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! -*- f90 -*-
!
! Contains wrappers for the following LAPACK routines:
!
! Driver routines for standard eigenvalue and singular value problems:
! syev, heev (SEP symmetric/hermitian, eigenvalues/vectors)
! syevd, heevd (SEP symmetric/hermitian, eigenvalues/vectors, D&C)
! syevx, heevx (.., expert) - Not Implemented
! syevr, heevr (.., RRR)
! spev, hpev, spevd, hpevd, spevx, hpevx (..., packed storage) - Not Implemented
! sbev, hbev, sbevd, hbevd, sbevx, hbevx (..., band) - Not Implemented
! stev, stevd, stevx, stevr (..., tridiagonal) - Not Implemented
! gees (NEP, general, Schur factorization)
! geesx (NEP, general, Schur factorization, expert) - Not Implemented
! geev (NEP, general, eigenvalues/vectors)
! geevx (NEP, general, eigenvalues/vectors, expert) - Not Implemented
! gesvd (SVD, general, singular values/vectors) - Not Implemented
! gesdd (SVD, general, singular values/vectors, D&C)
!
!
! <sym=sy,\0,he,\2>
subroutine <prefix><sym>ev(compute_v,lower,n,w,a,work,lwork,<_1=,,rwork\,,\2>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.
! w,v,info = heev(a,compute_v=1,lower=0,lwork=2*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,<_2=,,rwork\,,\2>&info)
callprotoargument char*,char*,int*,<ctype>*,int*,<ctypereal>*,<ctype>*,int*,<_3=,,float*\,,double*\,>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)
<ftype> dimension(n,n),check(shape(a,0)==shape(a,1)) :: a
intent(in,copy,out,out=v) :: a
<ftypereal> dimension(n),intent(out),depend(n) :: w
! <_lwork=3*n-1,\0,2*n-1,\2>
integer optional,intent(in),depend(n) :: lwork=<_lwork>
check(lwork>=<_lwork>) :: lwork
<ftype> dimension(lwork),intent(hide,cache),depend(lwork) :: work
<ftypereal> dimension(3*n-1),intent(hide,cache),depend(n) :: rwork
integer intent(out) :: info
end subroutine <prefix><sym>ev
subroutine <prefix><sym>evd(compute_v,lower,n,w,a,work,lwork,iwork,liwork,<_1=,,rwork\,lrwork\,,\2>info)
! w,v,info = syevd(a,compute_v=1,lower=0,lwork=min_lwork,overwrite_a=0)
! Compute all eigenvalues and, optionally, eigenvectors of a
! real symmetric matrix A using D&C.
!
! Performance tip:
! If compute_v=0 then set also overwrite_a=1.
! w,v,info = heevd(a,compute_v=1,lower=0,lwork=min_lwork,overwrite_a=0)
! Compute all eigenvalues and, optionally, eigenvectors of a
! complex Hermitian matrix A using D&C.
!
! 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,<_2=,,rwork\,&lrwork\,,\2>iwork,&liwork,&info)
callprotoargument char*,char*,int*,<ctype>*,int*,<ctypereal>*,<ctype>*,int*,<_3=,,float*\,int*\,,double*\,int*\,>int*,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)
<ftype> dimension(n,n),check(shape(a,0)==shape(a,1)) :: a
intent(in,copy,out,out=v) :: a
<ftypereal> dimension(n),intent(out),depend(n) :: w
! <_lwork=(compute_v?1+6*n+2*n*n:2*n+1),\0,(compute_v?2*n+n*n:n+1),\2>
integer optional,intent(in),depend(n,compute_v) :: lwork=<_lwork>
check(lwork>=<_lwork>) :: lwork
<ftype> dimension(lwork),intent(hide,cache),depend(lwork) :: work
integer intent(hide),depend(n,compute_v) :: liwork = (compute_v?3+5*n:1)
integer dimension(liwork),intent(hide,cache),depend(liwork) :: iwork
! <_lrwork=,,(compute_v?1+5*n+2*n*n:n),\2>
integer intent(hide),depend(n,compute_v) :: lrwork = <_lrwork>
<ftypereal> dimension(lrwork),intent(hide,cache),depend(n,lrwork) :: rwork
integer intent(out) :: info
end subroutine <prefix><sym>evd
subroutine <prefix><sym>evr(n,a,compute_v,lower,vrange,irange,atol,w,z,m,ldz,isuppz,work,lwork,<,,rwork\,lrwork\,,\2>iwork,liwork,info)
! w,v,info = {sy|he}evr(a,compute_v=1,lower=0,vrange=None,irange=None,atol=-1,lwork=min_lwork,overwrite_a=0)
!
! Compute range of eigenvalues and, optionally, eigenvectors of a
! real symmetric matrix A using RRR.
!
! Performance tip:
! If compute_v=0 then set also overwrite_a=1.
! Warning:
! If compute_v=0 and overwrite_a=1, the contents of a is destroyed.
callstatement if(irange_capi==Py_None);else{irange[0]++;irange[1]++;}(*f2py_func)((compute_v?"V":"N"),(vrange_capi==Py_None?(irange_capi==Py_None?"A":"I"):"V"),(lower?"L":"U"),&n,a,&n,vrange,vrange+1,irange,irange+1,&atol,&m,w,z,&ldz,isuppz,work,&lwork,<_2=,,rwork\,&lrwork\,,\2>iwork,&liwork,&info);if(irange_capi==Py_None);else{irange[0]--;irange[1]--;}if(vrange_capi==Py_None);else {capi_w_tmp-\>dimensions[0]=capi_z_tmp-\>dimensions[1]=m;/*capi_z_tmp-\>strides[0]=m*capi_z_tmp-\>descr-\>elsize;*/}
callprotoargument char*,char*,char*,int*,<ctype>*,int*,<ctypereal>*,<ctypereal>*,int*,int*,<ctypereal>*,int*,<ctypereal>*,<ctype>*,int*,int*,<ctype>*,int*,<_3=,,float*\,int*\,,double*\,int*\,>int*,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)
<ftype> dimension(n,n),check(shape(a,0)==shape(a,1)) :: a
intent(in,copy) :: a
<ftypereal> optional,dimension(2),intent(in) :: vrange
integer optional,dimension(2),intent(in),depend(n) :: irange
check(irange_capi==Py_None || (irange[0]>=0 && irange[1]<n)) irange
<ftypereal> optional,intent(in) :: atol = -1.0
integer intent(hide),depend(vrange,irange,n) :: m = (irange_capi==Py_None?n:irange[1]-irange[0]+1)
<ftypereal> dimension(m),intent(out),depend(m) :: w
integer intent(hide),depend(compute_v,n) :: ldz = (compute_v?n:1)
<ftype> dimension(ldz,m),intent(out,out=v),depend(ldz,m) :: z
integer intent(hide),depend(m),dimension(2*m) :: isuppz
! <_lwork=26*n,\0,18*n,\2> Includes bug fix in `man zheevr`.
integer optional,intent(in),depend(n) :: lwork=<_lwork>
check(lwork>=<_lwork>) lwork
<ftype> dimension(lwork),intent(hide,cache),depend(lwork) :: work
integer intent(hide),depend(n,compute_v) :: liwork = 10*n
integer dimension(liwork),intent(hide,cache),depend(liwork) :: iwork
! <_lrwork=,,24*n,\2>
integer intent(hide),depend(n) :: lrwork = <_lrwork>
<ftypereal> dimension(lrwork),intent(hide,cache),depend(n,lrwork) :: rwork
integer intent(out) :: info
end subroutine <prefix><sym>evr
subroutine <prefix>gees(compute_v,sort_t,<prefix>select,n,a,nrows,sdim,<wr\,wi,\0,w,\2>,vs,ldvs,work,lwork,<,,rwork\,,\2>bwork,info)
! t,sdim,(wr,wi|w),vs,info = gees(zselect,a,compute_v=1,sort_t=0,lwork=3*n,zselect_extra_args=(),overwrite_a=0)
! 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
! t,sdim,wr,wi,vs,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_<prefix>select_in_gees__user__routines,&n,a,&nrows,&sdim,<wr\,wi,\0,w,\2>,vs,&ldvs,work,&lwork,<,,rwork\,,\2>bwork,&info,1,1)
callprotoargument char*,char*,int(*)(<float*\,float*,double*\,double*,complex_float*,complex_double*>),int*,<ctype>*,int*,int*,<ctype>*,<float*\,,double*\,,,><ctype>*,int*,<ctype>*,int*,<,,float*\,,double*\,>int*,int*,int,int
use 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 <prefix>select
integer intent(hide),depend(a) :: n = shape(a,1)
<ftype> 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
<ftype> intent(out),dimension(n) :: <wr\,wi,\0,w,\2>
<ftype> intent(out),depend(ldvs,n),dimension(ldvs,n) :: vs
integer intent(hide),depend(compute_v,n) :: ldvs=((compute_v==1)?n:1)
<ftype> intent(hide,cache),depend(lwork),dimension(lwork) :: work
integer optional,intent(in),check(lwork >= MAX(1,3*n)),depend(n) :: lwork = 3*n
<ftypereal> intent(hide,cache),depend(n),dimension(n) :: rwork
logical intent(hide,cache),depend(n),dimension(n) :: bwork
integer intent(out) :: info
end subroutine <prefix>gees
subroutine <prefix>geev(compute_vl,compute_vr,n,a,<wr\,wi,\0,w,\2>,vl,ldvl,vr,ldvr,work,lwork,<,,rwork\,,\2>info)
! wr,wi,vl,vr,info = geev(a,compute_vl=1,compute_vr=1,lwork=4*n,overwrite_a=0)
! 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,<wr\,wi,\0,w,\2>,vl,&ldvl,vr,&ldvr,work,&lwork,<,,rwork\,,\2>&info);}
callprotoargument char*,char*,int*,<ctype>*,int*,<ctype>*,<float*\,,double*\,,,><ctype>*,int*,<ctype>*,int*,<ctype>*,int*,<,,float*\,,double*\,>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)
<ftype> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<ftype> dimension(n),intent(out),depend(n) :: <wr\,wi,\0,w,\2>
<ftype> dimension(ldvl,n),intent(out) :: vl
integer intent(hide),depend(n,compute_vl) :: ldvl=(compute_vl?n:1)
<ftype> dimension(ldvr,n),intent(out) :: vr
integer intent(hide),depend(n,compute_vr) :: ldvr=(compute_vr?n:1)
! <_lwork=(compute_vl||compute_vr)?4*n:3*n,\0,2*n,\2>
integer optional,intent(in),depend(n,compute_vl,compute_vr) :: lwork=<_lwork>
check(lwork>=<_lwork>) :: lwork
<ftype> dimension(lwork),intent(hide,cache),depend(lwork) :: work
<ftypereal> dimension(2*n),intent(hide,cache),depend(n) :: rwork
integer intent(out):: info
end subroutine <prefix>geev
subroutine <prefix>gesdd(m,n,minmn,du,dvt,a,compute_uv,u,s,vt,work,lwork,<,,rwork\,,\2>iwork,info)
! u,s,vh,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\,,\2>iwork,&info)
callprotoargument char*,int*,int*,<ctype>*,int*,<ctypereal>*,<ctype>*,int*,<ctype>*,int*,<ctype>*,int*,<,,float*\,,double*\,>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)
<ftype> dimension(m,n),intent(in,copy) :: a
<ftypereal> dimension(minmn),intent(out),depend(minmn) :: s
<ftype> dimension(du,du),intent(out),depend(du) :: u
<ftype> dimension(dvt,dvt),intent(out),depend(dvt) :: vt
<ftype> dimension(lwork),intent(hide,cache),depend(lwork) :: work
! <_lwork=(compute_uv?4*minmn*minmn+MAX(m\,n)+9*minmn:MAX(14*minmn+4\,10*minmn+827)+MAX(m\,n)),\0,(compute_uv?2*minmn*minmn+MAX(m\,n)+2*minmn:2*minmn+MAX(m\,n)),\2>
integer optional,intent(in),depend(minmn,compute_uv) &
:: lwork = <_lwork>
! 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
<ftypereal> dimension((compute_uv?5*minmn*minmn+7*minmn:5*minmn)),intent(hide,cache),depend(minmn,compute_uv) :: rwork
integer intent(hide,cache),dimension(8*minmn),depend(minmn) :: iwork
integer intent(out)::info
end subroutine <prefix>gesdd
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