ZLAVHE_ROOK(3)

🎀 zlavhe_rook(3)

Bestie, welcome to the Library Functions Manual page for TESTING/LIN/zlavhe_rook.f — yes, we’re doing Fortran LAPACK lore today. 💅

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💖 NAME

TESTING/LIN/zlavhe_rook.f

That’s it. That’s the name. Iconic minimalism. ✨

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✨ SYNOPSIS

🧚 Functions/Subroutines

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

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🌸 Function/Subroutine Documentation

   subroutine zlavhe_rook (character uplo, character trans, character diag,
       integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,
       integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer
       ldb, integer info)
       ZLAVHE_ROOK

🦋 Purpose

Okay so ZLAVHE_ROOK performs one of the 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 ZHETRF_ROOK. Slay. 🫶

If TRANS = 'N', it multiplies by U or U * D (or L or L * D). If TRANS = 'C', it multiplies by U' or D * U' (or L' or D * L'). No cap.

🧚 Parameters

💜 UPLO

• UPLO is CHARACTER*1.
• It specifies whether the factor stored in A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular

🌈 TRANS

• TRANS is CHARACTER*1.
• It specifies the operation to be performed:
  • = 'N': x := A*x
  • = 'C': x := A^H*x

🎀 DIAG

• DIAG is CHARACTER*1.
• It 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*16 array, dimension (LDA,N).
• The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF_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 ZHETRF_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 151 of file zlavhe_rook.f.

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💜 Author

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Source/version sign-off, bestie: LAPACK Version 3.12.0 — no separate date is listed on this page, so I’m not inventing one. This page was generated automatically by Doxygen for LAPACK from the source code. 💖✨