normF(A) is the Frobenius norm (square root of sum of squares). Also lowkey important: max(abs(A(i,j))) is not a consistent matrix norm. 💀

🎀 Parameters

NORM

NORM is CHARACTER*1 and specifies the value to be returned in DLANTP as described above. She's the selector, the vibe check. ✨

UPLO

UPLO is CHARACTER*1 and specifies whether the matrix A is upper or lower triangular.

• = 'U': Upper triangular
• = 'L': Lower triangular

DIAG

DIAG is CHARACTER*1 and specifies whether or not the matrix A is unit triangular.

• = 'N': Non-unit triangular
• = 'U': Unit triangular

N

N is INTEGER. It's the order of the matrix A. N >= 0. When N = 0, DLANTP is set to zero. Tiny but mighty. 👑

AP

AP is a DOUBLE PRECISION array, dimension (N*(N+1)/2). It holds the upper or lower triangular 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.

Note that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. So don't come for those diagonal entries — they're not even read. 🙈

WORK

WORK is a DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. So for the infinity norm she needs the workspace, otherwise she's like "not my department." 💅

👑 Author

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

Definition at line 123 of file dlantp.f.

---

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. Yep, the robots did this one. 🤖💖

---

And that's the tea: LAPACK, Version 3.12.0, source page SRC/dlantp.f(3). Byeeee! 🫶💖