hemm(3)

📦

version 3.12.0 · 4 versions

3.12.0 · centos-stream 10, fedora 43, fedora 44 (latest)
3.12.0 · opensuse-leap 16.0
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble

, in centos-stream 10, fedora 43, fedora 44

💖 hemm(3) 💖 — LAPACK

okay so bestie, pull up a chair and sip something 🫖 this is hemm(3) from LAPACK, and she is the {he,sy}mm icon: Hermitian/symmetric matrix-matrix multiply. Six routines, one job, zero skips. Let's go 💅

✨ NAME ✨

hemm — {he,sy}mm: Hermitian/symmetric matrix-matrix multiply

🎀 SYNOPSIS 🎀

🦋 Functions

subroutine chemm (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc) — CHEMM
subroutine csymm (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc) — CSYMM
subroutine dsymm (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc) — DSYMM
subroutine ssymm (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc) — SSYMM
subroutine zhemm (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc) — ZHEMM
subroutine zsymm (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc) — ZSYMM

🌈 Detailed Description 🌈

(not much tea here, the good stuff lives under Function Documentation 👇)

👑 Function Documentation 👑

💜 `subroutine chemm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,) a, integer lda, complex, dimension(ldb,) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)`

CHEMM

Purpose:

CHEMM does one of these two matrix-matrix operations, pick your fighter:

C := alpha*A*B + beta*C,

C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is an hermitian matrix, and B and C are m by n matrices. periodt 💅

Parameters

SIDE — CHARACTER*1. On entry, SIDE says whether the hermitian matrix A shows up on the left or the right of the operation, like this:
- SIDE = 'L' or 'l' → C := alpha*A*B + beta*C,
- SIDE = 'R' or 'r' → C := alpha*B*A + beta*C,
UPLO — CHARACTER*1. On entry, UPLO says whether we're referencing the upper or the lower triangular part of the hermitian matrix A, like this:
- UPLO = 'U' or 'u' → only the upper triangular part of the hermitian matrix is to be referenced.
- UPLO = 'L' or 'l' → only the lower triangular part of the hermitian matrix is to be referenced.
M — INTEGER. On entry, M is the number of rows of the matrix C. M must be at least zero.
N — INTEGER. On entry, N is the number of columns of the matrix C. N must be at least zero.
ALPHA — COMPLEX. On entry, ALPHA is the scalar alpha.
A — COMPLEX array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l', and is n otherwise.

Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the hermitian matrix, such that when UPLO = 'U' or 'u', the leading m by m 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; and when UPLO = 'L' or 'l', the leading m by m 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.

Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the hermitian matrix, such that when 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; and when 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.

heads up bestie 💀 the imaginary parts of the diagonal elements need not be set — they're assumed to be zero.

LDA — INTEGER. On entry, LDA is the first dimension of A as declared in the calling (sub)program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).
B — COMPLEX array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the matrix B.
LDB — INTEGER. On entry, LDB is the first dimension of B as declared in the calling (sub)program. LDB must be at least max( 1, m ).
BETA — COMPLEX. On entry, BETA is the scalar beta. When BETA is supplied as zero then C need not be set on input. (free real estate 😌)
C — COMPLEX array, dimension ( LDC, N ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix.
LDC — INTEGER. On entry, LDC is the first dimension of C as declared in the calling (sub)program. LDC must be at least max( 1, m ).

Author

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

Further Details:

Level 3 Blas routine.

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 190 of file chemm.f.

💙 `subroutine csymm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,) a, integer lda, complex, dimension(ldb,) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)`

CSYMM

Purpose:

CSYMM performs one of the matrix-matrix operations

C := alpha*A*B + beta*C,

C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices. 🦋

Parameters

SIDE — CHARACTER*1. On entry, SIDE says whether the symmetric matrix A appears on the left or the right in the operation, like this:
- SIDE = 'L' or 'l' → C := alpha*A*B + beta*C,
- SIDE = 'R' or 'r' → C := alpha*B*A + beta*C,
UPLO — CHARACTER*1. On entry, UPLO says whether the upper or lower triangular part of the symmetric matrix A is to be referenced, like this:
- UPLO = 'U' or 'u' → only the upper triangular part of the symmetric matrix is to be referenced.
- UPLO = 'L' or 'l' → only the lower triangular part of the symmetric matrix is to be referenced.
M — INTEGER. On entry, M is the number of rows of the matrix C. M must be at least zero.
N — INTEGER. On entry, N is the number of columns of the matrix C. N must be at least zero.
ALPHA — COMPLEX. On entry, ALPHA is the scalar alpha.
A — COMPLEX array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l', and is n otherwise.

Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m 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; and when UPLO = 'L' or 'l', the leading m by m 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.

Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when 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; and when 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.

LDA — INTEGER. On entry, LDA is the first dimension of A as declared in the calling (sub)program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).
B — COMPLEX array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the matrix B.
LDB — INTEGER. On entry, LDB is the first dimension of B as declared in the calling (sub)program. LDB must be at least max( 1, m ).
BETA — COMPLEX. On entry, BETA is the scalar beta. When BETA is supplied as zero then C need not be set on input.
C
C — C is COMPLEX array, dimension ( LDC, N ). Before you come in, the leading m by n part of the array C has to already hold the matrix C… except when beta is zero, bestie, in which case C literally does not need to be set on entry, we don't care 💅. On the way out, the array C gets fully overwritten by the m by n updated matrix. It's giving glow-up ✨.
LDC — LDC is INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ). That's the whole vibe check, no notes 🫶.

Author 🌸

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

Further Details: 🎀

Level 3 Blas routine. Say it with me: Level 3 Blas routine 👑

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 188 of file csymm.f.

✨ subroutine `dsymm` ✨

subroutine dsymm (character side, character uplo, integer m, integer n,
    double precision alpha, double precision, dimension(lda,*) a, integer
    lda, double precision, dimension(ldb,*) b, integer ldb, double precision
    beta, double precision, dimension(ldc,*) c, integer ldc)

DSYMM — the double precision one, and honestly? Iconic 💜

Purpose:

DSYMM performs one of the matrix-matrix operations

   C := alpha*A*B + beta*C,

   C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices. Two operations, one routine, main character energy fr fr 😭🔥

Parameters

SIDE — SIDE is CHARACTER*1. On entry, SIDE tells us whether the symmetric matrix A shows up on the left or the right in the operation, like this:

SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

UPLO — UPLO is CHARACTER*1. On entry, UPLO says whether the upper or lower triangular part of the symmetric matrix A is the one getting referenced:

UPLO = 'U' or 'u'   Only the upper triangular part of the
                    symmetric matrix is to be referenced.

UPLO = 'L' or 'l'   Only the lower triangular part of the
                    symmetric matrix is to be referenced.

M — M is INTEGER. On entry, M specifies the number of rows of the matrix C. M must be at least zero. Zero is allowed, we're not judging 🫶
N — N is INTEGER. On entry, N specifies the number of columns of the matrix C. N must be at least zero. Same deal bestie.
ALPHA — ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha ✨
A — A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise. Okay okay, deep breath, here's the tea:
- Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m 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. And when UPLO = 'L' or 'l', the leading m by m 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.
- Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when 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. And when 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.
LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ). Choose wisely bestie 💀
B — B is DOUBLE PRECISION array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the matrix B. That's it, that's the job ✨
LDB — LDB is INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
BETA — BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input 👀 (free pass, take it).
C — C is DOUBLE PRECISION array, dimension ( LDC, N ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. Served fresh 💅
LDC — LDC is INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).

Author 🌸

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

Further Details: 🎀

Level 3 Blas routine. Periodt 👑

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 188 of file dsymm.f.

✨ subroutine `ssymm` ✨

subroutine ssymm (character side, character uplo, integer m, integer n, real
    alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b,
    integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)

SSYMM — single precision edition, same energy, different bytes 🦋

Purpose:

SSYMM performs one of the matrix-matrix operations

   C := alpha*A*B + beta*C,

   C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices. Yeah it's the same routine but in REAL, we love consistency 🫶

Parameters

SIDE — SIDE is CHARACTER*1. On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation, as follows:

SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced, as follows:

UPLO = 'U' or 'u'   Only the upper triangular part of the
                    symmetric matrix is to be referenced.

UPLO = 'L' or 'l'   Only the lower triangular part of the
                    symmetric matrix is to be referenced.

M — M is INTEGER. On entry, M specifies the number of rows of the matrix C. M must be at least zero.
N — N is INTEGER. On entry, N specifies the number of columns of the matrix C. N must be at least zero.
ALPHA — ALPHA is REAL. On entry, ALPHA specifies the scalar alpha ✨
A — A is REAL array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise. Okay, the full rundown:
- Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m 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. And when UPLO = 'L' or 'l', the leading m by m 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.
- Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when 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. And when 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.
LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).
B — B is REAL array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the matrix B.
LDB — LDB is INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
BETA — BETA is REAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input 👀
C
C — COMPLEX*16 array, dimension ( LDC, N ). So like, before you even walk in the door, the leading m by n chunk of the array C has to already hold the matrix C — except when beta is zero, in which case bestie, C doesn't need to be set on entry at all, it's giving ✨no thoughts head empty✨. On exit tho? The array C gets overwritten by the m by n updated matrix. It ate and left no crumbs. 💅
LDC — LDC is INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ). fr fr, don't skip this one 🫶

Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details 🔍

Level 3 Blas routine.

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 188 of file ssymm.f. — iconic, historic, a whole moment in time 💖

subroutine `zhemm` 🦋

subroutine zhemm (character side, character uplo, integer m, integer n,
    complex*16 alpha, complex*16, dimension(lda,*) a, integer lda,
    complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta,
    complex*16, dimension(ldc,*) c, integer ldc)

ZHEMM 🌈

Purpose:

ZHEMM performs one of the matrix-matrix operations

C := alpha*A*B + beta*C,

C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is an hermitian matrix and B and C are m by n matrices. hermitian?? in THIS economy?? yes bestie, and she's serving 💅

Parameters

SIDE — SIDE is CHARACTER*1. On entry, SIDE specifies whether the hermitian matrix A appears on the left or right in the operation, like this:
- SIDE = 'L' or 'l' → C := alpha*A*B + beta*C,
- SIDE = 'R' or 'r' → C := alpha*B*A + beta*C,
UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced, as follows:
- UPLO = 'U' or 'u' → Only the upper triangular part of the hermitian matrix is to be referenced.
- UPLO = 'L' or 'l' → Only the lower triangular part of the hermitian matrix is to be referenced.

pick a side, any side, just not both 🙈

M — M is INTEGER. On entry, M specifies the number of rows of the matrix C. M must be at least zero.
N — N is INTEGER. On entry, N specifies the number of columns of the matrix C. N must be at least zero.
ALPHA — ALPHA is COMPLEX*16. On entry, ALPHA specifies the scalar alpha. the moment ✨
A — A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise.

Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the hermitian matrix, such that when UPLO = 'U' or 'u', the leading m by m 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, and when UPLO = 'L' or 'l', the leading m by m 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.

Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the hermitian matrix, such that when 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, and when 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.

Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero. so like, don't stress about those, they're literally not even reading them 😭

LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).
B — B is COMPLEX*16 array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the matrix B.
LDB — LDB is INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
BETA — BETA is COMPLEX*16. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. free real estate, bestie 💖
C — C is COMPLEX*16 array, dimension ( LDC, N ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. overwritten!! she's a whole new girl now 💅
LDC — LDC is INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).

Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details 🔍

Level 3 Blas routine.

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 190 of file zhemm.f. ⭐

subroutine `zsymm` 🌸

subroutine zsymm (character side, character uplo, integer m, integer n,
    complex*16 alpha, complex*16, dimension(lda,*) a, integer lda,
    complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta,
    complex*16, dimension(ldc,*) c, integer ldc)

ZSYMM 🌈

Purpose:

ZSYMM performs one of the matrix-matrix operations

C := alpha*A*B + beta*C,

C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices. symmetric queen, we love her, no notes 👑

Parameters

SIDE — SIDE is CHARACTER*1. On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation, as follows:
- SIDE = 'L' or 'l' → C := alpha*A*B + beta*C,
- SIDE = 'R' or 'r' → C := alpha*B*A + beta*C,
UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows:
- UPLO = 'U' or 'u' → Only the upper triangular part of the symmetric matrix is to be referenced.
- UPLO = 'L' or 'l' → Only the lower triangular part of the symmetric matrix is to be referenced.
M — M is INTEGER. On entry, M specifies the number of rows of the matrix C. M must be at least zero.
N — N is INTEGER. On entry, N specifies the number of columns of the matrix C. N must be at least zero.
ALPHA — ALPHA is COMPLEX*16. On entry, ALPHA specifies the scalar alpha.
A — A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise.

Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m 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, and when UPLO = 'L' or 'l', the leading m by m 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.

Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when 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, and when 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.

notice how there's no imaginary-diagonal note here? that's the hermitian vs symmetric of it all, iykyk 🧚

LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).
B — B is COMPLEX*16 array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the matrix B.
LDB — LDB is INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
BETA — BETA is COMPLEX*16. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. again!! don't set it, she said what she said 💅
BETA is COMPLEX*16. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. 💅
C — C is COMPLEX*16 array, dimension ( LDC, N ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. it literally updates in place, bestie ✨
LDC — LDC is INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ). 🫶

Author

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

Further Details

Level 3 Blas routine. periodt 🌈

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 188 of file zsymm.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

okay bestie that's the whole page, no cap 💖 This was LAPACK 3.12.0, generated Tue Nov 28 2023 12:08:43, for hemm(3). bye pookie, go update your matrices responsibly 🎀✨

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centos-stream 10: lapack 3.12.0-7.el10 · BSD-3-Clause-Open-MPI
fedora 43: lapack 3.12.0-10.fc43 · BSD-3-Clause-Open-MPI
fedora 43: lapack 3.12.0-10.fc43 · BSD-3-Clause-Open-MPI
fedora 44: lapack 3.12.0-11.fc44 · BSD-3-Clause-Open-MPI
fedora 44: lapack 3.12.0-11.fc44 · BSD-3-Clause-Open-MPI
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash on 2026-10-14: a language model's rewrite of the original, under its terms

hemm(3)

💖 hemm(3) 💖 — LAPACK

✨ NAME ✨

🎀 SYNOPSIS 🎀

🦋 Functions

🌈 Detailed Description 🌈

👑 Function Documentation 👑

💜 subroutine chemm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)

Purpose:

Parameters

Author

Further Details:

💙 subroutine csymm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)

Purpose:

Parameters

✨ subroutine dsymm ✨

✨ subroutine ssymm ✨

Author 👑

Further Details 🔍

subroutine zhemm 🦋

Author 👑

Further Details 🔍

subroutine zsymm 🌸

Author

Further Details

Author

💜 `subroutine chemm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,) a, integer lda, complex, dimension(ldb,) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)`

💙 `subroutine csymm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,) a, integer lda, complex, dimension(ldb,) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)`

✨ subroutine `dsymm` ✨

✨ subroutine `ssymm` ✨

subroutine `zhemm` 🦋

subroutine `zsymm` 🌸