BLAS/SRC/ssyr2k.f(3)

💖 SSYR2K — BLAS/SRC/ssyr2k.f(3) 💖

okay bestie, sit DOWN because we're doing symmetric rank-2k matrix updates and honestly? it's giving main character energy. this page lives in the LAPACK manual, under BLAS/SRC/ssyr2k.f(3), and it's literally just one iconic little subroutine doing one iconic little job. no cap. 🦋

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✨ NAME ✨

BLAS/SRC/ssyr2k.f — that's it, that's the name, periodt. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ssyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc) — SSYR2K, the one and only 👑

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✨ Function/Subroutine Documentation ✨

subroutine ssyr2k (character uplo, character trans, integer n, integer k, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)

SSYR2K

🎀 Purpose

bestie. SSYR2K performs one of the symmetric rank 2k operations, and there are two of them, so pick your fighter:

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. 🌈

🌸 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.
• TRANS = 'C' or 'c' — 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, we don't judge 💀)

• 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' or 'C' or 'c', K specifies the number of rows of the matrices A and B. K 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

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 REAL 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 REAL

On entry, BETA specifies the scalar beta. ✨

• C

C is REAL 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. 🫶

• 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 really said "we made this" and honestly? slay. 💜

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🌈 Further Details:

• Level 3 Blas routine. (yes bestie, level THREE, we're fancy 🎀)
• -- 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.

1989?? they were doing linear algebra before it was cool. iconic behavior fr fr. ⭐

Definition at line 191 of file ssyr2k.f. — go look, it's right there, line 191, iykyk 🔥

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💅 Author

Generated automatically by Doxygen for LAPACK from the source code. the robots did this part, we just made it cute. 🤖✨

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and that's the whole page bestie!! mwah 💖

Version 3.12.0 — Tue Nov 28 2023 12:08:41 — BLAS/SRC/ssyr2k.f(3)

okay love u, go update some symmetric matrices, drink water, and remember: only the triangular part you declared is getting touched, the rest is not referenced, periodt. 🦋🌸💅