her(3)

📦

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`her(3)` — Library Functions Manual — `her(3)` 💅

part 1 of 3 — bestie, we’re in BLAS territory and it’s honestly kind of iconic. ✨

🌸 NAME 🌸

her - {he,sy}r: Hermitian/symmetric rank-1 update

✨ SYNOPSIS ✨

Functions

Okay so here’s the whole squad, no cap:

subroutine cher (uplo, n, alpha, x, incx, a, lda)
    CHER
subroutine dsyr (uplo, n, alpha, x, incx, a, lda)
    DSYR
subroutine ssyr (uplo, n, alpha, x, incx, a, lda)
    SSYR
subroutine zher (uplo, n, alpha, x, incx, a, lda)
    ZHER
subroutine csyr (uplo, n, alpha, x, incx, a, lda)
    CSYR performs the symmetric rank-1 update of a complex symmetric
    matrix.
subroutine zsyr (uplo, n, alpha, x, incx, a, lda)
    ZSYR performs the symmetric rank-1 update of a complex symmetric
    matrix.

💫 Detailed Description 💫

No extra prose here, bestie — it just rolls straight into the function docs. 🫶

🧚 Function Documentation 🧚

💅 subroutine cher 💅

subroutine cher (character uplo, integer n, real alpha, complex,
    dimension(*) x, integer incx, complex, dimension(lda,*) a, integer lda)

🎀 Purpose 🎀

CHER performs the hermitian rank 1 operation:

A := alpha*x*x**H + A,

where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix. Periodt. 💖

🍓 Parameters 🍓

UPLO — UPLO is CHARACTER*1. On entry, UPLO says whether the upper or lower triangular part of the array A is referenced, like this:
- UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced.
- UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced.
N — N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. ✅
ALPHA — ALPHA is REAL. On entry, ALPHA specifies the scalar alpha. 🎀
X — X is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 🦋
INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 🚫
A — A is COMPLEX array, dimension ( LDA, N ).
- Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix, and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. 💫
- Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix, and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. 💫
- Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. Important lil detail, bestie. 🫶
LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). 👑

🌈 Author 🌈

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

⭐ Further Details: ⭐

Level 2 Blas routine.
-- Written on 22-October-1986.
- Jack Dongarra, Argonne National Lab.
- Jeremy Du Croz, Nag Central Office.
- Sven Hammarling, Nag Central Office.
- Richard Hanson, Sandia National Labs.

Definition at line 134 of file cher.f.

🦋 subroutine csyr 🦋

subroutine csyr (character uplo, integer n, complex alpha, complex,
    dimension( * ) x, integer incx, complex, dimension( lda, * ) a, integer
    lda)

CSYR performs the symmetric rank-1 update of a complex symmetric matrix. iykyk 💜

🎀 Purpose 🎀

CSYR performs the symmetric rank 1 operation:

A := alpha*x*x**H + A,

where alpha is a complex scalar, x is an n element vector and A is an n by n symmetric matrix. ✨

🍓 Parameters 🍓

UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows:
- UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced.
- UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced.
- Unchanged on exit. ✅
N — N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. 🌸
ALPHA — ALPHA is COMPLEX. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. 🎀
X — X is COMPLEX array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the N-element vector x. Unchanged on exit. 🦋
INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. 🚫
A — A is COMPLEX array, dimension ( LDA, N ).
- Before entry, with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix, and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. 💫
- Before entry, with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix, and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. 💫
LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, N ). Unchanged on exit. 👑

🌈 Author 🌈

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

Definition at line 134 of file csyr.f.

🧚 subroutine dsyr 🧚

subroutine dsyr (character uplo, integer n, double precision alpha, double
    precision, dimension(*) x, integer incx, double precision,
    dimension(lda,*) a, integer lda)

🎀 Purpose 🎀

DSYR performs the symmetric rank 1 operation:

A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix. slay. 🔥

🍓 Parameters 🍓

UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows:
- UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced.
- UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced.
N — N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. 🌸
ALPHA — ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 🎀
X — X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 🦋
INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 🚫
A — A is DOUBLE PRECISION array, dimension ( LDA, N ).
- Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix, and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. 💫
- Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix, and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. 💫
LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). 👑

🌈 Author 🌈

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

⭐ Further Details: ⭐

okay so we’re literally still mid-dsyr, and its Further Details block is giving old-school BLAS lore:

Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.

and then it wraps with Definition at line 131 of file dsyr.f. — periodt 💅

🌸 `ssyr` — real symmetric rank-1, no cap 🌸

subroutine ssyr (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(lda,*) a, integer lda)

SSYR

Purpose: bestie, SSYR performs the symmetric rank 1 operation

A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix. iconic behavior ✨

Parameters

UPLO — CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced, like this:
- UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced.
- UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced.
N — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
ALPHA — REAL. On entry, ALPHA specifies the scalar alpha.
X — REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
A — REAL array, dimension ( LDA, N ).
- Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix.
- Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.
LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).

Author

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

Further Details:

Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.

Definition at line 131 of file ssyr.f.

🦋 `zher` — hermitian rank-1, complex girlie edition 🦋

subroutine zher (character uplo, integer n, double precision alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(lda,*) a, integer lda)

ZHER

Purpose: ZHER performs the hermitian rank 1 operation

A := alpha*x*x**H + A,

where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix. she’s giving conjugate-transpose main character energy 💅

Parameters

UPLO — CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows:
- UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced.
- UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced.
N — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
ALPHA — DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
X — COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
A — COMPLEX*16 array, dimension ( LDA, N ).
- Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix.
- Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.
- Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. yes bestie, they get zeroed out 😭
LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).

Author

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

Further Details:

Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.

Definition at line 134 of file zher.f.

🎀 `zsyr` — complex symmetric rank-1 update, periodt 🎀

subroutine zsyr (character uplo, integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16, dimension( lda, * ) a, integer lda)

ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.

Purpose: ZSYR performs the symmetric rank 1 operation

A := alpha*x*x**H + A,

where alpha is a complex scalar, x is an n element vector and A is an n by n symmetric matrix. lowkey obsessed with how clean this is ✨

Parameters

UPLO — CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows:
- UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced.
- UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced.
- Unchanged on exit.
N — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA — COMPLEX*16. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X — COMPLEX*16 array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the N-element vector x. Unchanged on exit.
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
A — COMPLEX*16 array, dimension ( LDA, N ).
- Before entry, with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix.
- Before entry, with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.
LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, N ). Unchanged on exit.

Author

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

Definition at line 134 of file zsyr.f.

🎀 AUTHOR 🎀

Okay so plot twist bestie — nobody actually sat down and wrote this page by hand 💅. It's the OG automation slay:

Generated automatically by Doxygen for LAPACK from the source code.

That's it, that's the whole author section 🫶. Doxygen did the typing, LAPACK supplied the brains, and the source code is the real main character here ✨. So if you were hoping to @ somebody about a typo… it's giving the source code, iykyk 😭.

And that's a wrap on her(3), bestie 🎀 — you made it all the way to the end, which is honestly iconic of you 👑. This whole page shipped as part of LAPACK, Version 3.12.0 — so go forth, conjugate that Hermitian matrix, and remember: no cap, that diagonal was real the whole time 💀✨🌸

byeeee 💖

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

her(3)

her(3) — Library Functions Manual — her(3) 💅

🌸 NAME 🌸

✨ SYNOPSIS ✨

Functions

💫 Detailed Description 💫

🧚 Function Documentation 🧚

💅 subroutine cher 💅

🎀 Purpose 🎀

🍓 Parameters 🍓

🌈 Author 🌈

⭐ Further Details: ⭐

🦋 subroutine csyr 🦋

🎀 Purpose 🎀

🍓 Parameters 🍓

🌈 Author 🌈

🧚 subroutine dsyr 🧚

🎀 Purpose 🎀

🍓 Parameters 🍓

🌈 Author 🌈

⭐ Further Details: ⭐

🌸 ssyr — real symmetric rank-1, no cap 🌸

🦋 zher — hermitian rank-1, complex girlie edition 🦋

🎀 zsyr — complex symmetric rank-1 update, periodt 🎀

🎀 AUTHOR 🎀

`her(3)` — Library Functions Manual — `her(3)` 💅

🌸 `ssyr` — real symmetric rank-1, no cap 🌸

🦋 `zher` — hermitian rank-1, complex girlie edition 🦋

🎀 `zsyr` — complex symmetric rank-1 update, periodt 🎀