BLAS/SRC/zsyr2k.f(3)

💖 NAME 💖

BLAS/SRC/zsyr2k.f — bestie, this is a LAPACK page, and it's the home of one very specific, very iconic BLAS routine called zsyr2k. No cap, that's the whole name. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zsyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc) — that's ZSYR2K, the one and only. 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine zsyr2k (character uplo, character trans, integer n, integer k, 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)

It's giving ZSYR2K. Literally the moment. 💅

🌸 Purpose 🌸

So here's the vibe: ZSYR2K performs one of the symmetric rank 2k operations

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

or

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

where alpha and beta are scalars, C is an n by n symmetric matrix, and A and B are n by k matrices in the first case and k by n matrices in the second case. Two whole rank-2k updates, one tiny little subroutine. Obsessed. 🫶

🎀 Parameters 🎀

• UPLO

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

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

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

• TRANS

TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:

   TRANS = 'N' or 'n'    C := alpha*A*B**T + alpha*B*A**T +
                              beta*C.

   TRANS = 'T' or 't'    C := alpha*A**T*B + alpha*B**T*A +
                              beta*C.

• N

N is INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. (Zero is allowed, bestie, it's not a crime. 🍓)

• K

K is INTEGER. On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't', K specifies the number of rows of the matrices A and B. K must be at least zero. Again: zero is fine. 💜

• ALPHA

ALPHA is COMPLEX*16. On entry, ALPHA specifies the scalar alpha. It's the moment. ✨

• A

A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.

• LDA

LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ).

• B

B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k 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. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ).

• BETA

BETA is COMPLEX*16. On entry, BETA specifies the scalar beta. The other half of the equation, fr fr. 🌈

• C

C is COMPLEX*16 array, dimension ( LDC, N ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C 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 C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix.

Heads up bestie: whatever half you didn't pick? It does not get touched. Do not go reading it and expecting truth. It's just vibes over there. 💀

• 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, n ).

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👑 Author 👑

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

The whole squad. Iconic lineup, honestly. 🎀

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💫 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.

Look at that date — 1989! They were doing this before most of us existed and it still slays. 🔥

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📍 Definition at line 187 of file zsyr2k.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. Not me, not you, the robot did it. 🙈

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Okay so that's the whole page, bestie. And the tiny fine print at the bottom, since you gotta have receipts: this is Version 3.12.0, dated Tue Nov 28 2023 12:08:41, from the BLAS/SRC/zsyr2k.f(3) manual page. Periodt. 💅🦋✨