SRC/zlanhp.f(3)

🦋 NAME 🦋

okay bestie, this page is literally SRC/zlanhp.f — main character energy from the Library Functions Manual, and yes the header vibe is SRC/zlanhp.f(3). 💅

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• double precision function zlanhp (norm, uplo, n, ap, work) — ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.

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💜 Function/Subroutine Documentation 💜

🌸 Signature 🌸

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

ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.

🍓 Purpose 🍓

Okay so ZLANHP 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 hermitian matrix A, supplied in packed form. That is the whole assignment, and it ate. 💅

🌈 Returns 🌈

ZLANHP

Here is the exact value map, bestie — no cap, this is the formula:

!>
!>    ZLANHP = ( 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.
!>

And the caveat is important, bestie: max(abs(A(i,j))) is not a consistent matrix norm. Periodt. 👑

🧚 Parameters 🧚

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANHP as described above.
• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the hermitian 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, ZLANHP is set to zero.
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need not be set and are assumed to be zero.

• 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.

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👑 Author 👑

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

Definition at line 116 of file zlanhp.f.

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Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0, SRC/zlanhp.f(3) — and there’s no date line in the footer, bestie, so I am not inventing one 💀🫶