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For_scipy_modification_flapack.pyf.src
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For_scipy_modification_flapack.pyf.src
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!%f90 -*- f90 -*-
! Signatures for f2py wrappers of FORTRAN LAPACK functions.
!
! Author: Pearu Peterson
! Created: Jan-Feb 2002
! $Revision$ $Date$
!
! Additions by Travis Oliphant, Tiziano Zito, Collin RM Stocks, Fabian Pedregosa
! Skipper Seabold
!
! <prefix2=s,d> <ctype2=float,double> <ftype2=real,double precision>
! <prefix2c=c,z> <ftype2c=complex,double complex> <ctype2c=complex_float,complex_double>
python module _flapack
interface
include 'flapack_user.pyf.src'
subroutine <prefix2>gges(jobvsl,jobvsr,sort_t,<prefix2>select,n,a,lda,b,ldb,sdim,alphar,alphai,beta,vsl,ldvsl,vsr,ldvsr,work,lwork,bwork,info)
! For a pair of N-by-N real nonsymmetric matrices (A,B) computes
! the generalized eigenvalues, the generalized real Schur form (S,T),
! optionally, the left and/or right matrices of Schur vectors (VSL
! and VSR).
! (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
callstatement (*f2py_func)((jobvsl?"V":"N"),(jobvsr?"V":"N"),(sort_t?"S":"N"),cb_<prefix2>select_in_gges__user__routines,&n,a,&lda,b,&ldb,&sdim,alphar,alphai,beta,vsl,&ldvsl,vsr,&ldvsr,work,&lwork,bwork,&info)
callprotoargument char*,char*,char*,int(*)(<ctype2>*,<ctype2>*,<ctype2>*),int*,<ctype2>*,int*,<ctype2>*,int*,int*,<ctype2>*,<ctype2>*,<ctype2>*,<ctype2>*,int*,<ctype2>*,int*,<ctype2>*,int*,int*,int*
use gges__user__routines
integer optional,intent(in),check(jobvsl==0||jobvsl==1) :: jobvsl=1
integer optional,intent(in),check(jobvsr==0||jobvsr==1) :: jobvsr=1
integer optional,intent(in),check(sort_t==0||sort_t==1) :: sort_t=0
external <prefix2>select
integer intent(hide),depend(a) :: n=shape(a,1)
<ftype2> intent(in,out,copy),dimension(lda,*) :: a
integer intent(hide),depend(a) :: lda=shape(a,0)
<ftype2> intent(in,out,copy),dimension(ldb,*) :: b
integer intent(hide),depend(b) :: ldb=shape(b,0)
integer intent(out) :: sdim=0
<ftype2> intent(out),dimension(n) :: alphar
<ftype2> intent(out),dimension(n) :: alphai
<ftype2> intent(out),dimension(n) :: beta
<ftype2> intent(out),depend(ldvsl,n),dimension(ldvsl,n) :: vsl
integer optional,intent(in),depend(jobvsl,n) :: ldvsl=((jobvsl==1)?n:1)
<ftype2> intent(out),depend(ldvsr,n),dimension(ldvsr,n) :: vsr
integer optional,intent(in),depend(jobvsr,n) :: ldvsr=((jobvsr==1)?n:1)
<ftype2> intent(out),depend(lwork),dimension(MAX(lwork,1)) :: work
integer optional,intent(in),depend(n),check(lwork>=MAX(1,MAX(8*n, 6*n+16))||lwork==-1):: lwork=8*n+16
logical optional,intent(hide),depend(n),dimension(n) :: bwork
integer intent(out):: info
end subroutine <prefix2>gges
subroutine <prefix2c>gges(jobvsl,jobvsr,sort_t,<prefix2c>select,n,a,lda,b,ldb,sdim,alpha,beta,vsl,ldvsl,vsr,ldvsr,work,lwork,rwork,bwork,info)
! For a pair of N-by-N complex nonsymmetric matrices (A,B) computes
! the generalized eigenvalues, the generalized real Schur form (S,T),
! optionally, the left and/or right matrices of Schur vectors (VSL
! and VSR).
! (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**H )
callstatement (*f2py_func)((jobvsl?"V":"N"),(jobvsr?"V":"N"),(sort_t?"S":"N"),cb_<prefix2c>select_in_gges__user__routines,&n,a,&lda,b,&ldb,&sdim,alpha,beta,vsl,&ldvsl,vsr,&ldvsr,work,&lwork,rwork,bwork,&info)
callprotoargument char*,char*,char*,int(*)(<ctype2c>*,<ctype2c>*),int*,<ctype2c>*,int*,<ctype2c>*,int*,int*,<ctype2c>*,<ctype2c>*,<ctype2c>*,int*,<ctype2c>*,int*,<ctype2c>*,int*,<ctype2>*,int*,int*
use gges__user__routines
integer optional,intent(in),check(jobvsl==0||jobvsl==1) :: jobvsl=1
integer optional,intent(in),check(jobvsr==0||jobvsr==1) :: jobvsr=1
integer optional,intent(in),check(sort_t==0||sort_t==1) :: sort_t=0
external <prefix2c>select
integer intent(hide),depend(a) :: n=shape(a,1)
<ftype2c> intent(in,out,copy),dimension(lda,*) :: a
integer intent(hide),depend(a) :: lda=shape(a,0)
<ftype2c> intent(in,out,copy),dimension(ldb,*) :: b
integer intent(hide),depend(b) :: ldb=shape(b,0)
integer intent(out) :: sdim=0
<ftype2c> intent(out),dimension(n) :: alpha
<ftype2c> intent(out),dimension(n) :: beta
<ftype2c> intent(out),depend(ldvsl,n),dimension(ldvsl,n) :: vsl
integer optional,intent(in),depend(jobvsl,n) :: ldvsl=((jobvsl==1)?n:1)
<ftype2c> intent(out),depend(ldvsr,n),dimension(ldvsr,n) :: vsr
integer optional,intent(in),depend(jobvsr,n) :: ldvsr=((jobvsr==1)?n:1)
<ftype2c> intent(out),depend(lwork),dimension(MAX(lwork,1)) :: work
integer optional,intent(in),depend(n),check(lwork>=MAX(1,2*n)||lwork==-1):: lwork=2*n
<ftype2> intent(hide),dimension(8*n) :: rwork
logical optional,intent(hide),depend(n),dimension(n) :: bwork
integer intent(out):: info
end subroutine <prefix2c>gges
subroutine <prefix2>pbtrf(lower,n,kd,ab,ldab,info)
! Compute Cholesky decomposition of banded symmetric positive definite
! 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.
callstatement (*f2py_func)((lower?"L":"U"),&n,&kd,ab,&ldab,&info);
callprotoargument char*,int*,int*,<ctype2>*,int*,int*
integer optional,check(shape(ab,0)==ldab),depend(ab) :: ldab=shape(ab,0)
integer intent(hide),depend(ab) :: n=shape(ab,1)
integer intent(hide),depend(ab) :: kd=shape(ab,0)-1
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
<ftype2> dimension(ldab,n),intent(in,out,copy,out=c) :: ab
integer intent(out) :: info
end subroutine <prefix2>pbtrf
subroutine <prefix2c>pbtrf(lower,n,kd,ab,ldab,info)
! Compute Cholesky decomposition of banded symmetric positive definite
! 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.
callstatement (*f2py_func)((lower?"L":"U"),&n,&kd,ab,&ldab,&info);
callprotoargument char*,int*,int*,<ctype2c>*,int*,int*
integer optional,check(shape(ab,0)==ldab),depend(ab) :: ldab=shape(ab,0)
integer intent(hide),depend(ab) :: n=shape(ab,1)
integer intent(hide),depend(ab) :: kd=shape(ab,0)-1
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
<ftype2c> dimension(ldab,n),intent(in,out,copy,out=c) :: ab
integer intent(out) :: info
end subroutine <prefix2c>pbtrf
subroutine <prefix2>pbtrs(lower, n, kd, nrhs, ab, ldab, b, ldb, info)
! Solve a system of linear equations A*X = B with a symmetric
! positive definite band matrix A using the Cholesky factorization.
! AB is the triangular factur U or L from the Cholesky factorization
! previously computed with *PBTRF.
! A = U^T * U, AB = U if lower = 0
! A = L * L^T, AB = L if lower = 1
callstatement (*f2py_func)((lower?"L":"U"),&n,&kd,&nrhs,ab,&ldab,b,&ldb,&info);
callprotoargument char*,int*,int*,int*,<ctype2>*,int*,<ctype2>*,int*,int*
integer optional,check(shape(ab,0)==ldab),depend(ab) :: ldab=shape(ab,0)
integer intent(hide),depend(ab) :: n=shape(ab,1)
integer intent(hide),depend(ab) :: kd=shape(ab,0)-1
integer intent(hide),depend(b) :: ldb=shape(b,0)
integer intent(hide),depend(b) :: nrhs=shape(b,1)
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
<ftype2> dimension(ldb, nrhs),intent(in,out,copy,out=x) :: b
<ftype2> dimension(ldab,n),intent(in) :: ab
integer intent(out) :: info
end subroutine <tchar=s,d>pbtrs
subroutine <prefix2c>pbtrs(lower, n, kd, nrhs, ab, ldab, b, ldb, info)
! Solve a system of linear equations A*X = B with a symmetric
! positive definite band matrix A using the Cholesky factorization.
! AB is the triangular factur U or L from the Cholesky factorization
! previously computed with *PBTRF.
! A = U^T * U, AB = U if lower = 0
! A = L * L^T, AB = L if lower = 1
callstatement (*f2py_func)((lower?"L":"U"),&n,&kd,&nrhs,ab,&ldab,b,&ldb,&info);
callprotoargument char*,int*,int*,int*,<ctype2c>*,int*,<ctype2c>*,int*,int*
integer optional,check(shape(ab,0)==ldab),depend(ab) :: ldab=shape(ab,0)
integer intent(hide),depend(ab) :: n=shape(ab,1)
integer intent(hide),depend(ab) :: kd=shape(ab,0)-1
integer intent(hide),depend(b) :: ldb=shape(b,0)
integer intent(hide),depend(b) :: nrhs=shape(b,1)
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
<ftype2c> dimension(ldb, nrhs),intent(in,out,copy,out=x) :: b
<ftype2c> dimension(ldab,n),intent(in) :: ab
integer intent(out) :: info
end subroutine <prefix2c>pbtrs
subroutine <prefix>trtrs(lower, trans, unitdiag, n, nrhs, a, lda, b, ldb, info)
! Solve a system of linear equations A*X = B with a triangular
! matrix A.
callstatement (*f2py_func)((lower?"L":"U"),(trans?(trans==2?"C":"T"):"N"),(unitdiag?"U":"N"),&n,&nrhs,a,&lda,b,&ldb,&info);
callprotoargument char*,char*,char*,int*,int*,<ctype>*,int*,<ctype>*,int*,int*
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
integer optional,intent(in),check(trans>=0 && trans <=2) :: trans = 0
integer optional,intent(in),check(unitdiag==0||unitdiag==1) :: unitdiag = 0
integer optional,check(shape(a,0)==lda),depend(a) :: lda=shape(a,0)
integer intent(hide),depend(a) :: n=shape(a,1)
integer intent(hide),depend(b) :: ldb=shape(b,0)
integer intent(hide),depend(b) :: nrhs=shape(b,1)
<ftype> dimension(ldb, nrhs),intent(in,out,copy,out=x) :: b
<ftype> dimension(lda,n),intent(in) :: a
integer intent(out) :: info
end subroutine <prefix>trtrs
subroutine <prefix2>pbsv(lower,n,kd,nrhs,ab,ldab,b,ldb,info)
!
! Computes the solution to a real system of linear equations
! A * X = B,
! where A is an N-by-N symmetric positive definite band matrix and X
! and B are N-by-NRHS matrices.
!
! The Cholesky decomposition is used to factor A as
! A = U**T * U, if lower=1, or
! A = L * L**T, if lower=0
! where U is an upper triangular band matrix, and L is a lower
! triangular band matrix, with the same number of superdiagonals or
! subdiagonals as A. The factored form of A is then used to solve the
! system of equations A * X = B.
callstatement (*f2py_func)((lower?"L":"U"),&n,&kd,&nrhs,ab,&ldab,b,&ldb,&info);
callprotoargument char*,int*,int*,int*,<ctype2>*,int*,<ctype2>*,int*,int*
integer optional,check(shape(ab,0)==ldab),depend(ab) :: ldab=shape(ab,0)
integer intent(hide),depend(ab) :: n=shape(ab,1)
integer intent(hide),depend(ab) :: kd=shape(ab,0)-1
integer intent(hide),depend(b) :: ldb=shape(b,0)
integer intent(hide),depend(b) :: nrhs=shape(b,1)
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
<ftype2> dimension(ldb, nrhs),intent(in,out,copy,out=x) :: b
<ftype2> dimension(ldab,n),intent(in,out,copy,out=c) :: ab
integer intent(out) :: info
end subroutine <prefix2>pbsv
subroutine <prefix2c>pbsv(lower,n,kd,nrhs,ab,ldab,b,ldb,info)
!
! Computes the solution to a real system of linear equations
! A * X = B,
! where A is an N-by-N Hermitian positive definite band matrix and X
! and B are N-by-NRHS matrices.
!
! The Cholesky decomposition is used to factor A as
! A = U**H * U, if lower=1, or
! A = L * L**H, if lower=0
! where U is an upper triangular band matrix, and L is a lower
! triangular band matrix, with the same number of superdiagonals or
! subdiagonals as A. The factored form of A is then used to solve the
! system of equations A * X = B.
callstatement (*f2py_func)((lower?"L":"U"),&n,&kd,&nrhs,ab,&ldab,b,&ldb,&info);
callprotoargument char*,int*,int*,int*,<ctype2c>*,int*,<ctype2c>*,int*,int*
integer optional,check(shape(ab,0)==ldab),depend(ab) :: ldab=shape(ab,0)
integer intent(hide),depend(ab) :: n=shape(ab,1)
integer intent(hide),depend(ab) :: kd=shape(ab,0)-1
integer intent(hide),depend(b) :: ldb=shape(b,0)
integer intent(hide),depend(b) :: nrhs=shape(b,1)
integer optional,intent(in),check(lower==0||lower==1) :: lower = 0
<ftype2c> dimension(ldb, nrhs),intent(in,out,copy,out=x) :: b
<ftype2c> dimension(ldab,n),intent(in,out,copy,out=c) :: ab
integer intent(out) :: info
end subroutine <prefix2c>pbsv
subroutine <prefix>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*,<ctype>*,int*,int*,int*,<ctypereal>*,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
<ftypereal> dimension(n),intent(out),depend(n) :: pivscale
<ftype> dimension(m,n),intent(in,out,copy,out=ba) :: a
integer intent(out) :: info
end subroutine <prefix>gebal
subroutine <prefix>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*,<ctype>*,int*,<ctype>*,<ctype>*,int*,int*
integer intent(hide),depend(a) :: n = shape(a,0)
<ftype> dimension(n,n),intent(in,out,copy,out=ht,aligned8),check(shape(a,0)==shape(a,1)) :: a
integer intent(in),optional :: lo = 0
integer intent(in),optional,depend(n) :: hi = n-1
<ftype> dimension(n-1),intent(out),depend(n) :: tau
<ftype> dimension(lwork),intent(cache,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 <prefix>gehrd
subroutine <prefix>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*,<ctype>*,int*,int*,<ctype>*,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)
<ftype> 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
<ftype> 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 <prefix>gbsv
subroutine <prefix>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*,<ctype>*,int*,int*,<ctype>*,int*,int*
integer depend(a),intent(hide):: n = shape(a,0)
integer depend(b),intent(hide):: nrhs = shape(b,1)
<ftype> dimension(n,n),check(shape(a,0)==shape(a,1)) :: a
integer dimension(n),depend(n),intent(out) :: piv
<ftype> 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 <prefix>gesv
subroutine <prefix>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*,<ctype>*,int*,int*,int*
integer depend(a),intent(hide):: m = shape(a,0)
integer depend(a),intent(hide):: n = shape(a,1)
<ftype> 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 <prefix>getrf
subroutine <prefix>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*,<ctype>*,int*,int*,<ctype>*,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)
<ftype> dimension(n,n),intent(in) :: lu
check(shape(lu,0)==shape(lu,1)) :: lu
integer dimension(n),intent(in),depend(n) :: piv
<ftype> 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 <prefix>getrs
subroutine <prefix>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*,<ctype>*,int*,int*,<ctype>*,int*,int*
integer depend(lu),intent(hide):: n = shape(lu,0)
<ftype> 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
<ftype> dimension(lwork),intent(hide,cache),depend(lwork) :: work
end subroutine <prefix>getri
subroutine <prefix2>gesdd(m,n,minmn,u0,u1,vt0,vt1,a,compute_uv,full_matrices,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 or min(M,N) x N if full_matrices=False
! SIGMA - M x N zero matrix with a main diagonal filled with min(M,N)
! singular values
! transpose(V) - N x N matrix or N x min(M,N) if full_matrices=False
callstatement (*f2py_func)((compute_uv?(full_matrices?"A":"S"):"N"),&m,&n,a,&m,s,u,&u0,vt,&vt0,work,&lwork,iwork,&info)
callprotoargument char*,int*,int*,<ctype2>*,int*,<ctype2>*,<ctype2>*,int*,<ctype2>*,int*,<ctype2>*,int*,int*,int*
integer intent(in),optional,check(compute_uv==0||compute_uv==1):: compute_uv = 1
integer intent(in),optional,check(full_matrices==0||full_matrices==1):: full_matrices = 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) :: u0 = (compute_uv?m:1)
integer intent(hide),depend(compute_uv,minmn, full_matrices) :: u1 = (compute_uv?(full_matrices?m:minmn):1)
integer intent(hide),depend(compute_uv,minmn, full_matrices) :: vt0 = (compute_uv?(full_matrices?n:minmn):1)
integer intent(hide),depend(compute_uv,minmn) :: vt1 = (compute_uv?n:1)
<ftype2> dimension(m,n),intent(in,copy,aligned8) :: a
<ftype2> dimension(minmn),intent(out),depend(minmn) :: s
<ftype2> dimension(u0,u1),intent(out),depend(u0, u1) :: u
<ftype2> dimension(vt0,vt1),intent(out),depend(vt0, vt1) :: vt
<ftype2> 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 <prefix2>gesdd
subroutine <prefix2c>gesdd(m,n,minmn,u0,u1,vt0,vt1,a,compute_uv,full_matrices,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 or min(M,N) x N if full_matrices=False
! SIGMA - M x N zero matrix with a main diagonal filled with min(M,N)
! singular values
! transpose(V) - N x N matrix or N x min(M,N) if full_matrices=False
callstatement (*f2py_func)((compute_uv?(full_matrices?"A":"S"):"N"),&m,&n,a,&m,s,u,&u0,vt,&vt0,work,&lwork,rwork,iwork,&info)
callprotoargument char*,int*,int*,<ctype2c>*,int*,<ctype2>*,<ctype2c>*,int*,<ctype2c>*,int*,<ctype2c>*,int*,<ctype2>*,int*,int*
integer intent(in),optional,check(compute_uv==0||compute_uv==1):: compute_uv = 1
integer intent(in),optional,check(full_matrices==0||full_matrices==1):: full_matrices = 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) :: u0 = (compute_uv?m:1)
integer intent(hide),depend(compute_uv,minmn, full_matrices) :: u1 = (compute_uv?(full_matrices?m:minmn):1)
integer intent(hide),depend(compute_uv,minmn, full_matrices) :: vt0 = (compute_uv?(full_matrices?n:minmn):1)
integer intent(hide),depend(compute_uv,minmn) :: vt1 = (compute_uv?n:1)
<ftype2c> dimension(m,n),intent(in,copy) :: a
<ftype2> dimension(minmn),intent(out),depend(minmn) :: s
<ftype2c> dimension(u0,u1),intent(out),depend(u0,u1) :: u
<ftype2c> dimension(vt0,vt1),intent(out),depend(vt0,vt1) :: vt
<ftype2c> dimension(lwork),intent(hide,cache),depend(lwork) :: work
<ftype2> dimension((compute_uv?minmn*MAX(5*minmn+7, 2*MAX(m,n)+2*minmn+1):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 <prefix2c>gesdd
subroutine <prefix2>gelss(m,n,minmn,maxmn,nrhs,a,b,s,cond,r,work,lwork,info)
! v,x,s,rank,work,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*,<ctype2>*,int*,<ctype2>*,int*,<ctype2>*,<ctype2>*,int*,<ctype2>*,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)
<ftype2> dimension(m,n),intent(in,out,copy,out=v) :: a
integer depend(b),intent(hide):: nrhs = shape(b,1)
<ftype2> dimension(maxmn,nrhs),check(maxmn==shape(b,0)),depend(maxmn) :: b
intent(in,out,copy,out=x) b
<ftype2> intent(in),optional :: cond = -1.0
integer intent(out,out=rank) :: r
<ftype2> intent(out),dimension(minmn),depend(minmn) :: s
integer optional,intent(in),depend(nrhs,minmn,maxmn),&
check(lwork>=1||lwork==-1) &
:: lwork=3*minmn+MAX(2*minmn,MAX(maxmn,nrhs))
!check(lwork>=3*minmn+MAX(2*minmn,MAX(maxmn,nrhs)))
<ftype2> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out)::info
end subroutine <prefix2>gelss
subroutine <prefix2c>gelss(m,n,minmn,maxmn,nrhs,a,b,s,cond,r,work,rwork,lwork,info)
! v,x,s,rank,work,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*,<ctype2c>*,int*,<ctype2c>*,int*,<ctype2>*,<ctype2>*,int*,<ctype2c>*,int*,<ctype2>*,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)
<ftype2c> dimension(m,n),intent(in,out,copy,out=v) :: a
integer depend(b),intent(hide):: nrhs = shape(b,1)
<ftype2c> dimension(maxmn,nrhs),check(maxmn==shape(b,0)),depend(maxmn) :: b
intent(in,out,copy,out=x) b
<ftype2> intent(in),optional :: cond = -1.0
integer intent(out,out=rank) :: r
<ftype2> intent(out),dimension(minmn),depend(minmn) :: s
integer optional,intent(in),depend(nrhs,minmn,maxmn),&
check(lwork>=1||lwork==-1) &
:: lwork=2*minmn+MAX(maxmn,nrhs)
! check(lwork>=2*minmn+MAX(maxmn,nrhs))
<ftype2c> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
<ftype2> dimension(5*minmn-1),intent(hide),depend(lwork) :: rwork
integer intent(out)::info
end subroutine <prefix2c>gelss
! Alex Grig-> Add two extra LS solvers
! <prefix2=s,d> <ctype2=float,double> <ftype2=real,double precision>
! <prefix2c=c,z> <ftype2c=complex,double complex> <ctype2c=complex_float,complex_double>
!* SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
!* WORK, LWORK, INFO )
!* SUBROUTINE DGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
!* WORK, LWORK, INFO )
!* SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
!* WORK, LWORK, IWORK, INFO )
! Modify s, lwork
subroutine <prefix2>gelsy(m,n,minmn,maxmn,nrhs,a,b,jptv,cond,r,work,lwork,info)
! v,x,j,rank,work,info = gelsy(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,jptv,&cond,&r,work,&lwork,&info)
callprotoargument int*,int*,int*,<ctype2>*,int*,<ctype2>*,int*,int*,<ctype2>*,int*,<ctype2>*,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)
<ftype2> dimension(m,n),intent(in,out,copy,out=v) :: a
integer depend(b),intent(hide):: nrhs = shape(b,1)
<ftype2> dimension(maxmn,nrhs),check(maxmn==shape(b,0)),depend(maxmn) :: b
intent(in,out,copy,out=x) b
<ftype2> intent(in),optional :: cond = -1.0
integer intent(out,out=rank) :: r
integer intent(in,out,out=j),dimension(n),depend(n) :: jptv
!MAX( MN+3*N+1, 2*MN+NRHS )
integer optional,intent(in),depend(nrhs,m,n),&
check(lwork>=1||lwork==-1) &
:: lwork=MAX(m*n+3*n+1,2*m*n+nrhs)
!check(lwork>=3*minmn+MAX(2*minmn,MAX(maxmn,nrhs)))
<ftype2> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out)::info
end subroutine <prefix2>gelsy
subroutine <prefix2>gelsd(m,n,minmn,maxmn,nrhs,a,b,s,cond,r,work,lwork,size_iwork,iwork,info)
! v,x,s,rank,work,iwork,info = gelsd(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,iwork,&info)
callprotoargument int*,int*,int*,<ctype2>*,int*,<ctype2>*,int*,<ctype2>*,<ctype2>*,int*,<ctype2>*,int*,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)
<ftype2> dimension(m,n),intent(in,out,copy,out=v) :: a
integer depend(b),intent(hide):: nrhs = shape(b,1)
<ftype2> dimension(maxmn,nrhs),check(maxmn==shape(b,0)),depend(maxmn) :: b
intent(in,out,copy,out=x) b
<ftype2> intent(in),optional :: cond = -1.0
integer intent(out,out=rank) :: r
<ftype2> intent(out),dimension(minmn),depend(minmn) :: s
! Modified lwork and iwork
integer optional,intent(in),&
check(lwork>=1||lwork==-1) &
:: lwork
! Impossible to calculate lwork explicitely, need to obtain it from information call first
!check(lwork>=3*minmn+MAX(2*minmn,MAX(maxmn,nrhs)))
<ftype2> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(in) :: size_iwork
integer intent(out),dimension(size_iwork),depend(size_iwork) :: iwork
integer intent(out)::info
end subroutine <prefix2>gelsd
! Alex Grig<-
! Alex Grig -> Add helper subroutine for SVD update
subroutine <prefix2>lasd4( n, i, d, z, delta, rho, sigma, work, info )
! sigma, delta, work, info = lasd4(d,z,i,rho=1.0,overwrite_d=0,overwrite_z=0)
! Computes i-th square root of eigenvalue of rank one augmented diagonal matrix. Needed by SVD update procedure
callstatement (*f2py_func)( &n, &i, d, z, delta, &rho, &sigma, work, &info )
callprotoargument int*, int*, <ctype2>*, <ctype2>*, <ctype2>*, <ctype2>*, <ctype2>*, <ctype2>*, int*
integer intent(hide),depend(d):: n = shape(d,0)
integer intent(in),check( i>=0||i<= shape(d,0)):: i
<ftype2> dimension(n),intent(in) :: d
<ftype2> dimension(n),intent(in),depend(n) :: z
<ftype2> intent(out) :: sigma
<ftype2> dimension(n),intent(out),depend(n) :: delta
<ftype2> intent(in),optional:: rho = 1.0
<ftype2> dimension(n),intent(out),depend(n) :: work
integer intent(out),depend(n) :: info
end subroutine <prefix2>lasd4
! Alex Grig <-
subroutine <prefix2>geqp3(m,n,a,jpvt,tau,work,lwork,info)
! qr_a,jpvt,tau,work,info = geqp3(a,lwork=3*(n+1),overwrite_a=0)
! Compute a QR factorization of a real M-by-N matrix A with column pivoting:
! A * P = Q * R.
threadsafe
callstatement (*f2py_func)(&m,&n,a,&m,jpvt,tau,work,&lwork,&info)
callprotoargument int*,int*,<ctype2>*,int*,int*,<ctype2>*,<ctype2>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
<ftype2> dimension(m,n),intent(in,out,copy,out=qr,aligned8) :: a
integer dimension(n),intent(out) :: jpvt
<ftype2> dimension(MIN(m,n)),intent(out) :: tau
integer optional,intent(in),depend(n),check(lwork>=n||lwork==-1) :: lwork=3*(n+1)
<ftype2> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <prefix2>geqp3
subroutine <prefix2c>geqp3(m,n,a,jpvt,tau,work,lwork,rwork,info)
! qr_a,jpvt,tau,work,info = geqp3(a,lwork,overwrite_a=0)
! Compute a QR factorization of a complex M-by-N matrix A with column pivoting:
! A * P = Q * R.
threadsafe
callstatement (*f2py_func)(&m,&n,a,&m,jpvt,tau,work,&lwork,rwork,&info)
callprotoargument int*,int*,<ctype2c>*,int*,int*,<ctype2c>*,<ctype2c>*,int*,<ctype2>*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
<ftype2c> dimension(m,n),intent(in,out,copy,out=qr,aligned8) :: a
integer dimension(n),intent(out) :: jpvt
<ftype2c> dimension(MIN(m,n)),intent(out) :: tau
integer optional,intent(in),depend(n),check(lwork>=n||lwork==-1) :: lwork=3*(n+1)
<ftype2c> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
<ftype2c> dimension(2*n),intent(hide),depend(n) :: rwork
integer intent(out) :: info
end subroutine <prefix2c>geqp3
subroutine <prefix>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.
threadsafe
callstatement (*f2py_func)(&m,&n,a,&m,tau,work,&lwork,&info)
callprotoargument int*,int*,<ctype>*,int*,<ctype>*,<ctype>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
<ftype> dimension(m,n),intent(in,out,copy,out=qr,aligned8) :: a
<ftype> dimension(MIN(m,n)),intent(out) :: tau
integer optional,intent(in),depend(n),check(lwork>=n||lwork==-1) :: lwork=3*n
<ftype> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <prefix>geqrf
subroutine <prefix>gerqf(m,n,a,tau,work,lwork,info)
! rq_a,tau,work,info = gerqf(a,lwork=3*n,overwrite_a=0)
! Compute an RQ factorization of a real M-by-N matrix A:
! A = R * Q.
threadsafe
callstatement (*f2py_func)(&m,&n,a,&m,tau,work,&lwork,&info)
callprotoargument int*,int*,<ctype>*,int*,<ctype>*,<ctype>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
<ftype> dimension(m,n),intent(in,out,copy,out=qr,aligned8) :: a
<ftype> dimension(MIN(m,n)),intent(out) :: tau
integer optional,intent(in),depend(n),check(lwork>=m||lwork==-1) :: lwork=3*m
<ftype> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <prefix>gerqf
subroutine <prefix2>orgqr(m,n,k,a,tau,work,lwork,info)
! q,work,info = orgqr(a,lwork=3*n,overwrite_a=0)
! Generates an M-by-N real matrix Q with orthonormal columns,
! which is defined as the first N columns of a product of K elementary
! reflectors of order M (e.g. output of geqrf)
threadsafe
callstatement (*f2py_func)(&m,&n,&k,a,&m,tau,work,&lwork,&info)
callprotoargument int*,int*,int*,<ctype2>*,int*,<ctype2>*,<ctype2>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(tau):: k = shape(tau,0)
<ftype2> dimension(m,n),intent(in,out,copy,out=q) :: a
<ftype2> dimension(k),intent(in) :: tau
integer optional,intent(in),depend(n),check(lwork>=n||lwork==-1) :: lwork=3*n
<ftype2> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <prefix2>orgqr
subroutine <prefix2c>ungqr(m,n,k,a,tau,work,lwork,info)
! q,work,info = ungqr(a,lwork=3*n,overwrite_a=0)
! Generates an M-by-N complex matrix Q with unitary columns,
! which is defined as the first N columns of a product of K elementary
! reflectors of order M (e.g. output of geqrf)
threadsafe
callstatement (*f2py_func)(&m,&n,&k,a,&m,tau,work,&lwork,&info)
callprotoargument int*,int*,int*,<ctype2c>*,int*,<ctype2c>*,<ctype2c>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(tau):: k = shape(tau,0)
<ftype2c> dimension(m,n),intent(in,out,copy,out=q) :: a
<ftype2c> dimension(k),intent(in) :: tau
integer optional,intent(in),depend(n),check(lwork>=n||lwork==-1) :: lwork=3*n
<ftype2c> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <prefix2c>ungqr
subroutine <prefix2>ormqr(side,trans,m,n,k,a,lda,tau,c,ldc,work,lwork,info)
! cq,work,info = ormqr(side,trans,a,tau,c,lwork)
! multiplies the real matrix C with the real orthogonal matrix Q,
! which is defined as the first N columns of a product of K elementary
! reflectors of order M (e.g. output of geqrf)
threadsafe
callstatement (*f2py_func)(side,trans,&m,&n,&k,a,&lda,tau,c,&ldc,work,&lwork,&info)
callprotoargument char*,char*,int*,int*,int*,<ctype2>*,int*,<ctype2>*,<ctype2>*,int*,<ctype2>*,int*,int*
character intent(in),check(*side=='L'||*side=='R'):: side
character intent(in),check(*trans=='N'||*trans=='T'):: trans
integer intent(hide),depend(c):: m = shape(c,0)
integer intent(hide),depend(c):: n = shape(c,1)
integer intent(hide),depend(a):: k = shape(a,1)
<ftype2> dimension(lda,k),intent(in):: a
integer intent(hide),depend(a):: lda = shape(a, 0)
<ftype2> dimension(k),intent(in):: tau
<ftype2> dimension(ldc,n),intent(in,out,copy,out=cq):: c
integer intent(hide),depend(c):: ldc = shape(c, 0)
<ftype2> dimension(MAX(lwork,1)),intent(out):: work
integer intent(in):: lwork
integer intent(out) :: info
end subroutine <prefix2>ormqr
subroutine <prefix2c>unmqr(side,trans,m,n,k,a,lda,tau,c,ldc,work,lwork,info)
! cq,work,info = unmqr(side,trans,a,tau,c,lwork)
! multiplies the complex matrix C with the complex unitary matrix Q,
! which is defined as the first N columns of a product of K elementary
! reflectors of order M (e.g. output of geqrf)
threadsafe
callstatement (*f2py_func)(side,trans,&m,&n,&k,a,&lda,tau,c,&ldc,work,&lwork,&info)
callprotoargument char*,char*,int*,int*,int*,<ctype2c>*,int*,<ctype2c>*,<ctype2c>*,int*,<ctype2c>*,int*,int*
character intent(in),check(*side=='L'||*side=='R'):: side
character intent(in),check(*trans=='N'||*trans=='C'):: trans
integer intent(hide),depend(c):: m = shape(c,0)
integer intent(hide),depend(c):: n = shape(c,1)
integer intent(hide),depend(a):: k = shape(a,1)
<ftype2c> dimension(lda,k),intent(in):: a
integer intent(hide),depend(a):: lda = shape(a, 0)
<ftype2c> dimension(k),intent(in):: tau
<ftype2c> dimension(ldc,n),intent(in,out,copy,out=cq):: c
integer intent(hide),depend(c):: ldc = shape(c, 0)
<ftype2c> dimension(MAX(lwork,1)),intent(out):: work
integer intent(in):: lwork
integer intent(out) :: info
end subroutine <prefix2c>unmqr
subroutine <prefix2>orgrq(m,n,k,a,tau,work,lwork,info)
! q,work,info = orgrq(a,lwork=3*n,overwrite_a=0)
! Generates an M-by-N real matrix Q with orthonormal columns,
! which is defined as the first N columns of a product of K elementary
! reflectors of order M (e.g. output of gerqf)
threadsafe
callstatement (*f2py_func)(&m,&n,&k,a,&m,tau,work,&lwork,&info)
callprotoargument int*,int*,int*,<ctype2>*,int*,<ctype2>*,<ctype2>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(tau):: k = shape(tau,0)
<ftype2> dimension(m,n),intent(in,out,copy,out=q) :: a
<ftype2> dimension(k),intent(in) :: tau
integer optional,intent(in),depend(n),check(lwork>=m||lwork==-1) :: lwork=3*m
<ftype2> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <prefix2>orgrq
subroutine <prefix2c>ungrq(m,n,k,a,tau,work,lwork,info)
! q,work,info = ungrq(a,lwork=3*n,overwrite_a=0)
! Generates an M-by-N complex matrix Q with unitary columns,
! which is defined as the first N columns of a product of K elementary
! reflectors of order M (e.g. output of gerqf)
threadsafe
callstatement (*f2py_func)(&m,&n,&k,a,&m,tau,work,&lwork,&info)
callprotoargument int*,int*,int*,<ctype2c>*,int*,<ctype2c>*,<ctype2c>*,int*,int*
integer intent(hide),depend(a):: m = shape(a,0)
integer intent(hide),depend(a):: n = shape(a,1)
integer intent(hide),depend(tau):: k = shape(tau,0)
<ftype2c> dimension(m,n),intent(in,out,copy,out=q) :: a
<ftype2c> dimension(k),intent(in) :: tau
integer optional,intent(in),depend(n),check(lwork>=m||lwork==-1) :: lwork=3*m
<ftype2c> dimension(MAX(lwork,1)),intent(out),depend(lwork) :: work
integer intent(out) :: info
end subroutine <prefix2c>ungrq
subroutine <prefix2>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*,<ctype2>*,int*,<ctype2>*,<ctype2>*,<ctype2>*,int*,<ctype2>*,int*,<ctype2>*,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)
<ftype2> dimension(n,n),intent(in,copy,aligned8) :: a
check(shape(a,0)==shape(a,1)) :: a
<ftype2> dimension(n),intent(out),depend(n) :: wr
<ftype2> dimension(n),intent(out),depend(n) :: wi
<ftype2> dimension(ldvl,n),intent(out) :: vl
integer intent(hide),depend(n,compute_vl) :: ldvl=(compute_vl?n:1)
<ftype2> 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
<ftype2> dimension(lwork),intent(hide,cache),depend(lwork) :: work
integer intent(out):: info
end subroutine <prefix2>geev
subroutine <prefix2c>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*,<ctype2c>*,int*,<ctype2c>*,<ctype2c>*,int*,<ctype2c>*,int*,<ctype2c>*,int*,<ctype2>*,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)
<ftype2c> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<ftype2c> dimension(n),intent(out),depend(n) :: w
<ftype2c> dimension(ldvl,n),depend(ldvl),intent(out) :: vl
integer intent(hide),depend(compute_vl,n) :: ldvl=(compute_vl?n:1)
<ftype2c> 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
<ftype2c> dimension(lwork),intent(hide),depend(lwork) :: work
<ftype2> dimension(2*n),intent(hide,cache),depend(n) :: rwork
integer intent(out):: info
end subroutine <prefix2c>geev
subroutine <prefix2>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*,<ctype2>*,int*,<ctype2>*,int*,<ctype2>*,<ctype2>*,<ctype2>*,<ctype2>*,int*,<ctype2>*,int*,<ctype2>*,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)
<ftype2> dimension(n,n),intent(in,copy) :: a
check(shape(a,0)==shape(a,1)) :: a
<ftype2> dimension(n,n),depend(n),intent(in,copy) :: b
check(shape(b,0)==shape(b,1) && shape(b,0)==n) :: b
<ftype2> dimension(n),depend(n),intent(out) :: alphar