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# This file is a part of Julia. License is MIT: https://julialang.org/license
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"""
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Interface to BLAS subroutines.
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"""
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module BLAS
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import Base: copyto!
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using Base: require_one_based_indexing, USE_BLAS64
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export
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# Note: `xFUNC_NAME` is a placeholder for not exported BLAS functions
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# ref: http://www.netlib.org/blas/blasqr.pdf
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# Level 1
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# xROTG
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# xROTMG
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rot!,
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# xROTM
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# xSWAP
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scal!,
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scal,
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blascopy!,
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# xAXPY!,
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# xAXPBY!,
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# xDOT
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dotc,
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dotu,
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# xxDOT
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nrm2,
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asum,
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iamax,
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# Level 2
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gemv!,
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gemv,
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gbmv!,
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gbmv,
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hemv!,
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hemv,
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# xHBMV
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hpmv!,
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symv!,
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symv,
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sbmv!,
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sbmv,
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spmv!,
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trmv!,
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trmv,
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# xTBMV
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# xTPMV
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trsv!,
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trsv,
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# xTBSV
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# xTPSV
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ger!,
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# xGERU
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# xGERC
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her!,
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# xHPR
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# xHER2
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# xHPR2
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syr!,
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spr!,
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# xSYR2
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# xSPR2
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# Level 3
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gemm!,
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gemm,
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symm!,
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symm,
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hemm!,
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hemm,
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syrk!,
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syrk,
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herk!,
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herk,
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syr2k!,
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syr2k,
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her2k!,
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her2k,
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trmm!,
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trmm,
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trsm!,
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trsm
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using ..LinearAlgebra: libblastrampoline, BlasReal, BlasComplex, BlasFloat, BlasInt, DimensionMismatch, checksquare, stride1, chkstride1
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include("lbt.jl")
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# Legacy bindings that some packages (such as NNlib.jl) use.
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# We maintain these for backwards-compatibility but new packages
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# should not look at these, instead preferring to parse the output
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# of BLAS.get_config()
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const libblas = libblastrampoline
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const liblapack = libblastrampoline
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vendor() = :lbt
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"""
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get_config()
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Return an object representing the current `libblastrampoline` configuration.
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!!! compat "Julia 1.7"
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`get_config()` requires at least Julia 1.7.
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"""
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get_config() = lbt_get_config()
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if USE_BLAS64
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macro blasfunc(x)
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return Expr(:quote, Symbol(x, "64_"))
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end
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else
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macro blasfunc(x)
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return Expr(:quote, x)
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end
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end
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_tryparse_env_int(key) = tryparse(Int, get(ENV, key, ""))
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"""
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set_num_threads(n::Integer)
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set_num_threads(::Nothing)
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Set the number of threads the BLAS library should use equal to `n::Integer`.
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Also accepts `nothing`, in which case julia tries to guess the default number of threads.
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Passing `nothing` is discouraged and mainly exists for historical reasons.
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"""
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set_num_threads(nt::Integer)::Nothing = lbt_set_num_threads(Int32(nt))
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function set_num_threads(::Nothing)
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nt = something(
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_tryparse_env_int("OPENBLAS_NUM_THREADS"),
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_tryparse_env_int("OMP_NUM_THREADS"),
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_tryparse_env_int("VECLIB_MAXIMUM_THREADS"),
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max(1, Sys.CPU_THREADS รท 2),
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)
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return set_num_threads(nt)
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end
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"""
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get_num_threads()
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Get the number of threads the BLAS library is using.
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!!! compat "Julia 1.6"
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`get_num_threads` requires at least Julia 1.6.
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"""
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get_num_threads()::Int = lbt_get_num_threads()
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function check()
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# TODO: once we have bitfields of the BLAS functions that are actually forwarded,
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# ensure that we have a complete set here (warning on an incomplete BLAS implementation)
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config = get_config()
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# Ensure that one of our loaded libraries satisfies our interface requirement
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interface = USE_BLAS64 ? :ilp64 : :lp64
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if !any(lib.interface == interface for lib in config.loaded_libs)
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interfacestr = uppercase(string(interface))
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@error("No loaded BLAS libraries were built with $(interfacestr) support")
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println("Quitting.")
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exit()
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end
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end
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"Check that upper/lower (for special matrices) is correctly specified"
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function chkuplo(uplo::AbstractChar)
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if !(uplo == 'U' || uplo == 'L')
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throw(ArgumentError(lazy"uplo argument must be 'U' (upper) or 'L' (lower), got $uplo"))
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end
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uplo
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end
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# Level 1
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# A help function to pick the pointer and inc for 1d like inputs.
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@inline function vec_pointer_stride(x::AbstractArray, stride0check = nothing)
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Base._checkcontiguous(Bool, x) && return pointer(x), 1 # simplify runtime check when possible
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st, ptr = checkedstride(x), pointer(x)
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isnothing(stride0check) || (st == 0 && throw(stride0check))
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ptr += min(st, 0) * sizeof(eltype(x)) * (length(x) - 1)
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ptr, st
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end
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function checkedstride(x::AbstractArray)
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szs::Dims = size(x)
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sts::Dims = strides(x)
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_, st, n = Base.merge_adjacent_dim(szs, sts)
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n === ndims(x) && return st
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throw(ArgumentError("only support vector like inputs"))
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end
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## copy
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"""
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blascopy!(n, X, incx, Y, incy)
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Copy `n` elements of array `X` with stride `incx` to array `Y` with stride `incy`. Returns `Y`.
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"""
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function blascopy! end
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for (fname, elty) in ((:dcopy_,:Float64),
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(:scopy_,:Float32),
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(:zcopy_,:ComplexF64),
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(:ccopy_,:ComplexF32))
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@eval begin
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# SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
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function blascopy!(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
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ccall((@blasfunc($fname), libblastrampoline), Cvoid,
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(Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
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n, DX, incx, DY, incy)
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DY
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end
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end
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end
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## rot
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"""
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rot!(n, X, incx, Y, incy, c, s)
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Overwrite `X` with `c*X + s*Y` and `Y` with `-conj(s)*X + c*Y` for the first `n` elements of array `X` with stride `incx` and
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first `n` elements of array `Y` with stride `incy`. Returns `X` and `Y`.
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!!! compat "Julia 1.5"
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`rot!` requires at least Julia 1.5.
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"""
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function rot! end
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for (fname, elty, cty, sty, lib) in ((:drot_, :Float64, :Float64, :Float64, libblastrampoline),
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(:srot_, :Float32, :Float32, :Float32, libblastrampoline),
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(:zdrot_, :ComplexF64, :Float64, :Float64, libblastrampoline),
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(:csrot_, :ComplexF32, :Float32, :Float32, libblastrampoline),
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(:zrot_, :ComplexF64, :Float64, :ComplexF64, libblastrampoline),
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(:crot_, :ComplexF32, :Float32, :ComplexF32, libblastrampoline))
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@eval begin
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# SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
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function rot!(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer, C::$cty, S::$sty)
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ccall((@blasfunc($fname), $lib), Cvoid,
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(Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$cty}, Ref{$sty}),
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n, DX, incx, DY, incy, C, S)
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DX, DY
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end
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end
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end
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## scal
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"""
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scal!(n, a, X, incx)
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scal!(a, X)
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Overwrite `X` with `a*X` for the first `n` elements of array `X` with stride `incx`. Returns `X`.
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If `n` and `incx` are not provided, `length(X)` and `stride(X,1)` are used.
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"""
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function scal! end
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"""
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scal(n, a, X, incx)
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scal(a, X)
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Return `X` scaled by `a` for the first `n` elements of array `X` with stride `incx`.
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If `n` and `incx` are not provided, `length(X)` and `stride(X,1)` are used.
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"""
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function scal end
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for (fname, elty) in ((:dscal_,:Float64),
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(:sscal_,:Float32),
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(:zscal_,:ComplexF64),
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(:cscal_,:ComplexF32))
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@eval begin
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# SUBROUTINE DSCAL(N,DA,DX,INCX)
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function scal!(n::Integer, DA::$elty, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer)
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ccall((@blasfunc($fname), libblastrampoline), Cvoid,
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(Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt}),
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n, DA, DX, incx)
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DX
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end
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function scal!(DA::$elty, DX::AbstractArray{$elty})
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p, st = vec_pointer_stride(DX, ArgumentError("dest vector with 0 stride is not allowed"))
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GC.@preserve DX scal!(length(DX), DA, p, abs(st))
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DX
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end
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end
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end
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scal(n, DA, DX, incx) = scal!(n, DA, copy(DX), incx)
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scal(DA, DX) = scal!(DA, copy(DX))
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## dot
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"""
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dot(n, X, incx, Y, incy)
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Dot product of two vectors consisting of `n` elements of array `X` with stride `incx` and
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`n` elements of array `Y` with stride `incy`.
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# Examples
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```jldoctest
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julia> BLAS.dot(10, fill(1.0, 10), 1, fill(1.0, 20), 2)
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10.0
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```
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"""
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function dot end
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"""
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dotc(n, X, incx, U, incy)
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Dot function for two complex vectors, consisting of `n` elements of array `X`
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with stride `incx` and `n` elements of array `U` with stride `incy`,
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conjugating the first vector.
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# Examples
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```jldoctest
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julia> BLAS.dotc(10, fill(1.0im, 10), 1, fill(1.0+im, 20), 2)
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10.0 - 10.0im
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```
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"""
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function dotc end
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"""
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dotu(n, X, incx, Y, incy)
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Dot function for two complex vectors consisting of `n` elements of array `X`
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with stride `incx` and `n` elements of array `Y` with stride `incy`.
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# Examples
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```jldoctest
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julia> BLAS.dotu(10, fill(1.0im, 10), 1, fill(1.0+im, 20), 2)
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-10.0 + 10.0im
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```
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"""
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function dotu end
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for (fname, elty) in ((:cblas_ddot,:Float64),
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(:cblas_sdot,:Float32))
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@eval begin
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# DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
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# * .. Scalar Arguments ..
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# INTEGER INCX,INCY,N
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# * ..
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# * .. Array Arguments ..
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# DOUBLE PRECISION DX(*),DY(*)
|
| 344 |
|
|
function dot(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
|
| 345 |
|
|
ccall((@blasfunc($fname), libblastrampoline), $elty,
|
| 346 |
|
|
(BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}, BlasInt),
|
| 347 |
|
|
n, DX, incx, DY, incy)
|
| 348 |
|
|
end
|
| 349 |
|
|
end
|
| 350 |
|
|
end
|
| 351 |
|
|
for (fname, elty) in ((:cblas_zdotc_sub,:ComplexF64),
|
| 352 |
|
|
(:cblas_cdotc_sub,:ComplexF32))
|
| 353 |
|
|
@eval begin
|
| 354 |
|
|
# DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
|
| 355 |
|
|
# * .. Scalar Arguments ..
|
| 356 |
|
|
# INTEGER INCX,INCY,N
|
| 357 |
|
|
# * ..
|
| 358 |
|
|
# * .. Array Arguments ..
|
| 359 |
|
|
# DOUBLE PRECISION DX(*),DY(*)
|
| 360 |
|
|
function dotc(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
|
| 361 |
|
|
result = Ref{$elty}()
|
| 362 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 363 |
|
|
(BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}),
|
| 364 |
|
|
n, DX, incx, DY, incy, result)
|
| 365 |
|
|
result[]
|
| 366 |
|
|
end
|
| 367 |
|
|
end
|
| 368 |
|
|
end
|
| 369 |
|
|
for (fname, elty) in ((:cblas_zdotu_sub,:ComplexF64),
|
| 370 |
|
|
(:cblas_cdotu_sub,:ComplexF32))
|
| 371 |
|
|
@eval begin
|
| 372 |
|
|
# DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
|
| 373 |
|
|
# * .. Scalar Arguments ..
|
| 374 |
|
|
# INTEGER INCX,INCY,N
|
| 375 |
|
|
# * ..
|
| 376 |
|
|
# * .. Array Arguments ..
|
| 377 |
|
|
# DOUBLE PRECISION DX(*),DY(*)
|
| 378 |
|
|
function dotu(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
|
| 379 |
|
|
result = Ref{$elty}()
|
| 380 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 381 |
|
|
(BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}),
|
| 382 |
|
|
n, DX, incx, DY, incy, result)
|
| 383 |
|
|
result[]
|
| 384 |
|
|
end
|
| 385 |
|
|
end
|
| 386 |
|
|
end
|
| 387 |
|
|
|
| 388 |
|
|
for (elty, f) in ((Float32, :dot), (Float64, :dot),
|
| 389 |
|
|
(ComplexF32, :dotc), (ComplexF64, :dotc),
|
| 390 |
|
|
(ComplexF32, :dotu), (ComplexF64, :dotu))
|
| 391 |
|
|
@eval begin
|
| 392 |
|
|
function $f(x::AbstractArray{$elty}, y::AbstractArray{$elty})
|
| 393 |
|
|
n, m = length(x), length(y)
|
| 394 |
|
|
n == m || throw(DimensionMismatch(lazy"dot product arguments have lengths $n and $m"))
|
| 395 |
|
|
GC.@preserve x y $f(n, vec_pointer_stride(x)..., vec_pointer_stride(y)...)
|
| 396 |
|
|
end
|
| 397 |
|
|
end
|
| 398 |
|
|
end
|
| 399 |
|
|
|
| 400 |
|
|
## nrm2
|
| 401 |
|
|
|
| 402 |
|
|
"""
|
| 403 |
|
|
nrm2(n, X, incx)
|
| 404 |
|
|
|
| 405 |
|
|
2-norm of a vector consisting of `n` elements of array `X` with stride `incx`.
|
| 406 |
|
|
|
| 407 |
|
|
# Examples
|
| 408 |
|
|
```jldoctest
|
| 409 |
|
|
julia> BLAS.nrm2(4, fill(1.0, 8), 2)
|
| 410 |
|
|
2.0
|
| 411 |
|
|
|
| 412 |
|
|
julia> BLAS.nrm2(1, fill(1.0, 8), 2)
|
| 413 |
|
|
1.0
|
| 414 |
|
|
```
|
| 415 |
|
|
"""
|
| 416 |
|
|
function nrm2 end
|
| 417 |
|
|
|
| 418 |
|
|
for (fname, elty, ret_type) in ((:dnrm2_,:Float64,:Float64),
|
| 419 |
|
|
(:snrm2_,:Float32,:Float32),
|
| 420 |
|
|
(:dznrm2_,:ComplexF64,:Float64),
|
| 421 |
|
|
(:scnrm2_,:ComplexF32,:Float32))
|
| 422 |
|
|
@eval begin
|
| 423 |
|
|
# SUBROUTINE DNRM2(N,X,INCX)
|
| 424 |
|
|
function nrm2(n::Integer, X::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer)
|
| 425 |
|
|
ccall((@blasfunc($fname), libblastrampoline), $ret_type,
|
| 426 |
|
|
(Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
|
| 427 |
|
|
n, X, incx)
|
| 428 |
|
|
end
|
| 429 |
|
|
end
|
| 430 |
|
|
end
|
| 431 |
|
|
# openblas returns 0 for negative stride
|
| 432 |
|
|
function nrm2(x::AbstractArray)
|
| 433 |
|
|
p, st = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 434 |
1 (14 %) |
1 (14 %) |
1 (14 %)
samples spent in nrm2
1 (100 %) (ex.),
1 (100 %) (incl.)
when called from norm2
line 106
|
| 435 |
|
|
end
|
| 436 |
|
|
|
| 437 |
|
|
## asum
|
| 438 |
|
|
|
| 439 |
|
|
"""
|
| 440 |
|
|
asum(n, X, incx)
|
| 441 |
|
|
|
| 442 |
|
|
Sum of the magnitudes of the first `n` elements of array `X` with stride `incx`.
|
| 443 |
|
|
|
| 444 |
|
|
For a real array, the magnitude is the absolute value. For a complex array, the
|
| 445 |
|
|
magnitude is the sum of the absolute value of the real part and the absolute value
|
| 446 |
|
|
of the imaginary part.
|
| 447 |
|
|
|
| 448 |
|
|
# Examples
|
| 449 |
|
|
```jldoctest
|
| 450 |
|
|
julia> BLAS.asum(5, fill(1.0im, 10), 2)
|
| 451 |
|
|
5.0
|
| 452 |
|
|
|
| 453 |
|
|
julia> BLAS.asum(2, fill(1.0im, 10), 5)
|
| 454 |
|
|
2.0
|
| 455 |
|
|
```
|
| 456 |
|
|
"""
|
| 457 |
|
|
function asum end
|
| 458 |
|
|
|
| 459 |
|
|
for (fname, elty, ret_type) in ((:dasum_,:Float64,:Float64),
|
| 460 |
|
|
(:sasum_,:Float32,:Float32),
|
| 461 |
|
|
(:dzasum_,:ComplexF64,:Float64),
|
| 462 |
|
|
(:scasum_,:ComplexF32,:Float32))
|
| 463 |
|
|
@eval begin
|
| 464 |
|
|
# SUBROUTINE ASUM(N, X, INCX)
|
| 465 |
|
|
function asum(n::Integer, X::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer)
|
| 466 |
|
|
ccall((@blasfunc($fname), libblastrampoline), $ret_type,
|
| 467 |
|
|
(Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
|
| 468 |
|
|
n, X, incx)
|
| 469 |
|
|
end
|
| 470 |
|
|
end
|
| 471 |
|
|
end
|
| 472 |
|
|
function asum(x::AbstractArray)
|
| 473 |
|
|
p, st = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 474 |
|
|
GC.@preserve x asum(length(x), p, abs(st))
|
| 475 |
|
|
end
|
| 476 |
|
|
|
| 477 |
|
|
## axpy
|
| 478 |
|
|
|
| 479 |
|
|
"""
|
| 480 |
|
|
axpy!(a, X, Y)
|
| 481 |
|
|
|
| 482 |
|
|
Overwrite `Y` with `X*a + Y`, where `a` is a scalar. Return `Y`.
|
| 483 |
|
|
|
| 484 |
|
|
# Examples
|
| 485 |
|
|
```jldoctest
|
| 486 |
|
|
julia> x = [1.; 2; 3];
|
| 487 |
|
|
|
| 488 |
|
|
julia> y = [4. ;; 5 ;; 6];
|
| 489 |
|
|
|
| 490 |
|
|
julia> BLAS.axpy!(2, x, y)
|
| 491 |
|
|
1ร3 Matrix{Float64}:
|
| 492 |
|
|
6.0 9.0 12.0
|
| 493 |
|
|
```
|
| 494 |
|
|
"""
|
| 495 |
|
|
function axpy! end
|
| 496 |
|
|
|
| 497 |
|
|
for (fname, elty) in ((:daxpy_,:Float64),
|
| 498 |
|
|
(:saxpy_,:Float32),
|
| 499 |
|
|
(:zaxpy_,:ComplexF64),
|
| 500 |
|
|
(:caxpy_,:ComplexF32))
|
| 501 |
|
|
@eval begin
|
| 502 |
|
|
# SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
|
| 503 |
|
|
# DY <- DA*DX + DY
|
| 504 |
|
|
#* .. Scalar Arguments ..
|
| 505 |
|
|
# DOUBLE PRECISION DA
|
| 506 |
|
|
# INTEGER INCX,INCY,N
|
| 507 |
|
|
#* .. Array Arguments ..
|
| 508 |
|
|
# DOUBLE PRECISION DX(*),DY(*)
|
| 509 |
|
|
function axpy!(n::Integer, alpha::($elty), dx::Union{Ptr{$elty}, AbstractArray{$elty}}, incx::Integer, dy::Union{Ptr{$elty}, AbstractArray{$elty}}, incy::Integer)
|
| 510 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 511 |
|
|
(Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
|
| 512 |
|
|
n, alpha, dx, incx, dy, incy)
|
| 513 |
|
|
dy
|
| 514 |
|
|
end
|
| 515 |
|
|
end
|
| 516 |
|
|
end
|
| 517 |
|
|
|
| 518 |
|
|
function axpy!(alpha::Number, x::AbstractArray{T}, y::AbstractArray{T}) where T<:BlasFloat
|
| 519 |
|
|
if length(x) != length(y)
|
| 520 |
|
|
throw(DimensionMismatch(lazy"x has length $(length(x)), but y has length $(length(y))"))
|
| 521 |
|
|
end
|
| 522 |
|
|
GC.@preserve x y axpy!(length(x), T(alpha), vec_pointer_stride(x)...,
|
| 523 |
|
|
vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))...)
|
| 524 |
|
|
y
|
| 525 |
|
|
end
|
| 526 |
|
|
|
| 527 |
|
|
function axpy!(alpha::Number, x::Array{T}, rx::AbstractRange{Ti},
|
| 528 |
|
|
y::Array{T}, ry::AbstractRange{Ti}) where {T<:BlasFloat,Ti<:Integer}
|
| 529 |
|
|
if length(rx) != length(ry)
|
| 530 |
|
|
throw(DimensionMismatch("ranges of differing lengths"))
|
| 531 |
|
|
end
|
| 532 |
|
|
if minimum(rx) < 1 || maximum(rx) > length(x)
|
| 533 |
|
|
throw(ArgumentError(lazy"range out of bounds for x, of length $(length(x))"))
|
| 534 |
|
|
end
|
| 535 |
|
|
if minimum(ry) < 1 || maximum(ry) > length(y)
|
| 536 |
|
|
throw(ArgumentError(lazy"range out of bounds for y, of length $(length(y))"))
|
| 537 |
|
|
end
|
| 538 |
|
|
GC.@preserve x y axpy!(
|
| 539 |
|
|
length(rx),
|
| 540 |
|
|
T(alpha),
|
| 541 |
|
|
pointer(x, minimum(rx)),
|
| 542 |
|
|
step(rx),
|
| 543 |
|
|
pointer(y, minimum(ry)),
|
| 544 |
|
|
step(ry))
|
| 545 |
|
|
|
| 546 |
|
|
return y
|
| 547 |
|
|
end
|
| 548 |
|
|
|
| 549 |
|
|
"""
|
| 550 |
|
|
axpby!(a, X, b, Y)
|
| 551 |
|
|
|
| 552 |
|
|
Overwrite `Y` with `X*a + Y*b`, where `a` and `b` are scalars. Return `Y`.
|
| 553 |
|
|
|
| 554 |
|
|
# Examples
|
| 555 |
|
|
```jldoctest
|
| 556 |
|
|
julia> x = [1., 2, 3];
|
| 557 |
|
|
|
| 558 |
|
|
julia> y = [4., 5, 6];
|
| 559 |
|
|
|
| 560 |
|
|
julia> BLAS.axpby!(2., x, 3., y)
|
| 561 |
|
|
3-element Vector{Float64}:
|
| 562 |
|
|
14.0
|
| 563 |
|
|
19.0
|
| 564 |
|
|
24.0
|
| 565 |
|
|
```
|
| 566 |
|
|
"""
|
| 567 |
|
|
function axpby! end
|
| 568 |
|
|
|
| 569 |
|
|
for (fname, elty) in ((:daxpby_,:Float64), (:saxpby_,:Float32),
|
| 570 |
|
|
(:zaxpby_,:ComplexF64), (:caxpby_,:ComplexF32))
|
| 571 |
|
|
@eval begin
|
| 572 |
|
|
# SUBROUTINE DAXPBY(N,DA,DX,INCX,DB,DY,INCY)
|
| 573 |
|
|
# DY <- DA*DX + DB*DY
|
| 574 |
|
|
#* .. Scalar Arguments ..
|
| 575 |
|
|
# DOUBLE PRECISION DA,DB
|
| 576 |
|
|
# INTEGER INCX,INCY,N
|
| 577 |
|
|
#* .. Array Arguments ..
|
| 578 |
|
|
# DOUBLE PRECISION DX(*),DY(*)
|
| 579 |
|
|
function axpby!(n::Integer, alpha::($elty), dx::Union{Ptr{$elty},
|
| 580 |
|
|
AbstractArray{$elty}}, incx::Integer, beta::($elty),
|
| 581 |
|
|
dy::Union{Ptr{$elty}, AbstractArray{$elty}}, incy::Integer)
|
| 582 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid, (Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 583 |
|
|
Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt}),
|
| 584 |
|
|
n, alpha, dx, incx, beta, dy, incy)
|
| 585 |
|
|
dy
|
| 586 |
|
|
end
|
| 587 |
|
|
end
|
| 588 |
|
|
end
|
| 589 |
|
|
|
| 590 |
|
|
function axpby!(alpha::Number, x::AbstractArray{T}, beta::Number, y::AbstractArray{T}) where T<:BlasFloat
|
| 591 |
|
|
require_one_based_indexing(x, y)
|
| 592 |
|
|
if length(x) != length(y)
|
| 593 |
|
|
throw(DimensionMismatch(lazy"x has length $(length(x)), but y has length $(length(y))"))
|
| 594 |
|
|
end
|
| 595 |
|
|
GC.@preserve x y axpby!(length(x), T(alpha), vec_pointer_stride(x)..., T(beta),
|
| 596 |
|
|
vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))...)
|
| 597 |
|
|
y
|
| 598 |
|
|
end
|
| 599 |
|
|
|
| 600 |
|
|
## iamax
|
| 601 |
|
|
for (fname, elty) in ((:idamax_,:Float64),
|
| 602 |
|
|
(:isamax_,:Float32),
|
| 603 |
|
|
(:izamax_,:ComplexF64),
|
| 604 |
|
|
(:icamax_,:ComplexF32))
|
| 605 |
|
|
@eval begin
|
| 606 |
|
|
function iamax(n::Integer, dx::Union{Ptr{$elty}, AbstractArray{$elty}}, incx::Integer)
|
| 607 |
|
|
ccall((@blasfunc($fname), libblastrampoline),BlasInt,
|
| 608 |
|
|
(Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
|
| 609 |
|
|
n, dx, incx)
|
| 610 |
|
|
end
|
| 611 |
|
|
end
|
| 612 |
|
|
end
|
| 613 |
|
|
function iamax(dx::AbstractArray)
|
| 614 |
|
|
p, st = vec_pointer_stride(dx)
|
| 615 |
|
|
st <= 0 && return BlasInt(0)
|
| 616 |
|
|
iamax(length(dx), p, st)
|
| 617 |
|
|
end
|
| 618 |
|
|
|
| 619 |
|
|
"""
|
| 620 |
|
|
iamax(n, dx, incx)
|
| 621 |
|
|
iamax(dx)
|
| 622 |
|
|
|
| 623 |
|
|
Find the index of the element of `dx` with the maximum absolute value. `n` is the length of `dx`, and `incx` is the
|
| 624 |
|
|
stride. If `n` and `incx` are not provided, they assume default values of `n=length(dx)` and `incx=stride1(dx)`.
|
| 625 |
|
|
"""
|
| 626 |
|
|
iamax
|
| 627 |
|
|
|
| 628 |
|
|
# Level 2
|
| 629 |
|
|
## mv
|
| 630 |
|
|
### gemv
|
| 631 |
|
|
for (fname, elty) in ((:dgemv_,:Float64),
|
| 632 |
|
|
(:sgemv_,:Float32),
|
| 633 |
|
|
(:zgemv_,:ComplexF64),
|
| 634 |
|
|
(:cgemv_,:ComplexF32))
|
| 635 |
|
|
@eval begin
|
| 636 |
|
|
#SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
| 637 |
|
|
#* .. Scalar Arguments ..
|
| 638 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 639 |
|
|
# INTEGER INCX,INCY,LDA,M,N
|
| 640 |
|
|
# CHARACTER TRANS
|
| 641 |
|
|
#* .. Array Arguments ..
|
| 642 |
|
|
# DOUBLE PRECISION A(LDA,*),X(*),Y(*)
|
| 643 |
|
|
function gemv!(trans::AbstractChar, alpha::Union{($elty), Bool},
|
| 644 |
|
|
A::AbstractVecOrMat{$elty}, X::AbstractVector{$elty},
|
| 645 |
|
|
beta::Union{($elty), Bool}, Y::AbstractVector{$elty})
|
| 646 |
|
|
require_one_based_indexing(A, X, Y)
|
| 647 |
|
|
m,n = size(A,1),size(A,2)
|
| 648 |
|
|
if trans == 'N' && (length(X) != n || length(Y) != m)
|
| 649 |
|
|
throw(DimensionMismatch(lazy"A has dimensions $(size(A)), X has length $(length(X)) and Y has length $(length(Y))"))
|
| 650 |
|
|
elseif trans == 'C' && (length(X) != m || length(Y) != n)
|
| 651 |
|
|
throw(DimensionMismatch(lazy"the adjoint of A has dimensions $n, $m, X has length $(length(X)) and Y has length $(length(Y))"))
|
| 652 |
|
|
elseif trans == 'T' && (length(X) != m || length(Y) != n)
|
| 653 |
|
|
throw(DimensionMismatch(lazy"the transpose of A has dimensions $n, $m, X has length $(length(X)) and Y has length $(length(Y))"))
|
| 654 |
|
|
end
|
| 655 |
|
|
chkstride1(A)
|
| 656 |
|
|
lda = stride(A,2)
|
| 657 |
|
|
pX, sX = vec_pointer_stride(X, ArgumentError("input vector with 0 stride is not allowed"))
|
| 658 |
|
|
pY, sY = vec_pointer_stride(Y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 659 |
|
|
pA = pointer(A)
|
| 660 |
|
|
if lda < 0
|
| 661 |
|
|
pA += (size(A, 2) - 1) * lda * sizeof($elty)
|
| 662 |
|
|
lda = -lda
|
| 663 |
|
|
trans == 'N' ? (sX = -sX) : (sY = -sY)
|
| 664 |
|
|
end
|
| 665 |
|
|
lda >= size(A,1) || size(A,2) <= 1 || error("when `size(A,2) > 1`, `abs(stride(A,2))` must be at least `size(A,1)`")
|
| 666 |
|
|
lda = max(1, size(A,1), lda)
|
| 667 |
|
|
GC.@preserve A X Y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 668 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{$elty},
|
| 669 |
|
|
Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
|
| 670 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Clong),
|
| 671 |
|
|
trans, size(A,1), size(A,2), alpha,
|
| 672 |
|
|
pA, lda, pX, sX,
|
| 673 |
|
|
beta, pY, sY, 1)
|
| 674 |
|
|
Y
|
| 675 |
|
|
end
|
| 676 |
|
|
function gemv(trans::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, X::AbstractVector{$elty})
|
| 677 |
|
|
gemv!(trans, alpha, A, X, zero($elty), similar(X, $elty, size(A, (trans == 'N' ? 1 : 2))))
|
| 678 |
|
|
end
|
| 679 |
|
|
function gemv(trans::AbstractChar, A::AbstractMatrix{$elty}, X::AbstractVector{$elty})
|
| 680 |
|
|
gemv!(trans, one($elty), A, X, zero($elty), similar(X, $elty, size(A, (trans == 'N' ? 1 : 2))))
|
| 681 |
|
|
end
|
| 682 |
|
|
end
|
| 683 |
|
|
end
|
| 684 |
|
|
|
| 685 |
|
|
"""
|
| 686 |
|
|
gemv!(tA, alpha, A, x, beta, y)
|
| 687 |
|
|
|
| 688 |
|
|
Update the vector `y` as `alpha*A*x + beta*y` or `alpha*A'x + beta*y`
|
| 689 |
|
|
according to [`tA`](@ref stdlib-blas-trans).
|
| 690 |
|
|
`alpha` and `beta` are scalars. Return the updated `y`.
|
| 691 |
|
|
"""
|
| 692 |
|
|
gemv!
|
| 693 |
|
|
|
| 694 |
|
|
"""
|
| 695 |
|
|
gemv(tA, alpha, A, x)
|
| 696 |
|
|
|
| 697 |
|
|
Return `alpha*A*x` or `alpha*A'x` according to [`tA`](@ref stdlib-blas-trans).
|
| 698 |
|
|
`alpha` is a scalar.
|
| 699 |
|
|
"""
|
| 700 |
|
|
gemv(tA, alpha, A, x)
|
| 701 |
|
|
|
| 702 |
|
|
"""
|
| 703 |
|
|
gemv(tA, A, x)
|
| 704 |
|
|
|
| 705 |
|
|
Return `A*x` or `A'x` according to [`tA`](@ref stdlib-blas-trans).
|
| 706 |
|
|
"""
|
| 707 |
|
|
gemv(tA, A, x)
|
| 708 |
|
|
|
| 709 |
|
|
### (GB) general banded matrix-vector multiplication
|
| 710 |
|
|
|
| 711 |
|
|
"""
|
| 712 |
|
|
gbmv!(trans, m, kl, ku, alpha, A, x, beta, y)
|
| 713 |
|
|
|
| 714 |
|
|
Update vector `y` as `alpha*A*x + beta*y` or `alpha*A'*x + beta*y` according to [`trans`](@ref stdlib-blas-trans).
|
| 715 |
|
|
The matrix `A` is a general band matrix of dimension `m` by `size(A,2)` with `kl`
|
| 716 |
|
|
sub-diagonals and `ku` super-diagonals. `alpha` and `beta` are scalars. Return the updated `y`.
|
| 717 |
|
|
"""
|
| 718 |
|
|
function gbmv! end
|
| 719 |
|
|
|
| 720 |
|
|
"""
|
| 721 |
|
|
gbmv(trans, m, kl, ku, alpha, A, x)
|
| 722 |
|
|
|
| 723 |
|
|
Return `alpha*A*x` or `alpha*A'*x` according to [`trans`](@ref stdlib-blas-trans).
|
| 724 |
|
|
The matrix `A` is a general band matrix of dimension `m` by `size(A,2)` with `kl` sub-diagonals and `ku`
|
| 725 |
|
|
super-diagonals, and `alpha` is a scalar.
|
| 726 |
|
|
"""
|
| 727 |
|
|
function gbmv end
|
| 728 |
|
|
|
| 729 |
|
|
for (fname, elty) in ((:dgbmv_,:Float64),
|
| 730 |
|
|
(:sgbmv_,:Float32),
|
| 731 |
|
|
(:zgbmv_,:ComplexF64),
|
| 732 |
|
|
(:cgbmv_,:ComplexF32))
|
| 733 |
|
|
@eval begin
|
| 734 |
|
|
# SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
| 735 |
|
|
# * .. Scalar Arguments ..
|
| 736 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 737 |
|
|
# INTEGER INCX,INCY,KL,KU,LDA,M,N
|
| 738 |
|
|
# CHARACTER TRANS
|
| 739 |
|
|
# * .. Array Arguments ..
|
| 740 |
|
|
# DOUBLE PRECISION A(LDA,*),X(*),Y(*)
|
| 741 |
|
|
function gbmv!(trans::AbstractChar, m::Integer, kl::Integer, ku::Integer,
|
| 742 |
|
|
alpha::Union{($elty), Bool}, A::AbstractMatrix{$elty},
|
| 743 |
|
|
x::AbstractVector{$elty}, beta::Union{($elty), Bool},
|
| 744 |
|
|
y::AbstractVector{$elty})
|
| 745 |
|
|
require_one_based_indexing(A, x, y)
|
| 746 |
|
|
chkstride1(A)
|
| 747 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 748 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 749 |
|
|
GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 750 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
|
| 751 |
|
|
Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
|
| 752 |
|
|
Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 753 |
|
|
Ref{BlasInt}, Clong),
|
| 754 |
|
|
trans, m, size(A,2), kl,
|
| 755 |
|
|
ku, alpha, A, max(1,stride(A,2)),
|
| 756 |
|
|
px, stx, beta, py, sty, 1)
|
| 757 |
|
|
y
|
| 758 |
|
|
end
|
| 759 |
|
|
function gbmv(trans::AbstractChar, m::Integer, kl::Integer, ku::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 760 |
|
|
n = size(A,2)
|
| 761 |
|
|
leny = trans == 'N' ? m : n
|
| 762 |
|
|
gbmv!(trans, m, kl, ku, alpha, A, x, zero($elty), similar(x, $elty, leny))
|
| 763 |
|
|
end
|
| 764 |
|
|
function gbmv(trans::AbstractChar, m::Integer, kl::Integer, ku::Integer, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 765 |
|
|
gbmv(trans, m, kl, ku, one($elty), A, x)
|
| 766 |
|
|
end
|
| 767 |
|
|
end
|
| 768 |
|
|
end
|
| 769 |
|
|
|
| 770 |
|
|
### symv
|
| 771 |
|
|
|
| 772 |
|
|
"""
|
| 773 |
|
|
symv!(ul, alpha, A, x, beta, y)
|
| 774 |
|
|
|
| 775 |
|
|
Update the vector `y` as `alpha*A*x + beta*y`. `A` is assumed to be symmetric.
|
| 776 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 777 |
|
|
`alpha` and `beta` are scalars. Return the updated `y`.
|
| 778 |
|
|
"""
|
| 779 |
|
|
function symv! end
|
| 780 |
|
|
|
| 781 |
|
|
for (fname, elty, lib) in ((:dsymv_,:Float64,libblastrampoline),
|
| 782 |
|
|
(:ssymv_,:Float32,libblastrampoline),
|
| 783 |
|
|
(:zsymv_,:ComplexF64,libblastrampoline),
|
| 784 |
|
|
(:csymv_,:ComplexF32,libblastrampoline))
|
| 785 |
|
|
# Note that the complex symv are not BLAS but auiliary functions in LAPACK
|
| 786 |
|
|
@eval begin
|
| 787 |
|
|
# SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
| 788 |
|
|
# .. Scalar Arguments ..
|
| 789 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 790 |
|
|
# INTEGER INCX,INCY,LDA,N
|
| 791 |
|
|
# CHARACTER UPLO
|
| 792 |
|
|
# .. Array Arguments ..
|
| 793 |
|
|
# DOUBLE PRECISION A(LDA,*),X(*),Y(*)
|
| 794 |
|
|
function symv!(uplo::AbstractChar, alpha::Union{($elty), Bool},
|
| 795 |
|
|
A::AbstractMatrix{$elty}, x::AbstractVector{$elty},
|
| 796 |
|
|
beta::Union{($elty), Bool}, y::AbstractVector{$elty})
|
| 797 |
|
|
chkuplo(uplo)
|
| 798 |
|
|
require_one_based_indexing(A, x, y)
|
| 799 |
|
|
m, n = size(A)
|
| 800 |
|
|
if m != n
|
| 801 |
|
|
throw(DimensionMismatch(lazy"matrix A is $m by $n but must be square"))
|
| 802 |
|
|
end
|
| 803 |
|
|
if n != length(x)
|
| 804 |
|
|
throw(DimensionMismatch(lazy"A has size $(size(A)), and x has length $(length(x))"))
|
| 805 |
|
|
end
|
| 806 |
|
|
if m != length(y)
|
| 807 |
|
|
throw(DimensionMismatch(lazy"A has size $(size(A)), and y has length $(length(y))"))
|
| 808 |
|
|
end
|
| 809 |
|
|
chkstride1(A)
|
| 810 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 811 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 812 |
|
|
GC.@preserve x y ccall((@blasfunc($fname), $lib), Cvoid,
|
| 813 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 814 |
|
|
Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
|
| 815 |
|
|
Ptr{$elty}, Ref{BlasInt}, Clong),
|
| 816 |
|
|
uplo, n, alpha, A,
|
| 817 |
|
|
max(1,stride(A,2)), px, stx, beta,
|
| 818 |
|
|
py, sty, 1)
|
| 819 |
|
|
y
|
| 820 |
|
|
end
|
| 821 |
|
|
function symv(uplo::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 822 |
|
|
symv!(uplo, alpha, A, x, zero($elty), similar(x))
|
| 823 |
|
|
end
|
| 824 |
|
|
function symv(uplo::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 825 |
|
|
symv(uplo, one($elty), A, x)
|
| 826 |
|
|
end
|
| 827 |
|
|
end
|
| 828 |
|
|
end
|
| 829 |
|
|
|
| 830 |
|
|
"""
|
| 831 |
|
|
symv(ul, alpha, A, x)
|
| 832 |
|
|
|
| 833 |
|
|
Return `alpha*A*x`. `A` is assumed to be symmetric.
|
| 834 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 835 |
|
|
`alpha` is a scalar.
|
| 836 |
|
|
"""
|
| 837 |
|
|
symv(ul, alpha, A, x)
|
| 838 |
|
|
|
| 839 |
|
|
"""
|
| 840 |
|
|
symv(ul, A, x)
|
| 841 |
|
|
|
| 842 |
|
|
Return `A*x`. `A` is assumed to be symmetric.
|
| 843 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 844 |
|
|
"""
|
| 845 |
|
|
symv(ul, A, x)
|
| 846 |
|
|
|
| 847 |
|
|
### hemv
|
| 848 |
|
|
"""
|
| 849 |
|
|
hemv!(ul, alpha, A, x, beta, y)
|
| 850 |
|
|
|
| 851 |
|
|
Update the vector `y` as `alpha*A*x + beta*y`. `A` is assumed to be Hermitian.
|
| 852 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 853 |
|
|
`alpha` and `beta` are scalars. Return the updated `y`.
|
| 854 |
|
|
"""
|
| 855 |
|
|
function hemv! end
|
| 856 |
|
|
|
| 857 |
|
|
for (fname, elty) in ((:zhemv_,:ComplexF64),
|
| 858 |
|
|
(:chemv_,:ComplexF32))
|
| 859 |
|
|
@eval begin
|
| 860 |
|
|
function hemv!(uplo::AbstractChar, ฮฑ::Union{$elty, Bool}, A::AbstractMatrix{$elty}, x::AbstractVector{$elty}, ฮฒ::Union{$elty, Bool}, y::AbstractVector{$elty})
|
| 861 |
|
|
chkuplo(uplo)
|
| 862 |
|
|
require_one_based_indexing(A, x, y)
|
| 863 |
|
|
m, n = size(A)
|
| 864 |
|
|
if m != n
|
| 865 |
|
|
throw(DimensionMismatch(lazy"matrix A is $m by $n but must be square"))
|
| 866 |
|
|
end
|
| 867 |
|
|
if n != length(x)
|
| 868 |
|
|
throw(DimensionMismatch(lazy"A has size $(size(A)), and x has length $(length(x))"))
|
| 869 |
|
|
end
|
| 870 |
|
|
if m != length(y)
|
| 871 |
|
|
throw(DimensionMismatch(lazy"A has size $(size(A)), and y has length $(length(y))"))
|
| 872 |
|
|
end
|
| 873 |
|
|
chkstride1(A)
|
| 874 |
|
|
lda = max(1, stride(A, 2))
|
| 875 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 876 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 877 |
|
|
GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 878 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 879 |
|
|
Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
|
| 880 |
|
|
Ptr{$elty}, Ref{BlasInt}, Clong),
|
| 881 |
|
|
uplo, n, ฮฑ, A,
|
| 882 |
|
|
lda, px, stx, ฮฒ,
|
| 883 |
|
|
py, sty, 1)
|
| 884 |
|
|
y
|
| 885 |
|
|
end
|
| 886 |
|
|
function hemv(uplo::AbstractChar, ฮฑ::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 887 |
|
|
hemv!(uplo, ฮฑ, A, x, zero($elty), similar(x))
|
| 888 |
|
|
end
|
| 889 |
|
|
function hemv(uplo::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 890 |
|
|
hemv(uplo, one($elty), A, x)
|
| 891 |
|
|
end
|
| 892 |
|
|
end
|
| 893 |
|
|
end
|
| 894 |
|
|
|
| 895 |
|
|
"""
|
| 896 |
|
|
hemv(ul, alpha, A, x)
|
| 897 |
|
|
|
| 898 |
|
|
Return `alpha*A*x`. `A` is assumed to be Hermitian.
|
| 899 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 900 |
|
|
`alpha` is a scalar.
|
| 901 |
|
|
"""
|
| 902 |
|
|
hemv(ul, alpha, A, x)
|
| 903 |
|
|
|
| 904 |
|
|
"""
|
| 905 |
|
|
hemv(ul, A, x)
|
| 906 |
|
|
|
| 907 |
|
|
Return `A*x`. `A` is assumed to be Hermitian.
|
| 908 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 909 |
|
|
"""
|
| 910 |
|
|
hemv(ul, A, x)
|
| 911 |
|
|
|
| 912 |
|
|
### hpmv!, (HP) Hermitian packed matrix-vector operation defined as y := alpha*A*x + beta*y.
|
| 913 |
|
|
for (fname, elty) in ((:zhpmv_, :ComplexF64),
|
| 914 |
|
|
(:chpmv_, :ComplexF32))
|
| 915 |
|
|
@eval begin
|
| 916 |
|
|
# SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
|
| 917 |
|
|
# Y <- ALPHA*AP*X + BETA*Y
|
| 918 |
|
|
# * .. Scalar Arguments ..
|
| 919 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 920 |
|
|
# INTEGER INCX,INCY,N
|
| 921 |
|
|
# CHARACTER UPLO
|
| 922 |
|
|
# * .. Array Arguments ..
|
| 923 |
|
|
# DOUBLE PRECISION A(N,N),X(N),Y(N)
|
| 924 |
|
|
function hpmv!(uplo::AbstractChar,
|
| 925 |
|
|
n::Integer,
|
| 926 |
|
|
ฮฑ::$elty,
|
| 927 |
|
|
AP::Union{Ptr{$elty}, AbstractArray{$elty}},
|
| 928 |
|
|
x::Union{Ptr{$elty}, AbstractArray{$elty}},
|
| 929 |
|
|
incx::Integer,
|
| 930 |
|
|
ฮฒ::$elty,
|
| 931 |
|
|
y::Union{Ptr{$elty}, AbstractArray{$elty}},
|
| 932 |
|
|
incy::Integer)
|
| 933 |
|
|
|
| 934 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 935 |
|
|
(Ref{UInt8}, # uplo,
|
| 936 |
|
|
Ref{BlasInt}, # n,
|
| 937 |
|
|
Ref{$elty}, # ฮฑ,
|
| 938 |
|
|
Ptr{$elty}, # AP,
|
| 939 |
|
|
Ptr{$elty}, # x,
|
| 940 |
|
|
Ref{BlasInt}, # incx,
|
| 941 |
|
|
Ref{$elty}, # ฮฒ,
|
| 942 |
|
|
Ptr{$elty}, # y, output
|
| 943 |
|
|
Ref{BlasInt}, # incy
|
| 944 |
|
|
Clong), # length of uplo
|
| 945 |
|
|
uplo,
|
| 946 |
|
|
n,
|
| 947 |
|
|
ฮฑ,
|
| 948 |
|
|
AP,
|
| 949 |
|
|
x,
|
| 950 |
|
|
incx,
|
| 951 |
|
|
ฮฒ,
|
| 952 |
|
|
y,
|
| 953 |
|
|
incy,
|
| 954 |
|
|
1)
|
| 955 |
|
|
return y
|
| 956 |
|
|
end
|
| 957 |
|
|
end
|
| 958 |
|
|
end
|
| 959 |
|
|
|
| 960 |
|
|
function hpmv!(uplo::AbstractChar,
|
| 961 |
|
|
ฮฑ::Number, AP::AbstractArray{T}, x::AbstractArray{T},
|
| 962 |
|
|
ฮฒ::Number, y::AbstractArray{T}) where {T <: BlasComplex}
|
| 963 |
|
|
require_one_based_indexing(AP, x, y)
|
| 964 |
|
|
N = length(x)
|
| 965 |
|
|
if N != length(y)
|
| 966 |
|
|
throw(DimensionMismatch(lazy"x has length $(N), but y has length $(length(y))"))
|
| 967 |
|
|
end
|
| 968 |
|
|
if 2*length(AP) < N*(N + 1)
|
| 969 |
|
|
throw(DimensionMismatch(lazy"Packed hermitian matrix A has size smaller than length(x) = $(N)."))
|
| 970 |
|
|
end
|
| 971 |
|
|
chkstride1(AP)
|
| 972 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 973 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 974 |
|
|
GC.@preserve x y hpmv!(uplo, N, T(ฮฑ), AP, px, stx, T(ฮฒ), py, sty)
|
| 975 |
|
|
y
|
| 976 |
|
|
end
|
| 977 |
|
|
|
| 978 |
|
|
"""
|
| 979 |
|
|
hpmv!(uplo, ฮฑ, AP, x, ฮฒ, y)
|
| 980 |
|
|
|
| 981 |
|
|
Update vector `y` as `ฮฑ*A*x + ฮฒ*y`, where `A` is a Hermitian matrix provided
|
| 982 |
|
|
in packed format `AP`.
|
| 983 |
|
|
|
| 984 |
|
|
With `uplo = 'U'`, the array AP must contain the upper triangular part of the
|
| 985 |
|
|
Hermitian matrix packed sequentially, column by column, so that `AP[1]`
|
| 986 |
|
|
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[1, 2]` and `A[2, 2]`
|
| 987 |
|
|
respectively, and so on.
|
| 988 |
|
|
|
| 989 |
|
|
With `uplo = 'L'`, the array AP must contain the lower triangular part of the
|
| 990 |
|
|
Hermitian matrix packed sequentially, column by column, so that `AP[1]`
|
| 991 |
|
|
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[2, 1]` and `A[3, 1]`
|
| 992 |
|
|
respectively, and so on.
|
| 993 |
|
|
|
| 994 |
|
|
The scalar inputs `ฮฑ` and `ฮฒ` must be complex or real numbers.
|
| 995 |
|
|
|
| 996 |
|
|
The array inputs `x`, `y` and `AP` must all be of `ComplexF32` or `ComplexF64` type.
|
| 997 |
|
|
|
| 998 |
|
|
Return the updated `y`.
|
| 999 |
|
|
|
| 1000 |
|
|
!!! compat "Julia 1.5"
|
| 1001 |
|
|
`hpmv!` requires at least Julia 1.5.
|
| 1002 |
|
|
"""
|
| 1003 |
|
|
hpmv!
|
| 1004 |
|
|
|
| 1005 |
|
|
### sbmv, (SB) symmetric banded matrix-vector multiplication
|
| 1006 |
|
|
for (fname, elty) in ((:dsbmv_,:Float64),
|
| 1007 |
|
|
(:ssbmv_,:Float32))
|
| 1008 |
|
|
@eval begin
|
| 1009 |
|
|
# SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
| 1010 |
|
|
# * .. Scalar Arguments ..
|
| 1011 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 1012 |
|
|
# INTEGER INCX,INCY,K,LDA,N
|
| 1013 |
|
|
# CHARACTER UPLO
|
| 1014 |
|
|
# * .. Array Arguments ..
|
| 1015 |
|
|
# DOUBLE PRECISION A(LDA,*),X(*),Y(*)
|
| 1016 |
|
|
function sbmv!(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty}, beta::($elty), y::AbstractVector{$elty})
|
| 1017 |
|
|
chkuplo(uplo)
|
| 1018 |
|
|
require_one_based_indexing(A, x, y)
|
| 1019 |
|
|
chkstride1(A)
|
| 1020 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1021 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 1022 |
|
|
GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1023 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{$elty},
|
| 1024 |
|
|
Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
|
| 1025 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Clong),
|
| 1026 |
|
|
uplo, size(A,2), k, alpha,
|
| 1027 |
|
|
A, max(1,stride(A,2)), px, stx,
|
| 1028 |
|
|
beta, py, sty, 1)
|
| 1029 |
|
|
y
|
| 1030 |
|
|
end
|
| 1031 |
|
|
function sbmv(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1032 |
|
|
n = size(A,2)
|
| 1033 |
|
|
sbmv!(uplo, k, alpha, A, x, zero($elty), similar(x, $elty, n))
|
| 1034 |
|
|
end
|
| 1035 |
|
|
function sbmv(uplo::AbstractChar, k::Integer, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1036 |
|
|
sbmv(uplo, k, one($elty), A, x)
|
| 1037 |
|
|
end
|
| 1038 |
|
|
end
|
| 1039 |
|
|
end
|
| 1040 |
|
|
|
| 1041 |
|
|
"""
|
| 1042 |
|
|
sbmv(uplo, k, alpha, A, x)
|
| 1043 |
|
|
|
| 1044 |
|
|
Return `alpha*A*x` where `A` is a symmetric band matrix of order `size(A,2)` with `k`
|
| 1045 |
|
|
super-diagonals stored in the argument `A`.
|
| 1046 |
|
|
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 1047 |
|
|
"""
|
| 1048 |
|
|
sbmv(uplo, k, alpha, A, x)
|
| 1049 |
|
|
|
| 1050 |
|
|
"""
|
| 1051 |
|
|
sbmv(uplo, k, A, x)
|
| 1052 |
|
|
|
| 1053 |
|
|
Return `A*x` where `A` is a symmetric band matrix of order `size(A,2)` with `k`
|
| 1054 |
|
|
super-diagonals stored in the argument `A`.
|
| 1055 |
|
|
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 1056 |
|
|
"""
|
| 1057 |
|
|
sbmv(uplo, k, A, x)
|
| 1058 |
|
|
|
| 1059 |
|
|
"""
|
| 1060 |
|
|
sbmv!(uplo, k, alpha, A, x, beta, y)
|
| 1061 |
|
|
|
| 1062 |
|
|
Update vector `y` as `alpha*A*x + beta*y` where `A` is a symmetric band matrix of order
|
| 1063 |
|
|
`size(A,2)` with `k` super-diagonals stored in the argument `A`. The storage layout for `A`
|
| 1064 |
|
|
is described the reference BLAS module, level-2 BLAS at
|
| 1065 |
|
|
<http://www.netlib.org/lapack/explore-html/>.
|
| 1066 |
|
|
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 1067 |
|
|
|
| 1068 |
|
|
Return the updated `y`.
|
| 1069 |
|
|
"""
|
| 1070 |
|
|
sbmv!
|
| 1071 |
|
|
|
| 1072 |
|
|
### spmv!, (SP) symmetric packed matrix-vector operation defined as y := alpha*A*x + beta*y.
|
| 1073 |
|
|
for (fname, elty) in ((:dspmv_, :Float64),
|
| 1074 |
|
|
(:sspmv_, :Float32))
|
| 1075 |
|
|
@eval begin
|
| 1076 |
|
|
# SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
|
| 1077 |
|
|
# Y <- ALPHA*AP*X + BETA*Y
|
| 1078 |
|
|
# * .. Scalar Arguments ..
|
| 1079 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 1080 |
|
|
# INTEGER INCX,INCY,N
|
| 1081 |
|
|
# CHARACTER UPLO
|
| 1082 |
|
|
# * .. Array Arguments ..
|
| 1083 |
|
|
# DOUBLE PRECISION A(N,N),X(N),Y(N)
|
| 1084 |
|
|
function spmv!(uplo::AbstractChar,
|
| 1085 |
|
|
n::Integer,
|
| 1086 |
|
|
ฮฑ::$elty,
|
| 1087 |
|
|
AP::Union{Ptr{$elty}, AbstractArray{$elty}},
|
| 1088 |
|
|
x::Union{Ptr{$elty}, AbstractArray{$elty}},
|
| 1089 |
|
|
incx::Integer,
|
| 1090 |
|
|
ฮฒ::$elty,
|
| 1091 |
|
|
y::Union{Ptr{$elty}, AbstractArray{$elty}},
|
| 1092 |
|
|
incy::Integer)
|
| 1093 |
|
|
|
| 1094 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1095 |
|
|
(Ref{UInt8}, # uplo,
|
| 1096 |
|
|
Ref{BlasInt}, # n,
|
| 1097 |
|
|
Ref{$elty}, # ฮฑ,
|
| 1098 |
|
|
Ptr{$elty}, # AP,
|
| 1099 |
|
|
Ptr{$elty}, # x,
|
| 1100 |
|
|
Ref{BlasInt}, # incx,
|
| 1101 |
|
|
Ref{$elty}, # ฮฒ,
|
| 1102 |
|
|
Ptr{$elty}, # y, out
|
| 1103 |
|
|
Ref{BlasInt}, # incy
|
| 1104 |
|
|
Clong), # length of uplo
|
| 1105 |
|
|
uplo,
|
| 1106 |
|
|
n,
|
| 1107 |
|
|
ฮฑ,
|
| 1108 |
|
|
AP,
|
| 1109 |
|
|
x,
|
| 1110 |
|
|
incx,
|
| 1111 |
|
|
ฮฒ,
|
| 1112 |
|
|
y,
|
| 1113 |
|
|
incy,
|
| 1114 |
|
|
1)
|
| 1115 |
|
|
return y
|
| 1116 |
|
|
end
|
| 1117 |
|
|
end
|
| 1118 |
|
|
end
|
| 1119 |
|
|
|
| 1120 |
|
|
function spmv!(uplo::AbstractChar,
|
| 1121 |
|
|
ฮฑ::Real, AP::AbstractArray{T}, x::AbstractArray{T},
|
| 1122 |
|
|
ฮฒ::Real, y::AbstractArray{T}) where {T <: BlasReal}
|
| 1123 |
|
|
require_one_based_indexing(AP, x, y)
|
| 1124 |
|
|
N = length(x)
|
| 1125 |
|
|
if N != length(y)
|
| 1126 |
|
|
throw(DimensionMismatch(lazy"x has length $(N), but y has length $(length(y))"))
|
| 1127 |
|
|
end
|
| 1128 |
|
|
if 2*length(AP) < N*(N + 1)
|
| 1129 |
|
|
throw(DimensionMismatch(lazy"Packed symmetric matrix A has size smaller than length(x) = $(N)."))
|
| 1130 |
|
|
end
|
| 1131 |
|
|
chkstride1(AP)
|
| 1132 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1133 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 1134 |
|
|
GC.@preserve x y spmv!(uplo, N, T(ฮฑ), AP, px, stx, T(ฮฒ), py, sty)
|
| 1135 |
|
|
y
|
| 1136 |
|
|
end
|
| 1137 |
|
|
|
| 1138 |
|
|
"""
|
| 1139 |
|
|
spmv!(uplo, ฮฑ, AP, x, ฮฒ, y)
|
| 1140 |
|
|
|
| 1141 |
|
|
Update vector `y` as `ฮฑ*A*x + ฮฒ*y`, where `A` is a symmetric matrix provided
|
| 1142 |
|
|
in packed format `AP`.
|
| 1143 |
|
|
|
| 1144 |
|
|
With `uplo = 'U'`, the array AP must contain the upper triangular part of the
|
| 1145 |
|
|
symmetric matrix packed sequentially, column by column, so that `AP[1]`
|
| 1146 |
|
|
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[1, 2]` and `A[2, 2]`
|
| 1147 |
|
|
respectively, and so on.
|
| 1148 |
|
|
|
| 1149 |
|
|
With `uplo = 'L'`, the array AP must contain the lower triangular part of the
|
| 1150 |
|
|
symmetric matrix packed sequentially, column by column, so that `AP[1]`
|
| 1151 |
|
|
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[2, 1]` and `A[3, 1]`
|
| 1152 |
|
|
respectively, and so on.
|
| 1153 |
|
|
|
| 1154 |
|
|
The scalar inputs `ฮฑ` and `ฮฒ` must be real.
|
| 1155 |
|
|
|
| 1156 |
|
|
The array inputs `x`, `y` and `AP` must all be of `Float32` or `Float64` type.
|
| 1157 |
|
|
|
| 1158 |
|
|
Return the updated `y`.
|
| 1159 |
|
|
|
| 1160 |
|
|
!!! compat "Julia 1.5"
|
| 1161 |
|
|
`spmv!` requires at least Julia 1.5.
|
| 1162 |
|
|
"""
|
| 1163 |
|
|
spmv!
|
| 1164 |
|
|
|
| 1165 |
|
|
### spr!, (SP) symmetric packed matrix-vector operation defined as A := alpha*x*x' + A
|
| 1166 |
|
|
for (fname, elty) in ((:dspr_, :Float64),
|
| 1167 |
|
|
(:sspr_, :Float32))
|
| 1168 |
|
|
@eval begin
|
| 1169 |
|
|
function spr!(uplo::AbstractChar,
|
| 1170 |
|
|
n::Integer,
|
| 1171 |
|
|
ฮฑ::$elty,
|
| 1172 |
|
|
x::Union{Ptr{$elty}, AbstractArray{$elty}},
|
| 1173 |
|
|
incx::Integer,
|
| 1174 |
|
|
AP::Union{Ptr{$elty}, AbstractArray{$elty}})
|
| 1175 |
|
|
|
| 1176 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1177 |
|
|
(Ref{UInt8}, # uplo,
|
| 1178 |
|
|
Ref{BlasInt}, # n,
|
| 1179 |
|
|
Ref{$elty}, # ฮฑ,
|
| 1180 |
|
|
Ptr{$elty}, # x,
|
| 1181 |
|
|
Ref{BlasInt}, # incx,
|
| 1182 |
|
|
Ptr{$elty}, # AP,
|
| 1183 |
|
|
Clong), # length of uplo
|
| 1184 |
|
|
uplo,
|
| 1185 |
|
|
n,
|
| 1186 |
|
|
ฮฑ,
|
| 1187 |
|
|
x,
|
| 1188 |
|
|
incx,
|
| 1189 |
|
|
AP,
|
| 1190 |
|
|
1)
|
| 1191 |
|
|
return AP
|
| 1192 |
|
|
end
|
| 1193 |
|
|
end
|
| 1194 |
|
|
end
|
| 1195 |
|
|
|
| 1196 |
|
|
function spr!(uplo::AbstractChar,
|
| 1197 |
|
|
ฮฑ::Real, x::AbstractArray{T},
|
| 1198 |
|
|
AP::AbstractArray{T}) where {T <: BlasReal}
|
| 1199 |
|
|
chkuplo(uplo)
|
| 1200 |
|
|
require_one_based_indexing(AP, x)
|
| 1201 |
|
|
N = length(x)
|
| 1202 |
|
|
if 2*length(AP) < N*(N + 1)
|
| 1203 |
|
|
throw(DimensionMismatch(lazy"Packed symmetric matrix A has size smaller than length(x) = $(N)."))
|
| 1204 |
|
|
end
|
| 1205 |
|
|
chkstride1(AP)
|
| 1206 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1207 |
|
|
return GC.@preserve x spr!(uplo, N, T(ฮฑ), px, stx , AP)
|
| 1208 |
|
|
end
|
| 1209 |
|
|
|
| 1210 |
|
|
"""
|
| 1211 |
|
|
spr!(uplo, ฮฑ, x, AP)
|
| 1212 |
|
|
|
| 1213 |
|
|
Update matrix `A` as `A+ฮฑ*x*x'`, where `A` is a symmetric matrix provided
|
| 1214 |
|
|
in packed format `AP` and `x` is a vector.
|
| 1215 |
|
|
|
| 1216 |
|
|
With `uplo = 'U'`, the array AP must contain the upper triangular part of the
|
| 1217 |
|
|
symmetric matrix packed sequentially, column by column, so that `AP[1]`
|
| 1218 |
|
|
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[1, 2]` and `A[2, 2]`
|
| 1219 |
|
|
respectively, and so on.
|
| 1220 |
|
|
|
| 1221 |
|
|
With `uplo = 'L'`, the array AP must contain the lower triangular part of the
|
| 1222 |
|
|
symmetric matrix packed sequentially, column by column, so that `AP[1]`
|
| 1223 |
|
|
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[2, 1]` and `A[3, 1]`
|
| 1224 |
|
|
respectively, and so on.
|
| 1225 |
|
|
|
| 1226 |
|
|
The scalar input `ฮฑ` must be real.
|
| 1227 |
|
|
|
| 1228 |
|
|
The array inputs `x` and `AP` must all be of `Float32` or `Float64` type.
|
| 1229 |
|
|
Return the updated `AP`.
|
| 1230 |
|
|
|
| 1231 |
|
|
!!! compat "Julia 1.8"
|
| 1232 |
|
|
`spr!` requires at least Julia 1.8.
|
| 1233 |
|
|
"""
|
| 1234 |
|
|
spr!
|
| 1235 |
|
|
|
| 1236 |
|
|
### hbmv, (HB) Hermitian banded matrix-vector multiplication
|
| 1237 |
|
|
for (fname, elty) in ((:zhbmv_,:ComplexF64),
|
| 1238 |
|
|
(:chbmv_,:ComplexF32))
|
| 1239 |
|
|
@eval begin
|
| 1240 |
|
|
# SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
| 1241 |
|
|
# * .. Scalar Arguments ..
|
| 1242 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 1243 |
|
|
# INTEGER INCX,INCY,K,LDA,N
|
| 1244 |
|
|
# CHARACTER UPLO
|
| 1245 |
|
|
# * .. Array Arguments ..
|
| 1246 |
|
|
# DOUBLE PRECISION A(LDA,*),X(*),Y(*)
|
| 1247 |
|
|
function hbmv!(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty}, beta::($elty), y::AbstractVector{$elty})
|
| 1248 |
|
|
chkuplo(uplo)
|
| 1249 |
|
|
require_one_based_indexing(A, x, y)
|
| 1250 |
|
|
chkstride1(A)
|
| 1251 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1252 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
|
| 1253 |
|
|
GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1254 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{$elty},
|
| 1255 |
|
|
Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
|
| 1256 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Clong),
|
| 1257 |
|
|
uplo, size(A,2), k, alpha,
|
| 1258 |
|
|
A, max(1,stride(A,2)), px, stx,
|
| 1259 |
|
|
beta, py, sty, 1)
|
| 1260 |
|
|
y
|
| 1261 |
|
|
end
|
| 1262 |
|
|
function hbmv(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1263 |
|
|
n = size(A,2)
|
| 1264 |
|
|
hbmv!(uplo, k, alpha, A, x, zero($elty), similar(x, $elty, n))
|
| 1265 |
|
|
end
|
| 1266 |
|
|
function hbmv(uplo::AbstractChar, k::Integer, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1267 |
|
|
hbmv(uplo, k, one($elty), A, x)
|
| 1268 |
|
|
end
|
| 1269 |
|
|
end
|
| 1270 |
|
|
end
|
| 1271 |
|
|
|
| 1272 |
|
|
### trmv, Triangular matrix-vector multiplication
|
| 1273 |
|
|
|
| 1274 |
|
|
"""
|
| 1275 |
|
|
trmv(ul, tA, dA, A, b)
|
| 1276 |
|
|
|
| 1277 |
|
|
Return `op(A)*b`, where `op` is determined by [`tA`](@ref stdlib-blas-trans).
|
| 1278 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 1279 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 1280 |
|
|
are assumed to be all ones.
|
| 1281 |
|
|
"""
|
| 1282 |
|
|
function trmv end
|
| 1283 |
|
|
|
| 1284 |
|
|
"""
|
| 1285 |
|
|
trmv!(ul, tA, dA, A, b)
|
| 1286 |
|
|
|
| 1287 |
|
|
Return `op(A)*b`, where `op` is determined by [`tA`](@ref stdlib-blas-trans).
|
| 1288 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 1289 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 1290 |
|
|
are assumed to be all ones.
|
| 1291 |
|
|
The multiplication occurs in-place on `b`.
|
| 1292 |
|
|
"""
|
| 1293 |
|
|
function trmv! end
|
| 1294 |
|
|
|
| 1295 |
|
|
for (fname, elty) in ((:dtrmv_,:Float64),
|
| 1296 |
|
|
(:strmv_,:Float32),
|
| 1297 |
|
|
(:ztrmv_,:ComplexF64),
|
| 1298 |
|
|
(:ctrmv_,:ComplexF32))
|
| 1299 |
|
|
@eval begin
|
| 1300 |
|
|
# SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
|
| 1301 |
|
|
# * .. Scalar Arguments ..
|
| 1302 |
|
|
# INTEGER INCX,LDA,N
|
| 1303 |
|
|
# CHARACTER DIAG,TRANS,UPLO
|
| 1304 |
|
|
# * .. Array Arguments ..
|
| 1305 |
|
|
# DOUBLE PRECISION A(LDA,*),X(*)
|
| 1306 |
|
|
function trmv!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1307 |
|
|
chkuplo(uplo)
|
| 1308 |
|
|
require_one_based_indexing(A, x)
|
| 1309 |
|
|
n = checksquare(A)
|
| 1310 |
|
|
if n != length(x)
|
| 1311 |
|
|
throw(DimensionMismatch(lazy"A has size ($n,$n), x has length $(length(x))"))
|
| 1312 |
|
|
end
|
| 1313 |
|
|
chkstride1(A)
|
| 1314 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1315 |
|
|
GC.@preserve x ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1316 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
|
| 1317 |
|
|
Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
|
| 1318 |
|
|
Clong, Clong, Clong),
|
| 1319 |
|
|
uplo, trans, diag, n,
|
| 1320 |
|
|
A, max(1,stride(A,2)), px, stx, 1, 1, 1)
|
| 1321 |
|
|
x
|
| 1322 |
|
|
end
|
| 1323 |
|
|
function trmv(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1324 |
|
|
trmv!(uplo, trans, diag, A, copy(x))
|
| 1325 |
|
|
end
|
| 1326 |
|
|
end
|
| 1327 |
|
|
end
|
| 1328 |
|
|
|
| 1329 |
|
|
### trsv, Triangular matrix-vector solve
|
| 1330 |
|
|
|
| 1331 |
|
|
"""
|
| 1332 |
|
|
trsv!(ul, tA, dA, A, b)
|
| 1333 |
|
|
|
| 1334 |
|
|
Overwrite `b` with the solution to `A*x = b` or one of the other two variants determined by
|
| 1335 |
|
|
[`tA`](@ref stdlib-blas-trans) and [`ul`](@ref stdlib-blas-uplo).
|
| 1336 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 1337 |
|
|
are assumed to be all ones.
|
| 1338 |
|
|
Return the updated `b`.
|
| 1339 |
|
|
"""
|
| 1340 |
|
|
function trsv! end
|
| 1341 |
|
|
|
| 1342 |
|
|
"""
|
| 1343 |
|
|
trsv(ul, tA, dA, A, b)
|
| 1344 |
|
|
|
| 1345 |
|
|
Return the solution to `A*x = b` or one of the other two variants determined by
|
| 1346 |
|
|
[`tA`](@ref stdlib-blas-trans) and [`ul`](@ref stdlib-blas-uplo).
|
| 1347 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 1348 |
|
|
are assumed to be all ones.
|
| 1349 |
|
|
"""
|
| 1350 |
|
|
function trsv end
|
| 1351 |
|
|
|
| 1352 |
|
|
for (fname, elty) in ((:dtrsv_,:Float64),
|
| 1353 |
|
|
(:strsv_,:Float32),
|
| 1354 |
|
|
(:ztrsv_,:ComplexF64),
|
| 1355 |
|
|
(:ctrsv_,:ComplexF32))
|
| 1356 |
|
|
@eval begin
|
| 1357 |
|
|
# SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
|
| 1358 |
|
|
# .. Scalar Arguments ..
|
| 1359 |
|
|
# INTEGER INCX,LDA,N
|
| 1360 |
|
|
# CHARACTER DIAG,TRANS,UPLO
|
| 1361 |
|
|
# .. Array Arguments ..
|
| 1362 |
|
|
# DOUBLE PRECISION A(LDA,*),X(*)
|
| 1363 |
|
|
function trsv!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1364 |
|
|
chkuplo(uplo)
|
| 1365 |
|
|
require_one_based_indexing(A, x)
|
| 1366 |
|
|
n = checksquare(A)
|
| 1367 |
|
|
if n != length(x)
|
| 1368 |
|
|
throw(DimensionMismatch(lazy"size of A is $n != length(x) = $(length(x))"))
|
| 1369 |
|
|
end
|
| 1370 |
|
|
chkstride1(A)
|
| 1371 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1372 |
|
|
GC.@preserve x ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1373 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
|
| 1374 |
|
|
Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
|
| 1375 |
|
|
Clong, Clong, Clong),
|
| 1376 |
|
|
uplo, trans, diag, n,
|
| 1377 |
|
|
A, max(1,stride(A,2)), px, stx, 1, 1, 1)
|
| 1378 |
|
|
x
|
| 1379 |
|
|
end
|
| 1380 |
|
|
function trsv(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
|
| 1381 |
|
|
trsv!(uplo, trans, diag, A, copy(x))
|
| 1382 |
|
|
end
|
| 1383 |
|
|
end
|
| 1384 |
|
|
end
|
| 1385 |
|
|
|
| 1386 |
|
|
### ger
|
| 1387 |
|
|
|
| 1388 |
|
|
"""
|
| 1389 |
|
|
ger!(alpha, x, y, A)
|
| 1390 |
|
|
|
| 1391 |
|
|
Rank-1 update of the matrix `A` with vectors `x` and `y` as `alpha*x*y' + A`.
|
| 1392 |
|
|
"""
|
| 1393 |
|
|
function ger! end
|
| 1394 |
|
|
|
| 1395 |
|
|
for (fname, elty) in ((:dger_,:Float64),
|
| 1396 |
|
|
(:sger_,:Float32),
|
| 1397 |
|
|
(:zgerc_,:ComplexF64),
|
| 1398 |
|
|
(:cgerc_,:ComplexF32))
|
| 1399 |
|
|
@eval begin
|
| 1400 |
|
|
function ger!(ฮฑ::$elty, x::AbstractVector{$elty}, y::AbstractVector{$elty}, A::AbstractMatrix{$elty})
|
| 1401 |
|
|
require_one_based_indexing(A, x, y)
|
| 1402 |
|
|
m, n = size(A)
|
| 1403 |
|
|
if m != length(x) || n != length(y)
|
| 1404 |
|
|
throw(DimensionMismatch(lazy"A has size ($m,$n), x has length $(length(x)), y has length $(length(y))"))
|
| 1405 |
|
|
end
|
| 1406 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1407 |
|
|
py, sty = vec_pointer_stride(y, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1408 |
|
|
GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1409 |
|
|
(Ref{BlasInt}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 1410 |
|
|
Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
|
| 1411 |
|
|
Ref{BlasInt}),
|
| 1412 |
|
|
m, n, ฮฑ, px, stx, py, sty, A, max(1,stride(A,2)))
|
| 1413 |
|
|
A
|
| 1414 |
|
|
end
|
| 1415 |
|
|
end
|
| 1416 |
|
|
end
|
| 1417 |
|
|
|
| 1418 |
|
|
### syr
|
| 1419 |
|
|
|
| 1420 |
|
|
"""
|
| 1421 |
|
|
syr!(uplo, alpha, x, A)
|
| 1422 |
|
|
|
| 1423 |
|
|
Rank-1 update of the symmetric matrix `A` with vector `x` as `alpha*x*transpose(x) + A`.
|
| 1424 |
|
|
[`uplo`](@ref stdlib-blas-uplo) controls which triangle of `A` is updated. Returns `A`.
|
| 1425 |
|
|
"""
|
| 1426 |
|
|
function syr! end
|
| 1427 |
|
|
|
| 1428 |
|
|
for (fname, elty, lib) in ((:dsyr_,:Float64,libblastrampoline),
|
| 1429 |
|
|
(:ssyr_,:Float32,libblastrampoline),
|
| 1430 |
|
|
(:zsyr_,:ComplexF64,libblastrampoline),
|
| 1431 |
|
|
(:csyr_,:ComplexF32,libblastrampoline))
|
| 1432 |
|
|
@eval begin
|
| 1433 |
|
|
function syr!(uplo::AbstractChar, ฮฑ::$elty, x::AbstractVector{$elty}, A::AbstractMatrix{$elty})
|
| 1434 |
|
|
chkuplo(uplo)
|
| 1435 |
|
|
require_one_based_indexing(A, x)
|
| 1436 |
|
|
n = checksquare(A)
|
| 1437 |
|
|
if length(x) != n
|
| 1438 |
|
|
throw(DimensionMismatch(lazy"A has size ($n,$n), x has length $(length(x))"))
|
| 1439 |
|
|
end
|
| 1440 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1441 |
|
|
GC.@preserve x ccall((@blasfunc($fname), $lib), Cvoid,
|
| 1442 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 1443 |
|
|
Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
|
| 1444 |
|
|
uplo, n, ฮฑ, px, stx, A, max(1,stride(A, 2)))
|
| 1445 |
|
|
A
|
| 1446 |
|
|
end
|
| 1447 |
|
|
end
|
| 1448 |
|
|
end
|
| 1449 |
|
|
|
| 1450 |
|
|
### her
|
| 1451 |
|
|
|
| 1452 |
|
|
"""
|
| 1453 |
|
|
her!(uplo, alpha, x, A)
|
| 1454 |
|
|
|
| 1455 |
|
|
Methods for complex arrays only. Rank-1 update of the Hermitian matrix `A` with vector `x`
|
| 1456 |
|
|
as `alpha*x*x' + A`.
|
| 1457 |
|
|
[`uplo`](@ref stdlib-blas-uplo) controls which triangle of `A` is updated. Returns `A`.
|
| 1458 |
|
|
"""
|
| 1459 |
|
|
function her! end
|
| 1460 |
|
|
|
| 1461 |
|
|
for (fname, elty, relty) in ((:zher_,:ComplexF64, :Float64),
|
| 1462 |
|
|
(:cher_,:ComplexF32, :Float32))
|
| 1463 |
|
|
@eval begin
|
| 1464 |
|
|
function her!(uplo::AbstractChar, ฮฑ::$relty, x::AbstractVector{$elty}, A::AbstractMatrix{$elty})
|
| 1465 |
|
|
chkuplo(uplo)
|
| 1466 |
|
|
require_one_based_indexing(A, x)
|
| 1467 |
|
|
n = checksquare(A)
|
| 1468 |
|
|
if length(x) != n
|
| 1469 |
|
|
throw(DimensionMismatch(lazy"A has size ($n,$n), x has length $(length(x))"))
|
| 1470 |
|
|
end
|
| 1471 |
|
|
px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
|
| 1472 |
|
|
GC.@preserve x ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1473 |
|
|
(Ref{UInt8}, Ref{BlasInt}, Ref{$relty}, Ptr{$elty},
|
| 1474 |
|
|
Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Clong),
|
| 1475 |
|
|
uplo, n, ฮฑ, px, stx, A, max(1,stride(A,2)), 1)
|
| 1476 |
|
|
A
|
| 1477 |
|
|
end
|
| 1478 |
|
|
end
|
| 1479 |
|
|
end
|
| 1480 |
|
|
|
| 1481 |
|
|
# Level 3
|
| 1482 |
|
|
## (GE) general matrix-matrix multiplication
|
| 1483 |
|
|
|
| 1484 |
|
|
"""
|
| 1485 |
|
|
gemm!(tA, tB, alpha, A, B, beta, C)
|
| 1486 |
|
|
|
| 1487 |
|
|
Update `C` as `alpha*A*B + beta*C` or the other three variants according to
|
| 1488 |
|
|
[`tA`](@ref stdlib-blas-trans) and `tB`. Return the updated `C`.
|
| 1489 |
|
|
"""
|
| 1490 |
|
|
function gemm! end
|
| 1491 |
|
|
|
| 1492 |
|
|
for (gemm, elty) in
|
| 1493 |
|
|
((:dgemm_,:Float64),
|
| 1494 |
|
|
(:sgemm_,:Float32),
|
| 1495 |
|
|
(:zgemm_,:ComplexF64),
|
| 1496 |
|
|
(:cgemm_,:ComplexF32))
|
| 1497 |
|
|
@eval begin
|
| 1498 |
|
|
# SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
| 1499 |
|
|
# * .. Scalar Arguments ..
|
| 1500 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 1501 |
|
|
# INTEGER K,LDA,LDB,LDC,M,N
|
| 1502 |
|
|
# CHARACTER TRANSA,TRANSB
|
| 1503 |
|
|
# * .. Array Arguments ..
|
| 1504 |
|
|
# DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
|
| 1505 |
|
|
function gemm!(transA::AbstractChar, transB::AbstractChar,
|
| 1506 |
|
|
alpha::Union{($elty), Bool},
|
| 1507 |
|
|
A::AbstractVecOrMat{$elty}, B::AbstractVecOrMat{$elty},
|
| 1508 |
|
|
beta::Union{($elty), Bool},
|
| 1509 |
|
|
C::AbstractVecOrMat{$elty})
|
| 1510 |
|
|
# if any([stride(A,1), stride(B,1), stride(C,1)] .!= 1)
|
| 1511 |
|
|
# error("gemm!: BLAS module requires contiguous matrix columns")
|
| 1512 |
|
|
# end # should this be checked on every call?
|
| 1513 |
|
|
require_one_based_indexing(A, B, C)
|
| 1514 |
|
|
m = size(A, transA == 'N' ? 1 : 2)
|
| 1515 |
|
|
ka = size(A, transA == 'N' ? 2 : 1)
|
| 1516 |
|
|
kb = size(B, transB == 'N' ? 1 : 2)
|
| 1517 |
|
|
n = size(B, transB == 'N' ? 2 : 1)
|
| 1518 |
|
|
if ka != kb || m != size(C,1) || n != size(C,2)
|
| 1519 |
|
|
throw(DimensionMismatch(lazy"A has size ($m,$ka), B has size ($kb,$n), C has size $(size(C))"))
|
| 1520 |
|
|
end
|
| 1521 |
|
|
chkstride1(A)
|
| 1522 |
|
|
chkstride1(B)
|
| 1523 |
|
|
chkstride1(C)
|
| 1524 |
|
|
ccall((@blasfunc($gemm), libblastrampoline), Cvoid,
|
| 1525 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 1526 |
|
|
Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
|
| 1527 |
|
|
Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 1528 |
|
|
Ref{BlasInt}, Clong, Clong),
|
| 1529 |
|
|
transA, transB, m, n,
|
| 1530 |
|
|
ka, alpha, A, max(1,stride(A,2)),
|
| 1531 |
|
|
B, max(1,stride(B,2)), beta, C,
|
| 1532 |
|
|
max(1,stride(C,2)), 1, 1)
|
| 1533 |
|
|
C
|
| 1534 |
|
|
end
|
| 1535 |
|
|
function gemm(transA::AbstractChar, transB::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 1536 |
|
|
gemm!(transA, transB, alpha, A, B, zero($elty), similar(B, $elty, (size(A, transA == 'N' ? 1 : 2), size(B, transB == 'N' ? 2 : 1))))
|
| 1537 |
|
|
end
|
| 1538 |
|
|
function gemm(transA::AbstractChar, transB::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 1539 |
|
|
gemm(transA, transB, one($elty), A, B)
|
| 1540 |
|
|
end
|
| 1541 |
|
|
end
|
| 1542 |
|
|
end
|
| 1543 |
|
|
|
| 1544 |
|
|
"""
|
| 1545 |
|
|
gemm(tA, tB, alpha, A, B)
|
| 1546 |
|
|
|
| 1547 |
|
|
Return `alpha*A*B` or the other three variants according to [`tA`](@ref stdlib-blas-trans) and `tB`.
|
| 1548 |
|
|
"""
|
| 1549 |
|
|
gemm(tA, tB, alpha, A, B)
|
| 1550 |
|
|
|
| 1551 |
|
|
"""
|
| 1552 |
|
|
gemm(tA, tB, A, B)
|
| 1553 |
|
|
|
| 1554 |
|
|
Return `A*B` or the other three variants according to [`tA`](@ref stdlib-blas-trans) and `tB`.
|
| 1555 |
|
|
"""
|
| 1556 |
|
|
gemm(tA, tB, A, B)
|
| 1557 |
|
|
|
| 1558 |
|
|
|
| 1559 |
|
|
## (SY) symmetric matrix-matrix and matrix-vector multiplication
|
| 1560 |
|
|
for (mfname, elty) in ((:dsymm_,:Float64),
|
| 1561 |
|
|
(:ssymm_,:Float32),
|
| 1562 |
|
|
(:zsymm_,:ComplexF64),
|
| 1563 |
|
|
(:csymm_,:ComplexF32))
|
| 1564 |
|
|
@eval begin
|
| 1565 |
|
|
# SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
| 1566 |
|
|
# .. Scalar Arguments ..
|
| 1567 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 1568 |
|
|
# INTEGER LDA,LDB,LDC,M,N
|
| 1569 |
|
|
# CHARACTER SIDE,UPLO
|
| 1570 |
|
|
# .. Array Arguments ..
|
| 1571 |
|
|
# DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
|
| 1572 |
|
|
function symm!(side::AbstractChar, uplo::AbstractChar, alpha::Union{($elty), Bool},
|
| 1573 |
|
|
A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty},
|
| 1574 |
|
|
beta::Union{($elty), Bool}, C::AbstractMatrix{$elty})
|
| 1575 |
|
|
chkuplo(uplo)
|
| 1576 |
|
|
require_one_based_indexing(A, B, C)
|
| 1577 |
|
|
m, n = size(C)
|
| 1578 |
|
|
j = checksquare(A)
|
| 1579 |
|
|
M, N = size(B)
|
| 1580 |
|
|
if side == 'L'
|
| 1581 |
|
|
if j != m
|
| 1582 |
|
|
throw(DimensionMismatch(lazy"A has first dimension $j but needs to match first dimension of C, $m"))
|
| 1583 |
|
|
end
|
| 1584 |
|
|
if N != n
|
| 1585 |
|
|
throw(DimensionMismatch(lazy"B has second dimension $N but needs to match second dimension of C, $n"))
|
| 1586 |
|
|
end
|
| 1587 |
|
|
if j != M
|
| 1588 |
|
|
throw(DimensionMismatch(lazy"A has second dimension $j but needs to match first dimension of B, $M"))
|
| 1589 |
|
|
end
|
| 1590 |
|
|
else
|
| 1591 |
|
|
if j != n
|
| 1592 |
|
|
throw(DimensionMismatch(lazy"B has second dimension $j but needs to match second dimension of C, $n"))
|
| 1593 |
|
|
end
|
| 1594 |
|
|
if N != j
|
| 1595 |
|
|
throw(DimensionMismatch(lazy"A has second dimension $N but needs to match first dimension of B, $j"))
|
| 1596 |
|
|
end
|
| 1597 |
|
|
if M != m
|
| 1598 |
|
|
throw(DimensionMismatch(lazy"A has first dimension $M but needs to match first dimension of C, $m"))
|
| 1599 |
|
|
end
|
| 1600 |
|
|
end
|
| 1601 |
|
|
chkstride1(A)
|
| 1602 |
|
|
chkstride1(B)
|
| 1603 |
|
|
chkstride1(C)
|
| 1604 |
|
|
ccall((@blasfunc($mfname), libblastrampoline), Cvoid,
|
| 1605 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 1606 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
|
| 1607 |
|
|
Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
|
| 1608 |
|
|
Clong, Clong),
|
| 1609 |
|
|
side, uplo, m, n,
|
| 1610 |
|
|
alpha, A, max(1,stride(A,2)), B,
|
| 1611 |
|
|
max(1,stride(B,2)), beta, C, max(1,stride(C,2)),
|
| 1612 |
|
|
1, 1)
|
| 1613 |
|
|
C
|
| 1614 |
|
|
end
|
| 1615 |
|
|
function symm(side::AbstractChar, uplo::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 1616 |
|
|
symm!(side, uplo, alpha, A, B, zero($elty), similar(B))
|
| 1617 |
|
|
end
|
| 1618 |
|
|
function symm(side::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 1619 |
|
|
symm(side, uplo, one($elty), A, B)
|
| 1620 |
|
|
end
|
| 1621 |
|
|
end
|
| 1622 |
|
|
end
|
| 1623 |
|
|
|
| 1624 |
|
|
"""
|
| 1625 |
|
|
symm(side, ul, alpha, A, B)
|
| 1626 |
|
|
|
| 1627 |
|
|
Return `alpha*A*B` or `alpha*B*A` according to [`side`](@ref stdlib-blas-side).
|
| 1628 |
|
|
`A` is assumed to be symmetric. Only
|
| 1629 |
|
|
the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 1630 |
|
|
"""
|
| 1631 |
|
|
symm(side, ul, alpha, A, B)
|
| 1632 |
|
|
|
| 1633 |
|
|
"""
|
| 1634 |
|
|
symm(side, ul, A, B)
|
| 1635 |
|
|
|
| 1636 |
|
|
Return `A*B` or `B*A` according to [`side`](@ref stdlib-blas-side).
|
| 1637 |
|
|
`A` is assumed to be symmetric. Only the [`ul`](@ref stdlib-blas-uplo)
|
| 1638 |
|
|
triangle of `A` is used.
|
| 1639 |
|
|
"""
|
| 1640 |
|
|
symm(side, ul, A, B)
|
| 1641 |
|
|
|
| 1642 |
|
|
"""
|
| 1643 |
|
|
symm!(side, ul, alpha, A, B, beta, C)
|
| 1644 |
|
|
|
| 1645 |
|
|
Update `C` as `alpha*A*B + beta*C` or `alpha*B*A + beta*C` according to [`side`](@ref stdlib-blas-side).
|
| 1646 |
|
|
`A` is assumed to be symmetric. Only the [`ul`](@ref stdlib-blas-uplo) triangle of
|
| 1647 |
|
|
`A` is used. Return the updated `C`.
|
| 1648 |
|
|
"""
|
| 1649 |
|
|
symm!
|
| 1650 |
|
|
|
| 1651 |
|
|
## (HE) Hermitian matrix-matrix and matrix-vector multiplication
|
| 1652 |
|
|
for (mfname, elty) in ((:zhemm_,:ComplexF64),
|
| 1653 |
|
|
(:chemm_,:ComplexF32))
|
| 1654 |
|
|
@eval begin
|
| 1655 |
|
|
# SUBROUTINE DHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
| 1656 |
|
|
# .. Scalar Arguments ..
|
| 1657 |
|
|
# DOUBLE PRECISION ALPHA,BETA
|
| 1658 |
|
|
# INTEGER LDA,LDB,LDC,M,N
|
| 1659 |
|
|
# CHARACTER SIDE,UPLO
|
| 1660 |
|
|
# .. Array Arguments ..
|
| 1661 |
|
|
# DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
|
| 1662 |
|
|
function hemm!(side::AbstractChar, uplo::AbstractChar, alpha::Union{($elty), Bool},
|
| 1663 |
|
|
A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty},
|
| 1664 |
|
|
beta::Union{($elty), Bool}, C::AbstractMatrix{$elty})
|
| 1665 |
|
|
chkuplo(uplo)
|
| 1666 |
|
|
require_one_based_indexing(A, B, C)
|
| 1667 |
|
|
m, n = size(C)
|
| 1668 |
|
|
j = checksquare(A)
|
| 1669 |
|
|
M, N = size(B)
|
| 1670 |
|
|
if side == 'L'
|
| 1671 |
|
|
if j != m
|
| 1672 |
|
|
throw(DimensionMismatch(lazy"A has first dimension $j but needs to match first dimension of C, $m"))
|
| 1673 |
|
|
end
|
| 1674 |
|
|
if N != n
|
| 1675 |
|
|
throw(DimensionMismatch(lazy"B has second dimension $N but needs to match second dimension of C, $n"))
|
| 1676 |
|
|
end
|
| 1677 |
|
|
if j != M
|
| 1678 |
|
|
throw(DimensionMismatch(lazy"A has second dimension $j but needs to match first dimension of B, $M"))
|
| 1679 |
|
|
end
|
| 1680 |
|
|
else
|
| 1681 |
|
|
if j != n
|
| 1682 |
|
|
throw(DimensionMismatch(lazy"B has second dimension $j but needs to match second dimension of C, $n"))
|
| 1683 |
|
|
end
|
| 1684 |
|
|
if N != j
|
| 1685 |
|
|
throw(DimensionMismatch(lazy"A has second dimension $N but needs to match first dimension of B, $j"))
|
| 1686 |
|
|
end
|
| 1687 |
|
|
if M != m
|
| 1688 |
|
|
throw(DimensionMismatch(lazy"A has first dimension $M but needs to match first dimension of C, $m"))
|
| 1689 |
|
|
end
|
| 1690 |
|
|
end
|
| 1691 |
|
|
chkstride1(A)
|
| 1692 |
|
|
chkstride1(B)
|
| 1693 |
|
|
chkstride1(C)
|
| 1694 |
|
|
ccall((@blasfunc($mfname), libblastrampoline), Cvoid,
|
| 1695 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 1696 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
|
| 1697 |
|
|
Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
|
| 1698 |
|
|
Clong, Clong),
|
| 1699 |
|
|
side, uplo, m, n,
|
| 1700 |
|
|
alpha, A, max(1,stride(A,2)), B,
|
| 1701 |
|
|
max(1,stride(B,2)), beta, C, max(1,stride(C,2)),
|
| 1702 |
|
|
1, 1)
|
| 1703 |
|
|
C
|
| 1704 |
|
|
end
|
| 1705 |
|
|
function hemm(side::AbstractChar, uplo::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 1706 |
|
|
hemm!(side, uplo, alpha, A, B, zero($elty), similar(B))
|
| 1707 |
|
|
end
|
| 1708 |
|
|
function hemm(side::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 1709 |
|
|
hemm(side, uplo, one($elty), A, B)
|
| 1710 |
|
|
end
|
| 1711 |
|
|
end
|
| 1712 |
|
|
end
|
| 1713 |
|
|
|
| 1714 |
|
|
"""
|
| 1715 |
|
|
hemm(side, ul, alpha, A, B)
|
| 1716 |
|
|
|
| 1717 |
|
|
Return `alpha*A*B` or `alpha*B*A` according to [`side`](@ref stdlib-blas-side).
|
| 1718 |
|
|
`A` is assumed to be Hermitian. Only the [`ul`](@ref stdlib-blas-uplo) triangle
|
| 1719 |
|
|
of `A` is used.
|
| 1720 |
|
|
"""
|
| 1721 |
|
|
hemm(side, ul, alpha, A, B)
|
| 1722 |
|
|
|
| 1723 |
|
|
"""
|
| 1724 |
|
|
hemm(side, ul, A, B)
|
| 1725 |
|
|
|
| 1726 |
|
|
Return `A*B` or `B*A` according to [`side`](@ref stdlib-blas-side). `A` is assumed
|
| 1727 |
|
|
to be Hermitian. Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 1728 |
|
|
"""
|
| 1729 |
|
|
hemm(side, ul, A, B)
|
| 1730 |
|
|
|
| 1731 |
|
|
"""
|
| 1732 |
|
|
hemm!(side, ul, alpha, A, B, beta, C)
|
| 1733 |
|
|
|
| 1734 |
|
|
Update `C` as `alpha*A*B + beta*C` or `alpha*B*A + beta*C` according to
|
| 1735 |
|
|
[`side`](@ref stdlib-blas-side). `A` is assumed to be Hermitian. Only the
|
| 1736 |
|
|
[`ul`](@ref stdlib-blas-uplo) triangle of `A` is used. Return the updated `C`.
|
| 1737 |
|
|
"""
|
| 1738 |
|
|
hemm!
|
| 1739 |
|
|
|
| 1740 |
|
|
## syrk
|
| 1741 |
|
|
|
| 1742 |
|
|
"""
|
| 1743 |
|
|
syrk!(uplo, trans, alpha, A, beta, C)
|
| 1744 |
|
|
|
| 1745 |
|
|
Rank-k update of the symmetric matrix `C` as `alpha*A*transpose(A) + beta*C` or
|
| 1746 |
|
|
`alpha*transpose(A)*A + beta*C` according to [`trans`](@ref stdlib-blas-trans).
|
| 1747 |
|
|
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is used. Return `C`.
|
| 1748 |
|
|
"""
|
| 1749 |
|
|
function syrk! end
|
| 1750 |
|
|
|
| 1751 |
|
|
"""
|
| 1752 |
|
|
syrk(uplo, trans, alpha, A)
|
| 1753 |
|
|
|
| 1754 |
|
|
Return either the upper triangle or the lower triangle of `A`,
|
| 1755 |
|
|
according to [`uplo`](@ref stdlib-blas-uplo),
|
| 1756 |
|
|
of `alpha*A*transpose(A)` or `alpha*transpose(A)*A`,
|
| 1757 |
|
|
according to [`trans`](@ref stdlib-blas-trans).
|
| 1758 |
|
|
"""
|
| 1759 |
|
|
function syrk end
|
| 1760 |
|
|
|
| 1761 |
|
|
for (fname, elty) in ((:dsyrk_,:Float64),
|
| 1762 |
|
|
(:ssyrk_,:Float32),
|
| 1763 |
|
|
(:zsyrk_,:ComplexF64),
|
| 1764 |
|
|
(:csyrk_,:ComplexF32))
|
| 1765 |
|
|
@eval begin
|
| 1766 |
|
|
# SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
|
| 1767 |
|
|
# * .. Scalar Arguments ..
|
| 1768 |
|
|
# REAL ALPHA,BETA
|
| 1769 |
|
|
# INTEGER K,LDA,LDC,N
|
| 1770 |
|
|
# CHARACTER TRANS,UPLO
|
| 1771 |
|
|
# * .. Array Arguments ..
|
| 1772 |
|
|
# REAL A(LDA,*),C(LDC,*)
|
| 1773 |
|
|
function syrk!(uplo::AbstractChar, trans::AbstractChar,
|
| 1774 |
|
|
alpha::Union{($elty), Bool}, A::AbstractVecOrMat{$elty},
|
| 1775 |
|
|
beta::Union{($elty), Bool}, C::AbstractMatrix{$elty})
|
| 1776 |
|
|
chkuplo(uplo)
|
| 1777 |
|
|
require_one_based_indexing(A, C)
|
| 1778 |
|
|
n = checksquare(C)
|
| 1779 |
|
|
nn = size(A, trans == 'N' ? 1 : 2)
|
| 1780 |
|
|
if nn != n throw(DimensionMismatch(lazy"C has size ($n,$n), corresponding dimension of A is $nn")) end
|
| 1781 |
|
|
k = size(A, trans == 'N' ? 2 : 1)
|
| 1782 |
|
|
chkstride1(A)
|
| 1783 |
|
|
chkstride1(C)
|
| 1784 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1785 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 1786 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
|
| 1787 |
|
|
Ptr{$elty}, Ref{BlasInt}, Clong, Clong),
|
| 1788 |
|
|
uplo, trans, n, k,
|
| 1789 |
|
|
alpha, A, max(1,stride(A,2)), beta,
|
| 1790 |
|
|
C, max(1,stride(C,2)), 1, 1)
|
| 1791 |
|
|
C
|
| 1792 |
|
|
end
|
| 1793 |
|
|
end
|
| 1794 |
|
|
end
|
| 1795 |
|
|
function syrk(uplo::AbstractChar, trans::AbstractChar, alpha::Number, A::AbstractVecOrMat)
|
| 1796 |
|
|
T = eltype(A)
|
| 1797 |
|
|
n = size(A, trans == 'N' ? 1 : 2)
|
| 1798 |
|
|
syrk!(uplo, trans, convert(T,alpha), A, zero(T), similar(A, T, (n, n)))
|
| 1799 |
|
|
end
|
| 1800 |
|
|
syrk(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat) = syrk(uplo, trans, one(eltype(A)), A)
|
| 1801 |
|
|
|
| 1802 |
|
|
"""
|
| 1803 |
|
|
herk!(uplo, trans, alpha, A, beta, C)
|
| 1804 |
|
|
|
| 1805 |
|
|
Methods for complex arrays only. Rank-k update of the Hermitian matrix `C` as
|
| 1806 |
|
|
`alpha*A*A' + beta*C` or `alpha*A'*A + beta*C` according to [`trans`](@ref stdlib-blas-trans).
|
| 1807 |
|
|
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is updated. Returns `C`.
|
| 1808 |
|
|
"""
|
| 1809 |
|
|
function herk! end
|
| 1810 |
|
|
|
| 1811 |
|
|
"""
|
| 1812 |
|
|
herk(uplo, trans, alpha, A)
|
| 1813 |
|
|
|
| 1814 |
|
|
Methods for complex arrays only. Returns the [`uplo`](@ref stdlib-blas-uplo)
|
| 1815 |
|
|
triangle of `alpha*A*A'` or `alpha*A'*A`, according to [`trans`](@ref stdlib-blas-trans).
|
| 1816 |
|
|
"""
|
| 1817 |
|
|
function herk end
|
| 1818 |
|
|
|
| 1819 |
|
|
for (fname, elty, relty) in ((:zherk_, :ComplexF64, :Float64),
|
| 1820 |
|
|
(:cherk_, :ComplexF32, :Float32))
|
| 1821 |
|
|
@eval begin
|
| 1822 |
|
|
# SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
|
| 1823 |
|
|
# * .. Scalar Arguments ..
|
| 1824 |
|
|
# REAL ALPHA,BETA
|
| 1825 |
|
|
# INTEGER K,LDA,LDC,N
|
| 1826 |
|
|
# CHARACTER TRANS,UPLO
|
| 1827 |
|
|
# * ..
|
| 1828 |
|
|
# * .. Array Arguments ..
|
| 1829 |
|
|
# COMPLEX A(LDA,*),C(LDC,*)
|
| 1830 |
|
|
function herk!(uplo::AbstractChar, trans::AbstractChar,
|
| 1831 |
|
|
ฮฑ::Union{$relty, Bool}, A::AbstractVecOrMat{$elty},
|
| 1832 |
|
|
ฮฒ::Union{$relty, Bool}, C::AbstractMatrix{$elty})
|
| 1833 |
|
|
chkuplo(uplo)
|
| 1834 |
|
|
require_one_based_indexing(A, C)
|
| 1835 |
|
|
n = checksquare(C)
|
| 1836 |
|
|
nn = size(A, trans == 'N' ? 1 : 2)
|
| 1837 |
|
|
if nn != n
|
| 1838 |
|
|
throw(DimensionMismatch(lazy"the matrix to update has dimension $n but the implied dimension of the update is $(size(A, trans == 'N' ? 1 : 2))"))
|
| 1839 |
|
|
end
|
| 1840 |
|
|
chkstride1(A)
|
| 1841 |
|
|
chkstride1(C)
|
| 1842 |
|
|
k = size(A, trans == 'N' ? 2 : 1)
|
| 1843 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1844 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 1845 |
|
|
Ref{$relty}, Ptr{$elty}, Ref{BlasInt}, Ref{$relty},
|
| 1846 |
|
|
Ptr{$elty}, Ref{BlasInt}, Clong, Clong),
|
| 1847 |
|
|
uplo, trans, n, k,
|
| 1848 |
|
|
ฮฑ, A, max(1,stride(A,2)), ฮฒ,
|
| 1849 |
|
|
C, max(1,stride(C,2)), 1, 1)
|
| 1850 |
|
|
C
|
| 1851 |
|
|
end
|
| 1852 |
|
|
function herk(uplo::AbstractChar, trans::AbstractChar, ฮฑ::$relty, A::AbstractVecOrMat{$elty})
|
| 1853 |
|
|
n = size(A, trans == 'N' ? 1 : 2)
|
| 1854 |
|
|
herk!(uplo, trans, ฮฑ, A, zero($relty), similar(A, (n,n)))
|
| 1855 |
|
|
end
|
| 1856 |
|
|
herk(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat{$elty}) = herk(uplo, trans, one($relty), A)
|
| 1857 |
|
|
end
|
| 1858 |
|
|
end
|
| 1859 |
|
|
|
| 1860 |
|
|
## syr2k
|
| 1861 |
|
|
for (fname, elty) in ((:dsyr2k_,:Float64),
|
| 1862 |
|
|
(:ssyr2k_,:Float32),
|
| 1863 |
|
|
(:zsyr2k_,:ComplexF64),
|
| 1864 |
|
|
(:csyr2k_,:ComplexF32))
|
| 1865 |
|
|
@eval begin
|
| 1866 |
|
|
# SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
| 1867 |
|
|
#
|
| 1868 |
|
|
# .. Scalar Arguments ..
|
| 1869 |
|
|
# REAL PRECISION ALPHA,BETA
|
| 1870 |
|
|
# INTEGER K,LDA,LDB,LDC,N
|
| 1871 |
|
|
# CHARACTER TRANS,UPLO
|
| 1872 |
|
|
# ..
|
| 1873 |
|
|
# .. Array Arguments ..
|
| 1874 |
|
|
# REAL PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
|
| 1875 |
|
|
function syr2k!(uplo::AbstractChar, trans::AbstractChar,
|
| 1876 |
|
|
alpha::($elty), A::AbstractVecOrMat{$elty}, B::AbstractVecOrMat{$elty},
|
| 1877 |
|
|
beta::($elty), C::AbstractMatrix{$elty})
|
| 1878 |
|
|
chkuplo(uplo)
|
| 1879 |
|
|
require_one_based_indexing(A, B, C)
|
| 1880 |
|
|
n = checksquare(C)
|
| 1881 |
|
|
nn = size(A, trans == 'N' ? 1 : 2)
|
| 1882 |
|
|
if nn != n throw(DimensionMismatch(lazy"C has size ($n,$n), corresponding dimension of A is $nn")) end
|
| 1883 |
|
|
k = size(A, trans == 'N' ? 2 : 1)
|
| 1884 |
|
|
chkstride1(A)
|
| 1885 |
|
|
chkstride1(B)
|
| 1886 |
|
|
chkstride1(C)
|
| 1887 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1888 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 1889 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
|
| 1890 |
|
|
Ptr{$elty}, Ref{BlasInt}, Clong, Clong),
|
| 1891 |
|
|
uplo, trans, n, k,
|
| 1892 |
|
|
alpha, A, max(1,stride(A,2)), B, max(1,stride(B,2)), beta,
|
| 1893 |
|
|
C, max(1,stride(C,2)), 1, 1)
|
| 1894 |
|
|
C
|
| 1895 |
|
|
end
|
| 1896 |
|
|
end
|
| 1897 |
|
|
end
|
| 1898 |
|
|
|
| 1899 |
|
|
"""
|
| 1900 |
|
|
syr2k!(uplo, trans, alpha, A, B, beta, C)
|
| 1901 |
|
|
|
| 1902 |
|
|
Rank-2k update of the symmetric matrix `C` as
|
| 1903 |
|
|
`alpha*A*transpose(B) + alpha*B*transpose(A) + beta*C` or
|
| 1904 |
|
|
`alpha*transpose(A)*B + alpha*transpose(B)*A + beta*C`
|
| 1905 |
|
|
according to [`trans`](@ref stdlib-blas-trans).
|
| 1906 |
|
|
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is used. Returns `C`.
|
| 1907 |
|
|
"""
|
| 1908 |
|
|
function syr2k! end
|
| 1909 |
|
|
|
| 1910 |
|
|
"""
|
| 1911 |
|
|
syr2k(uplo, trans, alpha, A, B)
|
| 1912 |
|
|
|
| 1913 |
|
|
Returns the [`uplo`](@ref stdlib-blas-uplo) triangle of
|
| 1914 |
|
|
`alpha*A*transpose(B) + alpha*B*transpose(A)` or
|
| 1915 |
|
|
`alpha*transpose(A)*B + alpha*transpose(B)*A`,
|
| 1916 |
|
|
according to [`trans`](@ref stdlib-blas-trans).
|
| 1917 |
|
|
"""
|
| 1918 |
|
|
function syr2k(uplo::AbstractChar, trans::AbstractChar, alpha::Number, A::AbstractVecOrMat, B::AbstractVecOrMat)
|
| 1919 |
|
|
T = eltype(A)
|
| 1920 |
|
|
n = size(A, trans == 'N' ? 1 : 2)
|
| 1921 |
|
|
syr2k!(uplo, trans, convert(T,alpha), A, B, zero(T), similar(A, T, (n, n)))
|
| 1922 |
|
|
end
|
| 1923 |
|
|
"""
|
| 1924 |
|
|
syr2k(uplo, trans, A, B)
|
| 1925 |
|
|
|
| 1926 |
|
|
Return the [`uplo`](@ref stdlib-blas-uplo) triangle of `A*transpose(B) + B*transpose(A)`
|
| 1927 |
|
|
or `transpose(A)*B + transpose(B)*A`, according to [`trans`](@ref stdlib-blas-trans).
|
| 1928 |
|
|
"""
|
| 1929 |
|
|
syr2k(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat, B::AbstractVecOrMat) = syr2k(uplo, trans, one(eltype(A)), A, B)
|
| 1930 |
|
|
|
| 1931 |
|
|
for (fname, elty1, elty2) in ((:zher2k_,:ComplexF64,:Float64), (:cher2k_,:ComplexF32,:Float32))
|
| 1932 |
|
|
@eval begin
|
| 1933 |
|
|
# SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
| 1934 |
|
|
#
|
| 1935 |
|
|
# .. Scalar Arguments ..
|
| 1936 |
|
|
# COMPLEX ALPHA
|
| 1937 |
|
|
# REAL BETA
|
| 1938 |
|
|
# INTEGER K,LDA,LDB,LDC,N
|
| 1939 |
|
|
# CHARACTER TRANS,UPLO
|
| 1940 |
|
|
# ..
|
| 1941 |
|
|
# .. Array Arguments ..
|
| 1942 |
|
|
# COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
|
| 1943 |
|
|
function her2k!(uplo::AbstractChar, trans::AbstractChar, alpha::($elty1),
|
| 1944 |
|
|
A::AbstractVecOrMat{$elty1}, B::AbstractVecOrMat{$elty1},
|
| 1945 |
|
|
beta::($elty2), C::AbstractMatrix{$elty1})
|
| 1946 |
|
|
chkuplo(uplo)
|
| 1947 |
|
|
require_one_based_indexing(A, B, C)
|
| 1948 |
|
|
n = checksquare(C)
|
| 1949 |
|
|
nn = size(A, trans == 'N' ? 1 : 2)
|
| 1950 |
|
|
if nn != n throw(DimensionMismatch(lazy"C has size ($n,$n), corresponding dimension of A is $nn")) end
|
| 1951 |
|
|
chkstride1(A)
|
| 1952 |
|
|
chkstride1(B)
|
| 1953 |
|
|
chkstride1(C)
|
| 1954 |
|
|
k = size(A, trans == 'N' ? 2 : 1)
|
| 1955 |
|
|
ccall((@blasfunc($fname), libblastrampoline), Cvoid,
|
| 1956 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 1957 |
|
|
Ref{$elty1}, Ptr{$elty1}, Ref{BlasInt}, Ptr{$elty1}, Ref{BlasInt},
|
| 1958 |
|
|
Ref{$elty2}, Ptr{$elty1}, Ref{BlasInt}, Clong, Clong),
|
| 1959 |
|
|
uplo, trans, n, k,
|
| 1960 |
|
|
alpha, A, max(1,stride(A,2)), B, max(1,stride(B,2)),
|
| 1961 |
|
|
beta, C, max(1,stride(C,2)), 1, 1)
|
| 1962 |
|
|
C
|
| 1963 |
|
|
end
|
| 1964 |
|
|
function her2k(uplo::AbstractChar, trans::AbstractChar, alpha::($elty1), A::AbstractVecOrMat{$elty1}, B::AbstractVecOrMat{$elty1})
|
| 1965 |
|
|
n = size(A, trans == 'N' ? 1 : 2)
|
| 1966 |
|
|
her2k!(uplo, trans, alpha, A, B, zero($elty2), similar(A, $elty1, (n,n)))
|
| 1967 |
|
|
end
|
| 1968 |
|
|
her2k(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat{$elty1}, B::AbstractVecOrMat{$elty1}) =
|
| 1969 |
|
|
her2k(uplo, trans, one($elty1), A, B)
|
| 1970 |
|
|
end
|
| 1971 |
|
|
end
|
| 1972 |
|
|
|
| 1973 |
|
|
"""
|
| 1974 |
|
|
her2k!(uplo, trans, alpha, A, B, beta, C)
|
| 1975 |
|
|
|
| 1976 |
|
|
Rank-2k update of the Hermitian matrix `C` as
|
| 1977 |
|
|
`alpha*A*B' + alpha*B*A' + beta*C` or `alpha*A'*B + alpha*B'*A + beta*C`
|
| 1978 |
|
|
according to [`trans`](@ref stdlib-blas-trans). The scalar `beta` has to be real.
|
| 1979 |
|
|
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is used. Return `C`.
|
| 1980 |
|
|
"""
|
| 1981 |
|
|
function her2k! end
|
| 1982 |
|
|
|
| 1983 |
|
|
"""
|
| 1984 |
|
|
her2k(uplo, trans, alpha, A, B)
|
| 1985 |
|
|
|
| 1986 |
|
|
Return the [`uplo`](@ref stdlib-blas-uplo) triangle of `alpha*A*B' + alpha*B*A'`
|
| 1987 |
|
|
or `alpha*A'*B + alpha*B'*A`, according to [`trans`](@ref stdlib-blas-trans).
|
| 1988 |
|
|
"""
|
| 1989 |
|
|
her2k(uplo, trans, alpha, A, B)
|
| 1990 |
|
|
|
| 1991 |
|
|
"""
|
| 1992 |
|
|
her2k(uplo, trans, A, B)
|
| 1993 |
|
|
|
| 1994 |
|
|
Return the [`uplo`](@ref stdlib-blas-uplo) triangle of `A*B' + B*A'`
|
| 1995 |
|
|
or `A'*B + B'*A`, according to [`trans`](@ref stdlib-blas-trans).
|
| 1996 |
|
|
"""
|
| 1997 |
|
|
her2k(uplo, trans, A, B)
|
| 1998 |
|
|
|
| 1999 |
|
|
## (TR) Triangular matrix and vector multiplication and solution
|
| 2000 |
|
|
|
| 2001 |
|
|
"""
|
| 2002 |
|
|
trmm!(side, ul, tA, dA, alpha, A, B)
|
| 2003 |
|
|
|
| 2004 |
|
|
Update `B` as `alpha*A*B` or one of the other three variants determined by
|
| 2005 |
|
|
[`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
|
| 2006 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 2007 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 2008 |
|
|
are assumed to be all ones.
|
| 2009 |
|
|
Return the updated `B`.
|
| 2010 |
|
|
"""
|
| 2011 |
|
|
function trmm! end
|
| 2012 |
|
|
|
| 2013 |
|
|
"""
|
| 2014 |
|
|
trmm(side, ul, tA, dA, alpha, A, B)
|
| 2015 |
|
|
|
| 2016 |
|
|
Return `alpha*A*B` or one of the other three variants determined by
|
| 2017 |
|
|
[`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
|
| 2018 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 2019 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 2020 |
|
|
are assumed to be all ones.
|
| 2021 |
|
|
"""
|
| 2022 |
|
|
function trmm end
|
| 2023 |
|
|
|
| 2024 |
|
|
"""
|
| 2025 |
|
|
trsm!(side, ul, tA, dA, alpha, A, B)
|
| 2026 |
|
|
|
| 2027 |
|
|
Overwrite `B` with the solution to `A*X = alpha*B` or one of the other three variants
|
| 2028 |
|
|
determined by [`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
|
| 2029 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 2030 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 2031 |
|
|
are assumed to be all ones.
|
| 2032 |
|
|
Returns the updated `B`.
|
| 2033 |
|
|
"""
|
| 2034 |
|
|
function trsm! end
|
| 2035 |
|
|
|
| 2036 |
|
|
"""
|
| 2037 |
|
|
trsm(side, ul, tA, dA, alpha, A, B)
|
| 2038 |
|
|
|
| 2039 |
|
|
Return the solution to `A*X = alpha*B` or one of the other three variants determined by
|
| 2040 |
|
|
determined by [`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
|
| 2041 |
|
|
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
|
| 2042 |
|
|
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
|
| 2043 |
|
|
are assumed to be all ones.
|
| 2044 |
|
|
"""
|
| 2045 |
|
|
function trsm end
|
| 2046 |
|
|
|
| 2047 |
|
|
for (mmname, smname, elty) in
|
| 2048 |
|
|
((:dtrmm_,:dtrsm_,:Float64),
|
| 2049 |
|
|
(:strmm_,:strsm_,:Float32),
|
| 2050 |
|
|
(:ztrmm_,:ztrsm_,:ComplexF64),
|
| 2051 |
|
|
(:ctrmm_,:ctrsm_,:ComplexF32))
|
| 2052 |
|
|
@eval begin
|
| 2053 |
|
|
# SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
|
| 2054 |
|
|
# * .. Scalar Arguments ..
|
| 2055 |
|
|
# DOUBLE PRECISION ALPHA
|
| 2056 |
|
|
# INTEGER LDA,LDB,M,N
|
| 2057 |
|
|
# CHARACTER DIAG,SIDE,TRANSA,UPLO
|
| 2058 |
|
|
# * .. Array Arguments ..
|
| 2059 |
|
|
# DOUBLE PRECISION A(LDA,*),B(LDB,*)
|
| 2060 |
|
|
function trmm!(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar, alpha::Number,
|
| 2061 |
|
|
A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 2062 |
|
|
chkuplo(uplo)
|
| 2063 |
|
|
require_one_based_indexing(A, B)
|
| 2064 |
|
|
m, n = size(B)
|
| 2065 |
|
|
nA = checksquare(A)
|
| 2066 |
|
|
if nA != (side == 'L' ? m : n)
|
| 2067 |
|
|
throw(DimensionMismatch(lazy"size of A, $(size(A)), doesn't match $side size of B with dims, $(size(B))"))
|
| 2068 |
|
|
end
|
| 2069 |
|
|
chkstride1(A)
|
| 2070 |
|
|
chkstride1(B)
|
| 2071 |
|
|
ccall((@blasfunc($mmname), libblastrampoline), Cvoid,
|
| 2072 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
|
| 2073 |
|
|
Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
|
| 2074 |
|
|
Clong, Clong, Clong, Clong),
|
| 2075 |
|
|
side, uplo, transa, diag, m, n,
|
| 2076 |
|
|
alpha, A, max(1,stride(A,2)), B, max(1,stride(B,2)),
|
| 2077 |
|
|
1, 1, 1, 1)
|
| 2078 |
|
|
B
|
| 2079 |
|
|
end
|
| 2080 |
|
|
function trmm(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar,
|
| 2081 |
|
|
alpha::$elty, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 2082 |
|
|
trmm!(side, uplo, transa, diag, alpha, A, copy(B))
|
| 2083 |
|
|
end
|
| 2084 |
|
|
# SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
|
| 2085 |
|
|
# * .. Scalar Arguments ..
|
| 2086 |
|
|
# DOUBLE PRECISION ALPHA
|
| 2087 |
|
|
# INTEGER LDA,LDB,M,N
|
| 2088 |
|
|
# CHARACTER DIAG,SIDE,TRANSA,UPLO
|
| 2089 |
|
|
# * .. Array Arguments ..
|
| 2090 |
|
|
# DOUBLE PRECISION A(LDA,*),B(LDB,*)
|
| 2091 |
|
|
function trsm!(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar,
|
| 2092 |
|
|
alpha::$elty, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 2093 |
|
|
chkuplo(uplo)
|
| 2094 |
|
|
require_one_based_indexing(A, B)
|
| 2095 |
|
|
m, n = size(B)
|
| 2096 |
|
|
k = checksquare(A)
|
| 2097 |
|
|
if k != (side == 'L' ? m : n)
|
| 2098 |
|
|
throw(DimensionMismatch(lazy"size of A is ($k,$k), size of B is ($m,$n), side is $side, and transa='$transa'"))
|
| 2099 |
|
|
end
|
| 2100 |
|
|
chkstride1(A)
|
| 2101 |
|
|
chkstride1(B)
|
| 2102 |
|
|
ccall((@blasfunc($smname), libblastrampoline), Cvoid,
|
| 2103 |
|
|
(Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{UInt8},
|
| 2104 |
|
|
Ref{BlasInt}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
|
| 2105 |
|
|
Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
|
| 2106 |
|
|
Clong, Clong, Clong, Clong),
|
| 2107 |
|
|
side, uplo, transa, diag,
|
| 2108 |
|
|
m, n, alpha, A,
|
| 2109 |
|
|
max(1,stride(A,2)), B, max(1,stride(B,2)),
|
| 2110 |
|
|
1, 1, 1, 1)
|
| 2111 |
|
|
B
|
| 2112 |
|
|
end
|
| 2113 |
|
|
function trsm(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar, alpha::$elty, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
|
| 2114 |
|
|
trsm!(side, uplo, transa, diag, alpha, A, copy(B))
|
| 2115 |
|
|
end
|
| 2116 |
|
|
end
|
| 2117 |
|
|
end
|
| 2118 |
|
|
|
| 2119 |
|
|
end # module
|
| 2120 |
|
|
|
| 2121 |
|
|
function copyto!(dest::Array{T}, rdest::AbstractRange{Ti},
|
| 2122 |
|
|
src::Array{T}, rsrc::AbstractRange{Ti}) where {T<:BlasFloat,Ti<:Integer}
|
| 2123 |
|
|
if minimum(rdest) < 1 || maximum(rdest) > length(dest)
|
| 2124 |
|
|
throw(ArgumentError(lazy"range out of bounds for dest, of length $(length(dest))"))
|
| 2125 |
|
|
end
|
| 2126 |
|
|
if minimum(rsrc) < 1 || maximum(rsrc) > length(src)
|
| 2127 |
|
|
throw(ArgumentError(lazy"range out of bounds for src, of length $(length(src))"))
|
| 2128 |
|
|
end
|
| 2129 |
|
|
if length(rdest) != length(rsrc)
|
| 2130 |
|
|
throw(DimensionMismatch(lazy"ranges must be of the same length"))
|
| 2131 |
|
|
end
|
| 2132 |
|
|
GC.@preserve src dest BLAS.blascopy!(
|
| 2133 |
|
|
length(rsrc),
|
| 2134 |
|
|
pointer(src, minimum(rsrc)),
|
| 2135 |
|
|
step(rsrc),
|
| 2136 |
|
|
pointer(dest, minimum(rdest)),
|
| 2137 |
|
|
step(rdest))
|
| 2138 |
|
|
|
| 2139 |
|
|
return dest
|
| 2140 |
|
|
end
|