ZLANTP(3)

💖 ZLANTP(3) 💖 — Library Functions Manual

okay so bestie, welcome to the glow-up of the ZLANTP manual page ✨ this one is from /home/abui...RC/zlantp.f(3), and she is literally here to tell you all about a double precision function that returns norms and max abs values for a packed triangular matrix. no cap, every detail is staying 🫶.

🌸 NAME 🌸

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

That’s the NAME section — yes, literally the path, the whole path, and nothing but the path 💅.

✨ SYNOPSIS ✨

Functions/Subroutines

double precision function ZLANTP (norm, uplo, diag, n, ap, work)

ZLANTP 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. iconic behavior, honestly 🦋.

🔥 Function/Subroutine Documentation 🔥

double precision function ZLANTP (character norm, character uplo, character
    diag, integer n, complex*16, dimension( * ) ap, double precision,
    dimension( * ) work)

bestie, she’s a double precision function named ZLANTP, and the one-liner is: ZLANTP 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. periodt 💜.

🎀 Purpose 🎀

The purpose block is giving main character energy:

!>
!> ZLANTP  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.
!>

🌟 Returns 🌟

Returns ZLANTP, and the definition is this exact formula situation:

!>
!>    ZLANTP = ( 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.
!>

🚨 note bestie: max(abs(A(i,j))) is not a consistent matrix norm — the original says it and we’re keeping it, no editing allowed.

💅 Parameters 💅

NORM

NORM is CHARACTER*1. It specifies the value to be returned in ZLANTP as described above. pick your norm, bestie ✨.

UPLO

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

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

DIAG

DIAG is CHARACTER*1. It 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, ZLANTP is set to zero. zero is zero, she said what she said 💀.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2). It’s 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 elements, they’re not even being read 🫶.

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. lowkey only relevant for the infinity-norm girlies 🌈.

🫶 Author 🫶

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

Definition at line 124 of file zlantp.f. 📍

📜 Author 📜

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

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Signed off with LAPACK Version 3.12.0 energy, from /home/abui...RC/zlantp.f(3) — bye bestie, slay your norms 💅🎀✨