BLAS/SRC/csyr2k.f(3)

okay so bestie, welcome to the Library Functions Manual page for BLAS/SRC/csyr2k.f(3) — yes, the 3 is right there, we love a numbered manual section. The main character is CSYR2K, a Level 3 Blas routine, and she is absolutely serving symmetric rank 2k updates. 💅✨

💖 NAME 💖

BLAS/SRC/csyr2k.f

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

• subroutine csyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc) — CSYR2K

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🦋 Function/Subroutine Documentation 🦋

here's the full signature, copied exactly because we do not play with technical details:

subroutine csyr2k (character uplo, character trans, integer n, integer k,
     complex alpha, complex, dimension(lda,*) a, integer lda, complex,
     dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*)
     c, integer ldc)

CSYR2K

🎯 Purpose: 🎯

okay so CSYR2K performs one of the symmetric rank 2k operations, and the equations are giving math major with a skincare routine:

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. periods, bestie.

💖 Parameters 💖

every single parameter, because we keep all the details, periodt:

• UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced, like:
  • 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, and the vibes are:
  • 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.
• 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.
• ALPHA — ALPHA is COMPLEX. On entry, ALPHA specifies the scalar alpha.
• A — A is COMPLEX 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 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. On entry, BETA specifies the scalar beta.
• C — C is COMPLEX 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 ).

👑 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 187 of file csyr2k.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie — footer sign-off vibes: LAPACK, Version 3.12.0, BLAS/SRC/csyr2k.f(3) 💖✨🫶