complex16HEauxiliary(3)

📦

version 3.11.0 · 2 versions

3.11.0 · debian bookworm (latest)
3.10.0 · ubuntu jammy

💖 complex16HEauxiliary — LAPACK 💖

okay bestie, welcome to the LAPACK manual, the complex16HEauxiliary(3) page specifically, and no it is not as scary as it sounds. this is the little friend group of complex16 auxiliary routines that do their thing on HE matrices (that's Hermitian, for the uninitiated, iykyk). three routines. all iconic. let's go 🦋

✨ NAME ✨

complex16HEauxiliary — complex16 💅

🌸 SYNOPSIS 🌸

Functions

subroutine zheswapr (UPLO, N, A, LDA, I1, I2) — ZHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix. 🎀
double precision function zlanhe (NORM, UPLO, N, A, LDA, WORK) — ZLANHE 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. ✨
subroutine zlaqhe (UPLO, N, A, LDA, S, SCOND, AMAX, EQUED) — ZLAQHE scales a Hermitian matrix. 🔥

🫶 Detailed Description 🫶

This is the group of complex16 auxiliary functions for HE matrices. that's it, that's the whole vibe check. three besties, one mission. 💜

👑 Function Documentation 👑

🧚 subroutine zheswapr

subroutine zheswapr (character UPLO, integer N, complex*16, dimension( lda,
    n ) A, integer LDA, integer I1, integer I2)

ZHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix. swappin' rows AND columns, because it's Hermitian and it's ✨balanced✨ like that.

Purpose:

ZHESWAPR applies an elementary permutation on the rows and the columns of
a hermitian matrix.

Parameters

UPLO

UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

= 'U': Upper triangular, form is A = U*D*U**T;
= 'L': Lower triangular, form is A = L*D*L**T.

N

N is INTEGER The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N) On entry, the NB diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.

On exit, if INFO = 0, the (symmetric) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

I1

I1 is INTEGER Index of the first row to swap

I2

I2 is INTEGER Index of the second row to swap

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🦋 double precision function zlanhe

double precision function zlanhe (character NORM, character UPLO, integer N,
    complex*16, dimension( lda, * ) A, integer LDA, double precision,
    dimension( * ) WORK)

ZLANHE 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. literally the norm queen. 👑

Purpose:

ZLANHE  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.

Returns

ZLANHE

ZLANHE = ( 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. 💀 it's giving "close enough" but make it mathematically official.

Parameters

NORM

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

UPLO

UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced.

= 'U': Upper triangular part of A is referenced
= 'L': Lower triangular part of A is referenced

N

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

A

A is COMPLEX*16 array, dimension (LDA,N) The hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.

LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 subroutine zlaqhe

subroutine zlaqhe (character UPLO, integer N, complex*16, dimension( lda, *
    ) A, integer LDA, double precision, dimension( * ) S, double precision
    SCOND, double precision AMAX, character EQUED)

ZLAQHE scales a Hermitian matrix. glow-up time for A. 💅

Purpose:

ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
in the vector S.

Parameters

UPLO

UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored.

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

N

N is INTEGER The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).

LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

S

S is DOUBLE PRECISION array, dimension (N) The scale factors for A.

SCOND

SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1 Specifies whether or not equilibration was done.

= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (the bots did this one, and honestly? they ate. 🤖✨)

okay that's the whole page bestie, you're officially fluent in complex16HEauxiliary, no cap. go forth and call your routines. 🫶

Version 3.11.0 — Sun Nov 27 2022 — complex16HEauxiliary(3). that's the source/version/date energy, periodt. 💖

📦 where this page comes from

debian bookworm: liblapack-doc 3.11.0-2 · BSD-3-Clause
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash on 2026-10-14: a language model's rewrite of the original, under its terms