BLAS/SRC/zher2k.f(3)

💖 NAME 💖

BLAS/SRC/zher2k.f — okay bestie, this is the Library Functions Manual page for that exact file. It’s the home of ZHER2K, and we’re about to make hermitian rank 2k operations make sense. 💅

---

✨ SYNOPSIS ✨

💕 Functions/Subroutines 💕

• subroutine zher2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
• ZHER2K

---

💅 Function/Subroutine Documentation 💅

🫶 subroutine zher2k 🫶

subroutine zher2k (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, double precision beta,
    complex*16, dimension(ldc,*) c, integer ldc)

🎀 ZHER2K 🎀

💖 Purpose: 💖

Okay so ZHER2K performs one of the hermitian rank 2k operations, and the math is giving:

C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,

or

C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,

where alpha and beta are scalars with beta real, C is an n by n hermitian matrix, and A and B are n by k matrices in the first case and k by n matrices in the second case. Periodt. 💫

🌈 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, bestie:
  • 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**H + conjg( alpha )*B*A**H + beta*C.
  • TRANS = 'C' or 'c' — C := alpha*A**H*B + conjg( alpha )*B**H*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 = 'C' or 'c', K specifies the number of rows of the matrices A and B. K 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 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 ). Unchanged on exit. 🫶
• BETA — BETA is DOUBLE PRECISION . On entry, BETA specifies the scalar beta. 🍓
• C — C is COMPLEX*16 array, dimension ( LDC, N ). Okay, this one has layers:
  • 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 hermitian 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 hermitian 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. 💖
  • Note that the imaginary parts of the diagonal elements need not be set; they are assumed to be zero, and on exit they are set to zero. 🌀
• 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.
• -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. Ed Anderson, Cray Research Inc.

Definition at line 197 of file zher2k.f. ✅

📝 Author 📝

Author — Generated automatically by Doxygen for LAPACK from the source code.

---

mwah 💋 — that’s the whole page, bestie. The footer says LAPACK Version 3.12.0 and BLAS/SRC/zher2k.f(3), so you’re fully caught up. xoxo, your Unix bestie 💖✨