BLAS/SRC/zsyrk.f(3)

💖 BLAS/SRC/zsyrk.f(3) — the zsyrk glow-up 💖

Page BLAS/SRC/zsyrk.f(3) from the Library Functions Manual — yes, that's the manual name, bestie. This is the tea on zsyrk, a BLAS Level 3 routine doing symmetric rank-k update things. It's giving linear algebra, it's giving “only half of the symmetric matrix is invited,” and honestly it's iconic. 💅

✨ NAME ✨

BLAS/SRC/zsyrk.f — the file/page name, periodt. This is the manual entry for the zsyrk subroutine.

🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine zsyrk (uplo, trans, n, k, alpha, a, lda, beta, c, ldc) — ZSYRK, the short call signature, looking very main character.

       subroutine zsyrk (uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
           ZSYRK

🌈 Function/Subroutine Documentation 🌈

🫶 zsyrk 🫶

   subroutine zsyrk (character uplo, character trans, integer n, integer k,
       complex*16 alpha, complex*16, dimension(lda,*) a, integer lda,
       complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)

ZSYRK

Okay so ZSYRK is the routine name. Here's the purpose, no cap:

Purpose 🎀

ZSYRK performs one of the symmetric rank k operations

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

or

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

where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case. 💖

Parameters 💅

Now the parameters, bestie. Every single one matters, don't skip.

• UPLO — 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 — CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:
  • TRANS = 'N' or 'n' — C := alpha*A*A**T + beta*C.
  • TRANS = 'T' or 't' — C := alpha*A**T*A + beta*C.
• N — INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero.
• K — INTEGER. On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'T' or 't', K specifies the number of rows of the matrix A. K must be at least zero.
• ALPHA — COMPLEX*16. On entry, ALPHA specifies the scalar alpha.
• A — 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 — 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 ).
• BETA — COMPLEX*16. On entry, BETA specifies the scalar beta.
• C — 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.
• LDC — 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 ).

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 166 of file zsyrk.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole page, bestie. No cap, all the details are here, and the symmetric matrix half-party is fully documented. xoxo, your LAPACK bestie 💅✨ — LAPACK Version 3.12.0, page BLAS/SRC/zsyrk.f(3). 🫶