hpr(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

okay so bestie, this is hpr(3) from the Library Functions Manual, and she’s serving {hp,sp}r: Hermitian/symmetric rank-1 update realness 💅✨ like if you’ve ever needed a rank-1 update on a packed Hermitian or symmetric matrix, this is literally your girl. no cap, she’s iconic.

💖 NAME 💖

hpr — {hp,sp}r: Hermitian/symmetric rank-1 update 🫶

🌈 SYNOPSIS 🌈

🎀 Functions 🎀

chpr — subroutine chpr (uplo, n, alpha, x, incx, ap) — CHPR 💖
dspr — subroutine dspr (uplo, n, alpha, x, incx, ap) — DSPR ✨
sspr — subroutine sspr (uplo, n, alpha, x, incx, ap) — SSPR 🌸
zhpr — subroutine zhpr (uplo, n, alpha, x, incx, ap) — ZHPR 🦋
cspr — subroutine cspr (uplo, n, alpha, x, incx, ap) — CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix. 💜
zspr — subroutine zspr (uplo, n, alpha, x, incx, ap) — ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix. 🧚

🦋 Detailed Description 🦋

like, the actual documentation section, bestie — buckle up 🎀

💜 Function Documentation 💜

🌸 `subroutine chpr` 🌸

subroutine chpr (character uplo, integer n, real alpha, complex, dimension(*) x, integer incx, complex, dimension(*) ap)

CHPR

Purpose:

okay so CHPR 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, supplied in packed form. periodt. 💅

Parameters

UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
- UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
- UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP.
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.
AP — AP is COMPLEX array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP 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 tea.

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 129 of file chpr.f. ✨

🦋 `subroutine cspr` 🦋

subroutine cspr (character uplo, integer n, complex alpha, complex, dimension( * ) x, integer incx, complex, dimension( * ) ap)

CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix. 💜

Purpose:

CSPR 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, supplied in packed form.

Parameters

UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
- UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
- UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP. 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.
AP — AP is COMPLEX array, dimension at least ( ( N*( N + 1 ) )/2 ). Before entry, with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry, with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP 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. 🍓

Author

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

Definition at line 131 of file cspr.f. 🔥

🌈 `subroutine dspr` 🌈

subroutine dspr (character uplo, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(*) ap)

DSPR

Purpose:

DSPR 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, supplied in packed form. 💖

Parameters

UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
- UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
- UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP.
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.
AP — AP is DOUBLE PRECISION array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. 💜

Author

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

Further Details:

(part 2 picks up right here, bestie 🦋)

           !>
           !>  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 126 of file dspr.f.

✨ subroutine sspr ✨

subroutine sspr (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) ap)

🌸 Purpose 🌸

Okay so SSPR 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, supplied in packed form. Slay, that’s the whole vibe. ✨

💖 Parameters 💖

UPLO — CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
- UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
- UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP.
N — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. No cap. 🫶
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. 🚨
AP — REAL array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. 💅

Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. 🦋

🌟 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 126 of file sspr.f.

✨ subroutine zhpr ✨

subroutine zhpr (character uplo, integer n, double precision alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) ap)

🌸 Purpose 🌸

ZHPR 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, supplied in packed form. Iconic. 👑

💖 Parameters 💖

UPLO — CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
- UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
- UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP.
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.
AP — COMPLEX*16 array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. ✨

Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP 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. 💅

🌟 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 129 of file zhpr.f.

✨ subroutine zspr ✨

subroutine zspr (character uplo, integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) ap)

ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix. Main character energy fr fr. 🌈

🌸 Purpose 🌸

ZSPR 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, supplied in packed form. Periodt. ✨

💖 Parameters 💖

UPLO — CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
- UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
- UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP.

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. 🚨
AP — COMPLEX*16 array, dimension at least ( ( N*( N + 1 ) )/2 ). Before entry, with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. 🌸

Before entry, with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP 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. 🫶

🌟 Author 🌟

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

Definition at line 131 of file zspr.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

Okay bestie, that’s the whole hpr(3) situation! 💅 The footer vibes are LAPACK Version 3.12.0, page hpr(3) — mwah 💋✨

📦 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

hpr(3)

💖 NAME 💖

🌈 SYNOPSIS 🌈

🎀 Functions 🎀

🦋 Detailed Description 🦋

💜 Function Documentation 💜

🌸 subroutine chpr 🌸

🦋 subroutine cspr 🦋

🌈 subroutine dspr 🌈

✨ subroutine sspr ✨

🌸 Purpose 🌸

💖 Parameters 💖

🌟 Author 🌟

🦋 Further Details 🦋

✨ subroutine zhpr ✨

🌸 Purpose 🌸

💖 Parameters 💖

🌟 Author 🌟

🦋 Further Details 🦋

✨ subroutine zspr ✨

🌸 Purpose 🌸

💖 Parameters 💖

🌟 Author 🌟

🌈 Author 🌈

🌸 `subroutine chpr` 🌸

🦋 `subroutine cspr` 🦋

🌈 `subroutine dspr` 🌈