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🌸 NAME 🌸

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✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

       subroutine CLAVHE_ROOK (uplo, trans, diag, n, nrhs, a, lda, ipiv, b,
           ldb, info)
           CLAVHE_ROOK

🦋 Function/Subroutine Documentation 🦋

   subroutine CLAVHE_ROOK (character uplo, character trans, character diag,
       integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda,
       integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer
       ldb, integer info)
       CLAVHE_ROOK

💅 Purpose 💅

Okay so here's the tea: CLAVHE_ROOK performs one of these matrix-vector operations:

x := A*x  or  x := A^H*x,

where x is an N element vector and A is one of the factors from the block U*D*U' or L*D*L' factorization computed by CHETRF_ROOK. 🧚

• If TRANS = 'N', multiplies by U or U * D (or L or L * D)
• If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. Specifies whether the factor stored in A is upper or lower triangular. 🌈
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1. Specifies the operation to be performed:
  • = 'N': x := A*x
  • = 'C': x := A^H*x
• DIAG — DIAG is CHARACTER*1. Specifies whether or not the diagonal blocks are unit matrices. If the diagonal blocks are assumed to be unit, then A = U or A = L, otherwise A = U*D or A = L*D. 💅
  • = 'U': Diagonal blocks are assumed to be unit matrices.
  • = 'N': Diagonal blocks are assumed to be non-unit matrices.
• N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0. ⭐
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0. 🎀
• A — A is COMPLEX array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK. Stored as a 2-D triangular matrix. 🦋
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). ✨
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CHETRF_ROOK. 👑
  • If UPLO = 'U':
    • Only the last KB elements of IPIV are set.
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
    • If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • If UPLO = 'L':
    • Only the first KB elements of IPIV are set.
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
    • If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• B — B is COMPLEX array, dimension (LDB,NRHS). On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B. 🔥
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 💜
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -k, the k-th argument had an illegal value

👑 Author 👑

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

Definition at line 154 of file clavhe_rook.f. 📌

🌈 Author 🌈

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