SRC/clanhp.f(3)

💖 NAME 💖

okay bestie, welcome to SRC/clanhp.f(3) from the Library Functions Manual — the page for SRC/clanhp.f. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• real function clanhp (norm, uplo, n, ap, work) — CLANHP 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 🫶

real function clanhp (character norm, character uplo, integer n, complex,
    dimension( * ) ap, real, dimension( * ) work)

CLANHP 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. Yes, it said it in the synopsis too — it’s iconic like that. 👑

🌸 Purpose 🌸

CLANHP 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. 🦋

💅 Returns 💅

CLANHP:

!>
!>    CLANHP = ( 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. 😭

🎀 Parameters 🎀

NORM

NORM is CHARACTER*1 — specifies the value to be returned in CLANHP 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, CLANHP is set to zero. 🫶

AP

AP is COMPLEX 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 REAL 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 clanhp.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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mwah 💋 — the footer didn’t give us a date, but it did give us LAPACK Version 3.12.0 and SRC/clanhp.f(3). byeee bestie! 🌈