ZLANHP(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME

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

Hi bestie 💖 welcome to the Library Functions Manual page for zlanhp.f(3) — this is the ZLANHP entry, and yes, the whole name up top is literally that full path.

✨ 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.

🧚 Function/Subroutine Documentation

Here's the full signature, bestie, exactly as written:

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. That's the whole serve. 💅

🎀 Purpose

okay so the purpose is: 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. Literally that. No cap.

🔥 Returns

Returns ZLANHP, and the value depends on NORM like this, exactly:

!>
!>    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.
!>

Quick vibe check, without changing the facts: norm1 is the one norm of a matrix (maximum column sum), normI is the infinity norm of a matrix (maximum row sum), and normF is the Frobenius norm of a matrix (square root of sum of squares). And bestie, please note: max(abs(A(i,j))) is not a consistent matrix norm. 💀

🌈 Parameters

💜 NORM

NORM is a CHARACTER*1. It specifies the value to be returned in ZLANHP as described above.

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

🦋 UPLO

UPLO is a CHARACTER*1. It tells us whether the upper or lower triangular part of the hermitian matrix A is supplied.

!>          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 an INTEGER. It's the order of the matrix A. N >= 0. When N = 0, ZLANHP is set to zero.

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

🌸 AP

AP is a COMPLEX*16 array, dimension (N*(N+1)/2). It holds 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:

!>          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 a DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.

!>          WORK is DOUBLE PRECISION 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 116 of file zlanhp.f.

🫶 Author

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okay that's the whole page, bestie 💅 footer source/version/date sign-off: LAPACK Version 3.12.0 · /home/abui...RC/zlanhp.f(3) 🎀✨

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