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|
!%f90 -*- f90 -*-
! Signatures for f2py wrappers of FORTRAN LAPACK functions.
!
! Author: Pearu Peterson
! Created: Jan-Feb 2002
! $Revision: 1.10 $ $Date: 2004/10/04 00:49:04 $
!
! Additions by Travis Oliphant
!
! Usage:
! f2py -c flapack.pyf -L/usr/local/lib/atlas -llapack -lf77blas -lcblas -latlas -lg2c
python module generic_flapack
interface
subroutine <tchar=s,d,c,z>gebal(scale,permute,n,a,m,lo,hi,pivscale,info)
!
! ba,lo,hi,pivscale,info = gebal(a,scale=0,permute=0,overwrite_a=0)
! Balance general matrix a.
! hi,lo are such that ba[i][j]==0 if i>j and j=0...lo-1 or i=hi+1..n-1
! pivscale([0:lo], [lo:hi+1], [hi:n+1]) = (p1,d,p2) where (p1,p2)[j] is
! the index of the row and column interchanged with row and column j.
! d[j] is the scaling factor applied to row and column j.
! The order in which the interchanges are made is n-1 to hi+1, then 0 to lo-1.
!
! P * A * P = [[T1,X,Y],[0,B,Z],[0,0,T2]]
! BA = [[T1,X*D,Y],[0,inv(D)*B*D,ind(D)*Z],[0,0,T2]]
! where D = diag(d), T1,T2 are upper triangular matrices.
! lo,hi mark the starting and ending columns of submatrix B.
callstatement { (*f2py_func)((permute?(scale?"B":"P"):(scale?"S":"N")),&n,a,&m,&lo,&hi,pivscale,&info); hi--; lo--; }
callprotoargument char*,int*,<type_in_c>*,int*,int*,int*,<rtype_in_c>*,int*
integer intent(in),optional :: permute = 0
integer intent(in),optional :: scale = 0
integer intent(hide),depend(a,n) :: m = shape(a,0)
integer intent(hide),depend(a) :: n = shape(a,1)
check(m>=n) m
integer intent(out) :: hi,lo
<rtype_in> dimension(n),intent(out),depend(n) :: pivscale
<type_in> dimension(m,n),intent(in,out,copy,out=ba) :: a
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>gebal
subroutine <tchar=s,d,c,z>gehrd(n,lo,hi,a,tau,work,lwork,info)
!
! hq,tau,info = gehrd(a,lo=0,hi=n-1,lwork=n,overwrite_a=0)
! Reduce general matrix A to upper Hessenberg form H by unitary similarity
! transform Q^H * A * Q = H
!
! Q = H(lo) * H(lo+1) * ... * H(hi-1)
! H(i) = I - tau * v * v^H
! v[0:i+1] = 0, v[i+1]=1, v[hi+1:n] = 0
! v[i+2:hi+1] is stored in hq[i+2:hi+i,i]
! tau is tau[i]
!
! hq for n=7,lo=1,hi=5:
! [a a h h h h a
! a h h h h a
! h h h h h h
! v2h h h h h
! v2v3h h h h
! v2v3v4h h h
! a]
!
callstatement { hi++; lo++; (*f2py_func)(&n,&lo,&hi,a,&n,tau,work,&lwork,&info); }
callprotoargument int*,int*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,int*,int*
integer intent(hide),depend(a) :: n = shape(a,0)
<type_in> dimension(n,n),intent(in,out,copy,out=ht),check(shape(a,0)==shape(a,1)) :: a
integer intent(in),optional :: lo = 0
integer intent(in),optional,depend(n) :: hi = n-1
<type_in> dimension(n-1),intent(out),depend(n) :: tau
<type_in> dimension(lwork),intent(cahce,hide),depend(lwork) :: work
integer intent(in),optional,depend(n),check(lwork>=MAX(n,1)) :: lwork = MAX(n,1)
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>gehrd
subroutine <tchar=s,d,c,z>gbsv(n,kl,ku,nrhs,ab,piv,b,info)
!
! lub,piv,x,info = gbsv(kl,ku,ab,b,overwrite_ab=0,overwrite_b=0)
! Solve A * X = B
! A = P * L * U
! A is a band matrix of order n with kl subdiagonals and ku superdiagonals
! starting at kl-th row.
! X, B are n-by-nrhs matrices
!
callstatement {int i=2*kl+ku+1;(*f2py_func)(&n,&kl,&ku,&nrhs,ab,&i,piv,b,&n,&info);for(i=0;i<n;--piv[i++]);}
callprotoargument int*,int*,int*,int*,<type_in_c>*,int*,int*,<type_in_c>*,int*,int*
integer depend(ab),intent(hide):: n = shape(ab,1)
integer intent(in) :: kl
integer intent(in) :: ku
integer depend(b),intent(hide) :: nrhs = shape(b,1)
<type_in> dimension(2*kl+ku+1,n),depend(kl,ku), check(2*kl+ku+1==shape(ab,0)) :: ab
integer dimension(n),depend(n),intent(out) :: piv
<type_in> dimension(n,nrhs),depend(n),check(shape(ab,1)==shape(b,0)) :: b
integer intent(out) :: info
intent(in,out,copy,out=x) b
intent(in,out,copy,out=lub) ab
end subroutine <tchar=s,d,c,z>gbsv
subroutine <tchar=s,d,c,z>gesv(n,nrhs,a,piv,b,info)
! lu,piv,x,info = gesv(a,b,overwrite_a=0,overwrite_b=0)
! Solve A * X = B.
! A = P * L * U
! U is upper diagonal triangular, L is unit lower triangular,
! piv pivots columns.
callstatement {int i;(*f2py_func)(&n,&nrhs,a,&n,piv,b,&n,&info);for(i=0;i<n;--piv[i++]);}
callprotoargument int*,int*,<type_in_c>*,int*,int*,<type_in_c>*,int*,int*
integer depend(a),intent(hide):: n = shape(a,0)
integer depend(b),intent(hide):: nrhs = shape(b,1)
<type_in> dimension(n,n),check(shape(a,0)==shape(a,1)) :: a
integer dimension(n),depend(n),intent(out) :: piv
<type_in> dimension(n,nrhs),check(shape(a,0)==shape(b,0)),depend(n) :: b
integer intent(out)::info
intent(in,out,copy,out=x) b
intent(in,out,copy,out=lu) a
end subroutine <tchar=s,d,c,z>gesv
subroutine <tchar=s,d,c,z>getrf(m,n,a,piv,info)
! lu,piv,info = getrf(a,overwrite_a=0)
! Compute an LU factorization of a general M-by-N matrix A.
! A = P * L * U
threadsafe
callstatement {int i;(*f2py_func)(&m,&n,a,&m,piv,&info);for(i=0,n=MIN(m,n);i<n;--piv[i++]);}
callprotoargument int*,int*,<type_in_c>*,int*,int*,int*
integer depend(a),intent(hide):: m = shape(a,0)
integer depend(a),intent(hide):: n = shape(a,1)
<type_in> dimension(m,n),intent(in,out,copy,out=lu) :: a
integer dimension(MIN(m,n)),depend(m,n),intent(out) :: piv
integer intent(out):: info
end subroutine <tchar=s,d,c,z>getrf
subroutine <tchar=s,d,c,z>getrs(n,nrhs,lu,piv,b,info,trans)
! x,info = getrs(lu,piv,b,trans=0,overwrite_b=0)
! Solve A * X = B if trans=0
! Solve A^T * X = B if trans=1
! Solve A^H * X = B if trans=2
! A = P * L * U
threadsafe
callstatement {int i;for(i=0;i<n;++piv[i++]);(*f2py_func)((trans?(trans==2?"C":"T"):"N"),&n,&nrhs,lu,&n,piv,b,&n,&info);for(i=0;i<n;--piv[i++]);}
callprotoargument char*,int*,int*,<type_in_c>*,int*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(trans>=0 && trans <=2) :: trans = 0
integer depend(lu),intent(hide):: n = shape(lu,0)
integer depend(b),intent(hide):: nrhs = shape(b,1)
<type_in> dimension(n,n),intent(in) :: lu
check(shape(lu,0)==shape(lu,1)) :: lu
integer dimension(n),intent(in),depend(n) :: piv
<type_in> dimension(n,nrhs),intent(in,out,copy,out=x),depend(n),check(shape(lu,0)==shape(b,0)) :: b
integer intent(out):: info
end subroutine <tchar=s,d,c,z>getrs
subroutine <tchar=s,d,c,z>getri(n,lu,piv,work,lwork,info)
! inv_a,info = getri(lu,piv,lwork=3*n,overwrite_lu=0)
! Find A inverse A^-1.
! A = P * L * U
callstatement {int i;for(i=0;i<n;++piv[i++]);(*f2py_func)(&n,lu,&n,piv,work,&lwork,&info);for(i=0;i<n;--piv[i++]);}
callprotoargument int*,<type_in_c>*,int*,int*,<type_in_c>*,int*,int*
integer depend(lu),intent(hide):: n = shape(lu,0)
<type_in> dimension(n,n),intent(in,out,copy,out=inv_a) :: lu
check(shape(lu,0)==shape(lu,1)) :: lu
integer dimension(n),intent(in),depend(n) :: piv
integer intent(out):: info
integer optional,intent(in),depend(n),check(lwork>=n) :: lwork=3*n
<type_in> dimension(lwork),intent(hide,cache),depend(lwork) :: work
end subroutine <tchar=s,d,c,z>getri
subroutine <tchar=s,d>gesdd(m,n,minmn,du,dvt,a,compute_uv,u,s,vt,work,lwork,iwork,info)
! u,s,vt,info = gesdd(a,compute_uv=1,lwork=..,overwrite_a=0)
! Compute the singular value decomposition (SVD):
! A = U * SIGMA * transpose(V)
! A - M x N matrix
! U - M x M matrix
! SIGMA - M x N zero matrix with a main diagonal filled with min(M,N)
! singular values
! transpose(V) - N x N matrix
callstatement (*f2py_func)((compute_uv?"A":"N"),&m,&n,a,&m,s,u,&du,vt,&dvt,work,&lwork,iwork,&info)
callprotoargument char*,int*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,int*,int*
integer intent(in),optional,check(compute_uv==0||compute_uv==1):: compute_uv = 1
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(m,n):: minmn = MIN(m,n)
integer intent(hide),depend(compute_uv,minmn) :: du = (compute_uv?m:1)
integer intent(hide),depend(compute_uv,n) :: dvt = (compute_uv?n:1)
<type_in> dimension(m,n),intent(in,copy) :: a
<type_in> dimension(minmn),intent(out),depend(minmn) :: s
<type_in> dimension(du,du),intent(out),depend(du) :: u
<type_in> dimension(dvt,dvt),intent(out),depend(dvt) :: vt
<type_in> dimension(lwork),intent(hide,cache),depend(lwork) :: work
integer optional,intent(in),depend(minmn,compute_uv) &
:: lwork = (compute_uv?4*minmn*minmn+MAX(m,n)+9*minmn:MAX(14*minmn+4,10*minmn+2+25*(25+8))+MAX(m,n))
! gesdd docs are mess: optimal turns out to be less than minimal in docs
! check(lwork>=(compute_uv?3*minmn*minmn+MAX(MAX(m,n),4*minmn*(minmn+1)):MAX(14*minmn+4,10*minmn+2+25*(25+8))+MAX(m,n))) :: lwork
integer intent(hide,cache),dimension(8*minmn),depend(minmn) :: iwork
integer intent(out)::info
end subroutine <tchar=s,d>gesdd
subroutine <tchar=c,z>gesdd(m,n,minmn,du,dvt,a,compute_uv,u,s,vt,work,rwork,lwork,iwork,info)
! u,s,vt,info = gesdd(a,compute_uv=1,lwork=..,overwrite_a=0)
! Compute the singular value decomposition (SVD):
! A = U * SIGMA * conjugate-transpose(V)
! A - M x N matrix
! U - M x M matrix
! SIGMA - M x N zero matrix with a main diagonal filled with min(M,N)
! singular values
! conjugate-transpose(V) - N x N matrix
callstatement (*f2py_func)((compute_uv?"A":"N"),&m,&n,a,&m,s,u,&du,vt,&dvt,work,&lwork,rwork,iwork,&info)
callprotoargument char*,int*,int*,<type_in_c>*,int*,<rtype_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<rtype_in_c>*,int*,int*
integer intent(in),optional,check(compute_uv==0||compute_uv==1):: compute_uv = 1
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(m,n):: minmn = MIN(m,n)
integer intent(hide),depend(compute_uv,minmn) :: du = (compute_uv?m:1)
integer intent(hide),depend(compute_uv,n) :: dvt = (compute_uv?n:1)
<type_in> dimension(m,n),intent(in,copy) :: a
<rtype_in> dimension(minmn),intent(out),depend(minmn) :: s
<type_in> dimension(du,du),intent(out),depend(du) :: u
<type_in> dimension(dvt,dvt),intent(out),depend(dvt) :: vt
<type_in> dimension(lwork),intent(hide,cache),depend(lwork) :: work
<rtype_in> dimension((compute_uv?5*minmn*minmn+7*minmn:5*minmn)),intent(hide,cache),depend(minmn,compute_uv) :: rwork
integer optional,intent(in),depend(minmn,compute_uv) &
:: lwork = (compute_uv?2*minmn*minmn+MAX(m,n)+2*minmn:2*minmn+MAX(m,n))
check(lwork>=(compute_uv?2*minmn*minmn+MAX(m,n)+2*minmn:2*minmn+MAX(m,n))) :: lwork
integer intent(hide,cache),dimension(8*minmn),depend(minmn) :: iwork
integer intent(out)::info
end subroutine <tchar=c,z>gesdd
subroutine <tchar=s,d>gelss(m,n,minmn,maxmn,nrhs,a,b,s,cond,r,work,lwork,info)
! v,x,s,rank,info = gelss(a,b,cond=-1.0,overwrite_a=0,overwrite_b=0)
! Solve Minimize 2-norm(A * X - B).
callstatement (*f2py_func)(&m,&n,&nrhs,a,&m,b,&maxmn,s,&cond,&r,work,&lwork,&info)
callprotoargument int*,int*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(m,n):: minmn = MIN(m,n)
integer intent(hide),depend(m,n):: maxmn = MAX(m,n)
<type_in> dimension(m,n),intent(in,out,copy,out=v) :: a
integer depend(b),intent(hide):: nrhs = shape(b,1)
<type_in> dimension(maxmn,nrhs),check(maxmn==shape(b,0)),depend(maxmn) :: b
intent(in,out,copy,out=x) b
integer intent(out)::info
integer optional,intent(in),depend(nrhs,minmn,maxmn), &
check(lwork>=1) &
:: lwork=3*minmn+MAX(2*minmn,MAX(maxmn,nrhs))
!check(lwork>=3*minmn+MAX(2*minmn,MAX(maxmn,nrhs)))
<type_in> dimension(lwork),intent(hide),depend(lwork) :: work
<type_in> intent(in),optional :: cond = -1.0
integer intent(out,out=rank) :: r
<type_in> intent(out),dimension(minmn),depend(minmn) :: s
end subroutine <tchar=s,d>gelss
subroutine <tchar=c,z>gelss(m,n,minmn,maxmn,nrhs,a,b,s,cond,r,work,rwork,lwork,info)
! v,x,s,rank,info = gelss(a,b,cond=-1.0,overwrite_a=0,overwrite_b=0)
! Solve Minimize 2-norm(A * X - B).
callstatement (*f2py_func)(&m,&n,&nrhs,a,&m,b,&maxmn,s,&cond,&r,work,&lwork,rwork,&info)
callprotoargument int*,int*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<rtype_in_c>*,<rtype_in_c>*,int*,<type_in_c>*,int*,<rtype_in_c>*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(m,n):: minmn = MIN(m,n)
integer intent(hide),depend(m,n):: maxmn = MAX(m,n)
<type_in> dimension(m,n),intent(in,out,copy,out=v) :: a
integer depend(b),intent(hide):: nrhs = shape(b,1)
<type_in> dimension(maxmn,nrhs),check(maxmn==shape(b,0)),depend(maxmn) :: b
intent(in,out,copy,out=x) b
integer intent(out)::info
integer optional,intent(in),depend(nrhs,minmn,maxmn), &
check(lwork>=1) &
:: lwork=2*minmn+MAX(maxmn,nrhs)
! check(lwork>=2*minmn+MAX(maxmn,nrhs))
<type_in> dimension(lwork),intent(hide),depend(lwork) :: work
<rtype_in> dimension(5*minmn-1),intent(hide),depend(lwork) :: rwork
<rtype_in> intent(in),optional :: cond = -1.0
integer intent(out,out=rank) :: r
<rtype_in> intent(out),dimension(minmn),depend(minmn) :: s
end subroutine <tchar=c,z>gelss
subroutine <tchar=s,d,c,z>geqrf(m,n,a,tau,work,lwork,info)
! qr_a,tau,work,info = geqrf(a,lwork=3*n,overwrite_a=0)
! Compute a QR factorization of a real M-by-N matrix A:
! A = Q * R.
callstatement (*f2py_func)(&m,&n,a,&m,tau,work,&lwork,&info)
callprotoargument int*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
<type_in> dimension(m,n),intent(in,out,copy,out=qr) :: a
<type_in> dimension(MIN(m,n)),intent(out) :: tau
integer optional,intent(in),depend(n),check(lwork>=n||lwork==-1) :: lwork=3*n
<type_in> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>geqrf
subroutine <tchar=s,d>geev(compute_vl,compute_vr,n,a,wr,wi,vl,ldvl,vr,ldvr,work,lwork,info)
! wr,wi,vl,vr,info = geev(a,compute_vl=1,compute_vr=1,lwork=4*n,overwrite_a=0)
callstatement {(*f2py_func)((compute_vl?"V":"N"),(compute_vr?"V":"N"),&n,a,&n,wr,wi,vl,&ldvl,vr,&ldvr,work,&lwork,&info);}
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,int*
integer optional,intent(in):: compute_vl = 1
check(compute_vl==1||compute_vl==0) compute_vl
integer optional,intent(in):: compute_vr = 1
check(compute_vr==1||compute_vr==0) compute_vr
integer intent(hide),depend(a) :: n = shape(a,0)
<type_in> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<type_in> dimension(n),intent(out),depend(n) :: wr
<type_in> dimension(n),intent(out),depend(n) :: wi
<type_in> dimension(ldvl,n),intent(out) :: vl
integer intent(hide),depend(n,compute_vl) :: ldvl=(compute_vl?n:1)
<type_in> dimension(ldvr,n),intent(out) :: vr
integer intent(hide),depend(n,compute_vr) :: ldvr=(compute_vr?n:1)
integer optional,intent(in),depend(n,compute_vl,compute_vr) :: lwork=4*n
check(lwork>=((compute_vl||compute_vr)?4*n:3*n)) :: lwork
<type_in> dimension(lwork),intent(hide,cache),depend(lwork) :: work
integer intent(out):: info
end subroutine <tchar=s,d>geev
subroutine <tchar=c,z>geev(compute_vl,compute_vr,n,a,w,vl,ldvl,vr,ldvr,work,lwork,rwork,info)
! w,vl,vr,info = geev(a,compute_vl=1,compute_vr=1,lwork=2*n,overwrite_a=0)
callstatement (*f2py_func)((compute_vl?"V":"N"),(compute_vr?"V":"N"),&n,a,&n,w,vl,&ldvl,vr,&ldvr,work,&lwork,rwork,&info)
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<rtype_in_c>*,int*
integer optional,intent(in):: compute_vl = 1
check(compute_vl==1||compute_vl==0) compute_vl
integer optional,intent(in):: compute_vr = 1
check(compute_vr==1||compute_vr==0) compute_vr
integer intent(hide),depend(a) :: n = shape(a,0)
<type_in> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<type_in> dimension(n),intent(out),depend(n) :: w
<type_in> dimension(ldvl,n),depend(ldvl),intent(out) :: vl
integer intent(hide),depend(compute_vl,n) :: ldvl=(compute_vl?n:1)
<type_in> dimension(ldvr,n),depend(ldvr),intent(out) :: vr
integer intent(hide),depend(compute_vr,n) :: ldvr=(compute_vr?n:1)
integer optional,intent(in),depend(n) :: lwork=2*n
check(lwork>=2*n) :: lwork
<type_in> dimension(lwork),intent(hide),depend(lwork) :: work
<rtype_in> dimension(2*n),intent(hide,cache),depend(n) :: rwork
integer intent(out):: info
end subroutine <tchar=c,z>geev
subroutine <tchar=s,d>gegv(compute_vl,compute_vr,n,a,b,alphar,alphai,beta,vl,ldvl,vr,ldvr,work,lwork,info)
! Compute the generalized eigenvalues (alphar +/- alphai*i, beta)
! of the real nonsymmetric matrices A and B: det(A-w*B)=0 where w=alpha/beta.
! Optionally, compute the left and/or right generalized eigenvectors:
! (A - w B) r = 0, l^H * (A - w B) = 0
!
! alphar,alphai,beta,vl,vr,info = gegv(a,b,compute_vl=1,compute_vr=1,lwork=8*n,overwrite_a=0,overwrite_b=0)
callstatement (*f2py_func)((compute_vl?"V":"N"),(compute_vr?"V":"N"),&n,a,&n,b,&n,alphar,alphai,beta,vl,&ldvl,vr,&ldvr,work,&lwork,&info)
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,int*
integer optional,intent(in):: compute_vl = 1
check(compute_vl==1||compute_vl==0) compute_vl
integer optional,intent(in):: compute_vr = 1
check(compute_vr==1||compute_vr==0) compute_vr
integer intent(hide),depend(a) :: n = shape(a,0)
<type_in> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<type_in> dimension(n,n),depend(n),intent(in,copy) :: b
check(shape(b,0)==shape(b,1) && shape(b,0)==n) :: b
<type_in> dimension(n),depend(n),intent(out) :: alphar
<type_in> dimension(n),depend(n),intent(out) :: alphai
<type_in> dimension(n),depend(n),intent(out) :: beta
<type_in> dimension(ldvl,n),intent(out),depend(ldvl) :: vl
integer intent(hide),depend(compute_vl,n) :: ldvl=(compute_vl?n:1)
<type_in> dimension(ldvr,n),intent(out),depend(ldvr) :: vr
integer intent(hide),depend(compute_vr,n) :: ldvr=(compute_vr?n:1)
integer optional,intent(in),depend(n) :: lwork=8*n
check(lwork>=8*n) :: lwork
<type_in> dimension(lwork),intent(hide),depend(lwork) :: work
integer intent(out):: info
end subroutine <tchar=s,d>gegv
subroutine <tchar=c,z>gegv(compute_vl,compute_vr,n,a,b,alpha,beta,vl,ldvl,vr,ldvr,work,lwork,rwork,info)
! Compute the generalized eigenvalues (alpha, beta)
! of the comples nonsymmetric matrices A and B: det(A-w*B)=0 where w=alpha/beta.
! Optionally, compute the left and/or right generalized eigenvectors:
! (A - w B) r = 0, l^H * (A - w B) = 0
!
! alpha,beta,vl,vr,info = gegv(a,b,compute_vl=1,compute_vr=1,lwork=2*n,overwrite_a=0,overwrite_b=0)
callstatement (*f2py_func)((compute_vl?"V":"N"),(compute_vr?"V":"N"),&n,a,&n,b,&n,alpha,beta,vl,&ldvl,vr,&ldvr,work,&lwork,rwork,&info)
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<rtype_in_c>*,int*
integer optional,intent(in):: compute_vl = 1
check(compute_vl==1||compute_vl==0) compute_vl
integer optional,intent(in):: compute_vr = 1
check(compute_vr==1||compute_vr==0) compute_vr
integer intent(hide),depend(a) :: n = shape(a,0)
<type_in> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<type_in> dimension(n,n),depend(n),intent(in,copy) :: b
check(shape(b,0)==shape(b,1) && shape(b,0)==n) :: b
<type_in> dimension(n),depend(n),intent(out) :: alpha
<type_in> dimension(n),depend(n),intent(out) :: beta
<type_in> dimension(ldvl,n),intent(out),depend(ldvl) :: vl
integer intent(hide),depend(compute_vl,n) :: ldvl=(compute_vl?n:1)
<type_in> dimension(ldvr,n),intent(out),depend(ldvr) :: vr
integer intent(hide),depend(compute_vr,n) :: ldvr=(compute_vr?n:1)
integer optional,intent(in),depend(n) :: lwork=2*n
check(lwork>=2*n) :: lwork
<type_in> dimension(lwork),intent(hide),depend(lwork) :: work
<rtype_in> dimension(8*n),intent(hide),depend(n) :: rwork
integer intent(out):: info
end subroutine <tchar=c,z>gegv
subroutine <tchar=s,d>syev(compute_v,lower,n,w,a,work,lwork,info)
! w,v,info = syev(a,compute_v=1,lower=0,lwork=3*n-1,overwrite_a=0)
! Compute all eigenvalues and, optionally, eigenvectors of a
! real symmetric matrix A.
!
! Performance tip:
! If compute_v=0 then set also overwrite_a=1.
callstatement (*f2py_func)((compute_v?"V":"N"),(lower?"L":"U"),&n,a,&n,w,work,&lwork,&info)
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,int*,int*
integer optional,intent(in):: compute_v = 1
check(compute_v==1||compute_v==0) compute_v
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer intent(hide),depend(a):: n = shape(a,0)
<type_in> dimension(n,n),check(shape(a,0)==shape(a,1)) :: a
intent(in,copy,out,out=v) :: a
<type_in> dimension(n),intent(out),depend(n) :: w
integer optional,intent(in),depend(n) :: lwork=3*n-1
check(lwork>=3*n-1) :: lwork
<type_in> dimension(lwork),intent(hide),depend(lwork) :: work
integer intent(out) :: info
end subroutine <tchar=s,d>syev
subroutine <tchar=c,z>heev(compute_v,lower,n,w,a,work,lwork,rwork,info)
! w,v,info = syev(a,compute_v=1,lower=0,lwork=3*n-1,overwrite_a=0)
! Compute all eigenvalues and, optionally, eigenvectors of a
! complex Hermitian matrix A.
!
! Warning:
! If compute_v=0 and overwrite_a=1, the contents of a is destroyed.
callstatement (*f2py_func)((compute_v?"V":"N"),(lower?"L":"U"),&n,a,&n,w,work,&lwork,rwork,&info)
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,int*,<rtype_in_c>*,int*
integer optional,intent(in):: compute_v = 1
check(compute_v==1||compute_v==0) compute_v
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer intent(hide),depend(a):: n = shape(a,0)
<type_in> dimension(n,n),check(shape(a,0)==shape(a,1)) :: a
intent(in,copy,out,out=v) :: a
<type_in> dimension(n),intent(out),depend(n) :: w
integer optional,intent(in),depend(n) :: lwork=2*n-1
check(lwork>=2*n-1) :: lwork
<type_in> dimension(lwork),intent(hide),depend(lwork) :: work
<rtype_in> dimension(3*n-1),intent(hide),depend(n) :: rwork
integer intent(out) :: info
end subroutine <tchar=c,z>heev
subroutine <tchar=s,d,c,z>posv(n,nrhs,a,b,info,lower)
! c,x,info = posv(a,b,lower=0,overwrite_a=0,overwrite_b=0)
! Solve A * X = B.
! A is symmetric positive defined
! A = U^T * U, C = U if lower = 0
! A = L * L^T, C = L if lower = 1
! C is triangular matrix of the corresponding Cholesky decomposition.
callstatement (*f2py_func)((lower?"L":"U"),&n,&nrhs,a,&n,b,&n,&info)
callprotoargument char*,int*,int*,<type_in_c>*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer depend(a),intent(hide):: n = shape(a,0)
integer depend(b),intent(hide):: nrhs = shape(b,1)
<type_in> dimension(n,n),intent(in,out,copy,out=c) :: a
check(shape(a,0)==shape(a,1)) :: a
<type_in> dimension(n,nrhs),intent(in,out,copy,out=x),depend(n):: b
check(shape(a,0)==shape(b,0)) :: b
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>posv
subroutine <tchar=s,d>potrf(n,a,info,lower,clean)
! c,info = potrf(a,lower=0,clean=1,overwrite_a=0)
! Compute Cholesky decomposition of symmetric positive defined matrix:
! A = U^T * U, C = U if lower = 0
! A = L * L^T, C = L if lower = 1
! C is triangular matrix of the corresponding Cholesky decomposition.
! clean==1 zeros strictly lower or upper parts of U or L, respectively
callstatement (*f2py_func)((lower?"L":"U"),&n,a,&n,&info); if(clean){int i,j;if(lower){for(i=0;i<n;++i) for(j=i+1;j<n;++j) *(a+j*n+i)=0.0;} else {for(i=0;i<n;++i) for(j=i+1;j<n;++j) *(a+i*n+j)=0.0;}}
callprotoargument char*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer optional,intent(in),check(clean==0||clean==1) :: clean = 1
integer depend(a),intent(hide):: n = shape(a,0)
<type_in> dimension(n,n),intent(in,out,copy,out=c) :: a
check(shape(a,0)==shape(a,1)) :: a
integer intent(out) :: info
end subroutine <tchar=s,d>potrf
subroutine <tchar=c,z>potrf(n,a,info,lower,clean)
! c,info = potrf(a,lower=0,clean=1,overwrite_a=0)
! Compute Cholesky decomposition of symmetric positive defined matrix:
! A = U^H * U, C = U if lower = 0
! A = L * L^H, C = L if lower = 1
! C is triangular matrix of the corresponding Cholesky decomposition.
! clean==1 zeros strictly lower or upper parts of U or L, respectively
callstatement (*f2py_func)((lower?"L":"U"),&n,a,&n,&info); if(clean){int i,j,k;if(lower){for(i=0;i<n;++i) for(j=i+1;j<n;++j) {k=j*n+i;(a+k)->r=(a+k)->i=0.0;}} else {for(i=0;i<n;++i) for(j=i+1;j<n;++j) {k=i*n+j;(a+k)->r=(a+k)->i=0.0;}}}
callprotoargument char*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer optional,intent(in),check(clean==0||clean==1) :: clean = 1
integer depend(a),intent(hide):: n = shape(a,0)
<type_in> dimension(n,n),intent(in,out,copy,out=c) :: a
check(shape(a,0)==shape(a,1)) :: a
integer intent(out) :: info
end subroutine <tchar=c,z>potrf
subroutine <tchar=s,d,c,z>potrs(n,nrhs,c,b,info,lower)
! x,info = potrs(c,b,lower=0=1,overwrite_b=0)
! Solve A * X = B.
! A is symmetric positive defined
! A = U^T * U, C = U if lower = 0
! A = L * L^T, C = L if lower = 1
! C is triangular matrix of the corresponding Cholesky decomposition.
callstatement (*f2py_func)((lower?"L":"U"),&n,&nrhs,c,&n,b,&n,&info)
callprotoargument char*,int*,int*,<type_in_c>*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer depend(c),intent(hide):: n = shape(c,0)
integer depend(b),intent(hide):: nrhs = shape(b,1)
<type_in> dimension(n,n),intent(in) :: c
check(shape(c,0)==shape(c,1)) :: c
<type_in> dimension(n,nrhs),intent(in,out,copy,out=x),depend(n):: b
check(shape(c,0)==shape(b,0)) :: b
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>potrs
subroutine <tchar=s,d,c,z>potri(n,c,info,lower)
! inv_a,info = potri(c,lower=0,overwrite_c=0)
! Compute A inverse A^-1.
! A = U^T * U, C = U if lower = 0
! A = L * L^T, C = L if lower = 1
! C is triangular matrix of the corresponding Cholesky decomposition.
callstatement (*f2py_func)((lower?"L":"U"),&n,c,&n,&info)
callprotoargument char*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer depend(c),intent(hide):: n = shape(c,0)
<type_in> dimension(n,n),intent(c,in,out,copy,out=inv_a) :: c
check(shape(c,0)==shape(c,1)) :: c
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>potri
subroutine <tchar=s,d,c,z>lauum(n,c,info,lower)
! a,info = lauum(c,lower=0,overwrite_c=0)
! Compute product
! U^T * U, C = U if lower = 0
! L * L^T, C = L if lower = 1
! C is triangular matrix of the corresponding Cholesky decomposition.
callstatement (*f2py_func)((lower?"L":"U"),&n,c,&n,&info)
callprotoargument char*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer depend(c),intent(hide):: n = shape(c,0)
<type_in> dimension(n,n),intent(in,out,copy,out=a) :: c
check(shape(c,0)==shape(c,1)) :: c
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>lauum
subroutine <tchar=s,d,c,z>trtri(n,c,info,lower,unitdiag)
! inv_c,info = trtri(c,lower=0,unitdiag=1,overwrite_c=0)
! Compute C inverse C^-1 where
! C = U if lower = 0
! C = L if lower = 1
! C is non-unit triangular matrix if unitdiag = 0
! C is unit triangular matrix if unitdiag = 1
callstatement (*f2py_func)((lower?"L":"U"),(unitdiag?"U":"N"),&n,c,&n,&info)
callprotoargument char*,char*,int*,<type_in_c>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer optional,intent(in),check(unitdiag==0||unitdiag==1) :: unitdiag = 0
integer depend(c),intent(hide):: n = shape(c,0)
<type_in> dimension(n,n),intent(in,out,copy,out=inv_c) :: c
check(shape(c,0)==shape(c,1)) :: c
integer intent(out) :: info
end subroutine <tchar=s,d,c,z>trtri
subroutine <tchar=s,d,c,z>laswp(n,a,nrows,k1,k2,piv,off,inc,m)
! a = laswp(a,piv,k1=0,k2=len(piv)-1,off=0,inc=1,overwrite_a=0)
! Perform row interchanges on the matrix A for each of row k1 through k2
!
! piv pivots rows.
callstatement {int i;m=len(piv);for(i=0;i<m;++piv[i++]);++k1;++k2; (*f2py_func)(&n,a,&nrows,&k1,&k2,piv+off,&inc); for(i=0;i<m;--piv[i++]);}
callprotoargument int*,<type_in_c>*,int*,int*,int*,int*,int*
integer depend(a),intent(hide):: nrows = shape(a,0)
integer depend(a),intent(hide):: n = shape(a,1)
<type_in> dimension(nrows,n),intent(in,out,copy) :: a
integer dimension(*),intent(in),depend(nrows) :: piv
check(len(piv)<=nrows) :: piv
!XXX: how to check that all elements in piv are < n?
integer optional,intent(in) :: k1 = 0
check(0<=k1) :: k1
integer optional,intent(in),depend(k1,piv,off) :: k2 = len(piv)-1
check(k1<=k2 && k2<len(piv)-off) :: k2
integer optional, intent(in),check(inc>0||inc<0) :: inc = 1
integer optional,intent(in),depend(piv) :: off=0
check(off>=0 && off<len(piv)) :: off
integer intent(hide),depend(piv,inc,off) :: m = (len(piv)-off)/abs(inc)
check(len(piv)-off>(m-1)*abs(inc)) :: m
end subroutine <tchar=s,d,c,z>laswp
subroutine <tchar=c,z>gees(compute_v,sort_t,<tchar>select,n,a,nrows,sdim,w,vs,ldvs,work,lwork,rwork,bwork,info)
! t,sdim,w,vs,work,info=gees(compute_v=1,sort_t=0,select,a,lwork=3*n)
! For an NxN matrix compute the eigenvalues, the schur form T, and optionally
! the matrix of Schur vectors Z. This gives the Schur factorization
! A = Z * T * Z^H -- a complex matrix is in Schur form if it is upper
! triangular
callstatement (*f2py_func)((compute_v?"V":"N"),(sort_t?"S":"N"),cb_<tchar>select_in_<tchar>gees__user__routines,&n,a,&nrows,&sdim,w,vs,&ldvs,work,&lwork,rwork,bwork,&info,1,1)
callprotoargument char*,char*,int(*)(<type_in_c>*),int*,<type_in_c>*,int*,int*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<rtype_in_c>*,int*,int*,int,int
use <tchar>gees__user__routines
integer optional,intent(in),check(compute_v==0||compute_v==1) :: compute_v = 1
integer optional,intent(in),check(sort_t==0||sort_t==1) :: sort_t = 0
external <tchar>select
integer intent(hide),depend(a) :: n = shape(a,1)
<type_in> intent(in,out,copy,out=t),check(shape(a,0)==shape(a,1)),dimension(n,n) :: a
integer intent(hide),depend(a) :: nrows=shape(a,0)
integer intent(out) :: sdim=0
<type_in> intent(out),dimension(n) :: w
<type_in> intent(out),depend(ldvs,n),dimension(ldvs,n) :: vs
integer intent(hide),depend(compute_v,n) :: ldvs=((compute_v==1)?n:1)
<type_in> intent(out),depend(lwork),dimension(MAX(lwork,1)) :: work
integer optional,intent(in),check((lwork==-1)||(lwork >= MAX(1,2*n))),depend(n) :: lwork = 3*n
<rtype_in> optional,intent(hide),depend(n),dimension(n) :: rwork
logical optional,intent(hide),depend(n),dimension(n) :: bwork
integer intent(out) :: info
end subroutine <tchar=c,z>gees
subroutine <tchar=d,s>gees(compute_v,sort_t,<tchar>select,n,a,nrows,sdim,wr,wi,vs,ldvs,work,lwork,bwork,info)
! t,sdim,w,vs,work,info=gees(compute_v=1,sort_t=0,select,a,lwork=3*n)
! For an NxN matrix compute the eigenvalues, the schur form T, and optionally
! the matrix of Schur vectors Z. This gives the Schur factorization
! A = Z * T * Z^H -- a real matrix is in Schur form if it is upper quasi-
! triangular with 1x1 and 2x2 blocks.
callstatement (*f2py_func)((compute_v?"V":"N"),(sort_t?"S":"N"),cb_<tchar>select_in_<tchar>gees__user__routines,&n,a,&nrows,&sdim,wr,wi,vs,&ldvs,work,&lwork,bwork,&info,1,1)
callprotoargument char*,char*,int(*)(<type_in_c>*,<type_in_c>*),int*,<type_in_c>*,int*,int*,<type_in_c>*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,int*,int*,int,int
use <tchar>gees__user__routines
integer optional,intent(in),check(compute_v==0||compute_v==1) :: compute_v = 1
integer optional,intent(in),check(sort_t==0||sort_t==1) :: sort_t = 0
external <tchar>select
integer intent(hide),depend(a) :: n = shape(a,1)
<type_in> intent(in,out,copy,out=t),check(shape(a,0)==shape(a,1)),dimension(n,n) :: a
integer intent(hide),depend(a) :: nrows=shape(a,0)
integer intent(out) :: sdim=0
<type_in> intent(out),dimension(n) :: wr
<type_in> intent(out),dimension(n) :: wi
<type_in> intent(out),depend(ldvs,n),dimension(ldvs,n) :: vs
integer intent(hide),depend(compute_v,n) :: ldvs=((compute_v==1)?n:1)
<type_in> intent(out),depend(lwork),dimension(MAX(lwork,1)) :: work
integer optional,intent(in),check((lwork==-1)||(lwork >= MAX(1,2*n))),depend(n) :: lwork = 3*n
<rtype_in> optional,intent(hide),depend(n),dimension(n) :: rwork
logical optional,intent(hide),depend(n),dimension(n) :: bwork
integer intent(out) :: info
end subroutine <tchar=s,d>gees
subroutine <tchar=s,d>ggev(compute_vl,compute_vr,n,a,b,alphar,alphai,beta,vl,ldvl,vr,ldvr,work,lwork,info)
callstatement {(*f2py_func)((compute_vl?"V":"N"),(compute_vr?"V":"N"),&n,a,&n,b,&n,alphar,alphai,beta,vl,&ldvl,vr,&ldvr,work,&lwork,&info);}
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,int*
integer optional,intent(in):: compute_vl = 1
check(compute_vl==1||compute_vl==0) compute_vl
integer optional,intent(in):: compute_vr = 1
check(compute_vr==1||compute_vr==0) compute_vr
integer intent(hide),depend(a) :: n = shape(a,0)
<type_in> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<type_in> intent(in,copy), dimension(n,n) :: b
check(shape(b,0)==shape(b,1)) :: b
<type_in> intent(out), dimension(n), depend(n) :: alphar
<type_in> intent(out), dimension(n), depend(n) :: alphai
<type_in> intent(out), dimension(n), depend(n) :: beta
<type_in> depend(ldvl,n), dimension(ldvl,n),intent(out) :: vl
integer intent(hide),depend(n,compute_vl) :: ldvl=(compute_vl?n:1)
<type_in> depend(ldvr,n), dimension(ldvr,n),intent(out) :: vr
integer intent(hide),depend(n,compute_vr) :: ldvr=(compute_vr?n:1)
integer optional,intent(in),depend(n,compute_vl,compute_vr) :: lwork=8*n
check((lwork==-1) || (lwork>=MAX(1,8*n))) :: lwork
<type_in> intent(out), dimension(MAX(lwork,1)), depend(lwork) :: work
integer intent(out):: info
end subroutine <tchar>ggev
subroutine <tchar=c,z>ggev(compute_vl,compute_vr,n,a,b,alpha,beta,vl,ldvl,vr,ldvr,work,lwork,rwork,info)
callstatement {(*f2py_func)((compute_vl?"V":"N"),(compute_vr?"V":"N"),&n,a,&n,b,&n,alpha,beta,vl,&ldvl,vr,&ldvr,work,&lwork,rwork,&info);}
callprotoargument char*,char*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,<type_in_c>*,<type_in_c>*,int*,<type_in_c>*,int*,<type_in_c>*,int*,<rtype_in_c>*,int*
integer optional,intent(in):: compute_vl = 1
check(compute_vl==1||compute_vl==0) compute_vl
integer optional,intent(in):: compute_vr = 1
check(compute_vr==1||compute_vr==0) compute_vr
integer intent(hide),depend(a) :: n = shape(a,0)
<type_in> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<type_in> intent(in,copy), dimension(n,n) :: b
check(shape(b,0)==shape(b,1)) :: b
<type_in> intent(out), dimension(n), depend(n) :: alpha
<type_in> intent(out), dimension(n), depend(n) :: beta
<type_in> depend(ldvl,n), dimension(ldvl,n),intent(out) :: vl
integer intent(hide),depend(n,compute_vl) :: ldvl=(compute_vl?n:1)
<type_in> depend(ldvr,n), dimension(ldvr,n),intent(out) :: vr
integer intent(hide),depend(n,compute_vr) :: ldvr=(compute_vr?n:1)
integer optional,intent(in),depend(n,compute_vl,compute_vr) :: lwork=8*n
check((lwork==-1) || (lwork>=MAX(1,8*n))) :: lwork
<type_in> intent(out), dimension(MAX(lwork,1)), depend(lwork) :: work
<rtype_in> intent(hide), dimension(8*n), depend(n) :: rwork
integer intent(out):: info
end subroutine <tchar>ggev
end interface
end python module generic_flapack
! This file was auto-generated with f2py (version:2.10.173).
! See http://cens.ioc.ee/projects/f2py2e/
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