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Fix of det for singular matrices etc. #1499

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Merged
ViralBShah merged 1 commit into from
Nov 4, 2012
Merged

Fix of det for singular matrices etc. #1499

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22 changes: 11 additions & 11 deletions base/lapack.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -327,13 +327,13 @@ for (gebrd, gelqf, geqlf, geqrf, geqp3, gerqf, getrf, elty) in
info = Array(Int32, 1)
m, n = size(A)
lda = stride(A, 2)
ipiv = Array(Int32, n)
ipiv = Array(Int32, min(m,n))
ccall(dlsym(Base.liblapack, $(string(getrf))), Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{$elty},
Ptr{Int32}, Ptr{Int32}, Ptr{Int32}),
&m, &n, A, &lda, ipiv, info)
if info[1] != 0 throw(LapackException(info[1])) end
A, ipiv
if info[1] < 0 throw(LapackException(info[1])) end
A, ipiv, info[1]
end
end
end
Expand Down Expand Up @@ -392,8 +392,8 @@ for (gels, gesv, getrs, getri, elty) in
(Ptr{Int32}, Ptr{Int32}, Ptr{$elty}, Ptr{Int32}, Ptr{Int32},
Ptr{$elty}, Ptr{Int32}, Ptr{Int32}),
&n, &size(B,2), A, &stride(A,2), ipiv, B, &stride(B,2), info)
if info[1] != 0 throw(LapackException(info[1])) end
A, ipiv, B
if info[1] < 0 throw(LapackException(info[1])) end
B, A, ipiv, info[1]
end
# SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
#* .. Scalar Arguments ..
Expand Down Expand Up @@ -1096,8 +1096,8 @@ for (trtri, trtrs, elty) in
(Ptr{Uint8}, Ptr{Uint8}, Ptr{Int32}, Ptr{$elty}, Ptr{Int32},
Ptr{Int32}),
&uplo, &diag, &n, A, &lda, info)
if info[1] != 0 error("trtri!: error $(info[1])") end
A
if info[1] < 0 error("trtri!: error $(info[1])") end
A, info[1]
end
# SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO )
# * .. Scalar Arguments ..
Expand All @@ -1117,8 +1117,8 @@ for (trtri, trtrs, elty) in
Ptr{$elty}, Ptr{Int32}, Ptr{$elty}, Ptr{Int32}, Ptr{Int32}),
&uplo, &trans, &diag, &n, &size(B,2), A, &stride(A,2),
B, &stride(B,2), info)
if info[1] != 0 throw(LapackException(info[1])) end
B
if info[1] < 0 throw(LapackException(info[1])) end
B, info[1]
end
end
end
Expand Down Expand Up @@ -1237,13 +1237,13 @@ for (syconv, syev, sysv, sytrf, sytri, sytrs, elty) in
Ptr{$elty}, Ptr{Int32}, Ptr{$elty}, Ptr{Int32}, Ptr{Int32}),
&uplo, &n, &size(B,2), A, &stride(A,2), ipiv, B, &stride(B,2),
work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if info[1] < 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = int32(real(work[1]))
work = Array($elty, lwork)
end
end
B, A, ipiv
B, A, ipiv, info[1]
end
# SUBROUTINE DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
Expand Down
59 changes: 44 additions & 15 deletions base/linalg_dense.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -455,9 +455,10 @@ cholpd{T<:LapackType}(A::Matrix{T}) = cholpd!(copy(A), true, -1.)
type LUDense{T} <: Factorization{T}
lu::Matrix{T}
ipiv::Vector{Int32}
function LUDense(lu::Matrix{T}, ipiv::Vector{Int32})
info::Int32
function LUDense(lu::Matrix{T}, ipiv::Vector{Int32}, info::Int32)
m, n = size(lu)
m == numel(ipiv) ? new(lu, ipiv) : error("LUDense: dimension mismatch")
m == n ? new(lu, ipiv, info) : error("LUDense only defined for square matrices")
end
end

Expand All @@ -480,8 +481,8 @@ function factors{T<:LapackType}(lu::LUDense{T})
end

function lud!{T<:LapackType}(A::Matrix{T})
lu, ipiv = Lapack.getrf!(A)
LUDense{T}(lu, ipiv)
lu, ipiv, info = Lapack.getrf!(A)
LUDense{T}(lu, ipiv, info)
end

lud{T<:LapackType}(A::Matrix{T}) = lud!(copy(A))
Expand All @@ -491,17 +492,28 @@ lud{T<:Number}(A::Matrix{T}) = lud(float64(A))
lu{T<:Number}(A::Matrix{T}) = factors(lud(A))

function det(lu::LUDense)
m, n = size(lu.lu)
if m != n error("det only defined for square matrices") end
if lu.info > 0; return zero(typeof(lu.lu[1])); end
prod(diag(lu.lu)) * (bool(sum(lu.ipiv .!= 1:n) % 2) ? -1 : 1)
end

det(A::Matrix) = det(lud(A))
function det(A::Matrix)
m, n = size(A)
if m != n; error("det only defined for square matrices"); end
if istriu(A) | istril(A); return prod(diag(A)); end
return det(lud(A))
end

(\){T<:LapackType}(lu::LUDense{T}, B::StridedVecOrMat{T}) =
function (\){T<:LapackType}(lu::LUDense{T}, B::StridedVecOrMat{T})
if lu.info > 0; error("Singular system"); end
Lapack.getrs!('N', lu.lu, lu.ipiv, copy(B))
end

inv{T<:LapackType}(lu::LUDense{T}) = Lapack.getri!(copy(lu.lu), lu.ipiv)
function inv{T<:LapackType}(lu::LUDense{T})
m, n = size(lu.lu)
if m != n; error("inv only defined for square matrices"); end
if lu.info > 0; return error("Singular system"); end
Lapack.getri!(copy(lu.lu), lu.ipiv)
end

## QR decomposition without column pivots
type QRDense{T} <: Factorization{T}
Expand Down Expand Up @@ -537,7 +549,9 @@ Ac_mul_B{T<:LapackType}(A::QRDense{T}, B::StridedVecOrMat{T}) =
## Least squares solution. Should be more careful about cases with m < n
function (\){T<:LapackType}(A::QRDense{T}, B::StridedVecOrMat{T})
n = length(A.tau)
Lapack.trtrs!('U','N','N',A.hh[1:n,:],(A'*B)[1:n,:])
ans, info = Lapack.trtrs!('U','N','N',A.hh[1:n,:],(A'*B)[1:n,:])
if info > 0; error("Singular system"); end
return ans
end

type QRPDense{T} <: Factorization{T}
Expand Down Expand Up @@ -576,7 +590,8 @@ qrp{T<:Real}(x::StridedMatrix{T}) = qrp(float64(x))

function (\){T<:LapackType}(A::QRPDense{T}, B::StridedVecOrMat{T})
n = length(A.tau)
x = Lapack.trtrs!('U','N','N',A.hh[1:n,:],(A'*B)[1:n,:])
x, info = Lapack.trtrs!('U','N','N',A.hh[1:n,:],(A'*B)[1:n,:])
if info > 0; error("Singular system"); end
isa(B, Vector) ? x[invperm(A.jpvt)] : x[:,invperm(A.jpvt)]
end

Expand Down Expand Up @@ -659,10 +674,24 @@ function (\){T<:LapackType}(A::StridedMatrix{T}, B::StridedVecOrMat{T})
X = copy(B)

if m == n # Square
if istriu(A) return Lapack.trtrs!('U', 'N', 'N', Acopy, X) end
if istril(A) return Lapack.trtrs!('L', 'N', 'N', Acopy, X) end
if ishermitian(A) return Lapack.sysv!('U', Acopy, X)[1] end
return Lapack.gesv!(Acopy, X)[3]
if istriu(A)
ans, info = Lapack.trtrs!('U', 'N', 'N', Acopy, X)
if info > 0; error("Singular system"); end
return ans
end
if istril(A)
ans, info = Lapack.trtrs!('L', 'N', 'N', Acopy, X)
if info > 0; error("Singular system"); end
return ans
end
if ishermitian(A)
ans, ~, ~, info = Lapack.sysv!('U', Acopy, X)
if info > 0; error("Singular system"); end
return ans
end
ans, ~, ~, info = Lapack.gesv!(Acopy, X)
if info > 0; error("Singular system"); end
return ans
end
Lapack.gelsd!(Acopy, X)[1]
end
Expand Down