Moving out basic tools to higher level.

1 files changed, 0 insertions, 549 deletions

diff --git a/scipy/basic/linalg.py b/scipy/basic/linalg.py
deleted file mode 100644
index a669b27c4..000000000
--- a/scipy/basic/linalg.py
+++ /dev/null
@@ -1,549 +0,0 @@
-"""Lite version of scipy.linalg.
-"""
-# This module is a lite version of LinAlg.py module which contains
-# high-level Python interface to the LAPACK library.  The lite version
-# only accesses the following LAPACK functions: dgesv, zgesv, dgeev,
-# zgeev, dgesdd, zgesdd, dgelsd, zgelsd, dsyevd, zheevd, dgetrf, dpotrf.
-
-from scipy.base import *
-import lapack_lite
-import math
-
-# Error object
-class LinAlgError(Exception):
-    pass
-
-# Helper routines
-_lapack_type = {'f': 0, 'd': 1, 'F': 2, 'D': 3}
-_lapack_letter = ['s', 'd', 'c', 'z']
-_array_kind = {'i':0, 'l': 0, 'f': 0, 'd': 0, 'F': 1, 'D': 1}
-_array_precision = {'i': 1, 'l': 1, 'f': 0, 'd': 1, 'F': 0, 'D': 1}
-_array_type = [['f', 'd'], ['F', 'D']]
-
-def _commonType(*arrays):
-    kind = 0
-#    precision = 0
-#   force higher precision in lite version
-    precision = 1
-    for a in arrays:
-        t = a.dtypechar
-        kind = max(kind, _array_kind[t])
-        precision = max(precision, _array_precision[t])
-    return _array_type[kind][precision]
-
-def _castCopyAndTranspose(type, *arrays):
-    cast_arrays = ()
-    for a in arrays:
-        cast_arrays = cast_arrays + (transpose(a).astype(type),)
-    if len(cast_arrays) == 1:
-            return cast_arrays[0]
-    else:
-        return cast_arrays
-
-# _fastCopyAndTranpose is an optimized version of _castCopyAndTranspose.
-# It assumes the input is 2D (as all the calls in here are).
-
-_fastCT = fastCopyAndTranspose
-
-def _fastCopyAndTranspose(type, *arrays):
-    cast_arrays = ()
-    for a in arrays:
-        if a.dtypechar == type:
-            cast_arrays = cast_arrays + (_fastCT(a),)
-        else:
-            cast_arrays = cast_arrays + (_fastCT(a.astype(type)),)
-    if len(cast_arrays) == 1:
-            return cast_arrays[0]
-    else:
-        return cast_arrays
-
-def _assertRank2(*arrays):
-    for a in arrays:
-        if len(a.shape) != 2:
-            raise LinAlgError, 'Array must be two-dimensional'
-
-def _assertSquareness(*arrays):
-    for a in arrays:
-        if max(a.shape) != min(a.shape):
-            raise LinAlgError, 'Array must be square'
-
-
-# Linear equations
-
-def solve_linear_equations(a, b):
-    one_eq = len(b.shape) == 1
-    if one_eq:
-        b = b[:, NewAxis]
-    _assertRank2(a, b)
-    _assertSquareness(a)
-    n_eq = a.shape[0]
-    n_rhs = b.shape[1]
-    if n_eq != b.shape[0]:
-        raise LinAlgError, 'Incompatible dimensions'
-    t =_commonType(a, b)
-#    lapack_routine = _findLapackRoutine('gesv', t)
-    if _array_kind[t] == 1: # Complex routines take different arguments
-        lapack_routine = lapack_lite.zgesv
-    else:
-        lapack_routine = lapack_lite.dgesv
-    a, b = _fastCopyAndTranspose(t, a, b)
-    pivots = zeros(n_eq, 'i')
-    results = lapack_routine(n_eq, n_rhs, a, n_eq, pivots, b, n_eq, 0)
-    if results['info'] > 0:
-        raise LinAlgError, 'Singular matrix'
-    if one_eq:
-        return ravel(b) # I see no need to copy here
-    else:
-        return transpose(b) # no need to copy
-
-
-# Matrix inversion
-
-def inverse(a):
-    return solve_linear_equations(a, identity(a.shape[0]))
-
-
-# Cholesky decomposition
-
-def cholesky_decomposition(a):
-    _assertRank2(a)
-    _assertSquareness(a)
-    t =_commonType(a)
-    a = _castCopyAndTranspose(t, a)
-    m = a.shape[0]
-    n = a.shape[1]
-    if _array_kind[t] == 1:
-        lapack_routine = lapack_lite.zpotrf
-    else:
-        lapack_routine = lapack_lite.dpotrf
-    results = lapack_routine('L', n, a, m, 0)
-    if results['info'] > 0:
-        raise LinAlgError, 'Matrix is not positive definite - Cholesky decomposition cannot be computed'
-    return transpose(triu(a,k=0)).copy()
-
-
-# Eigenvalues
-
-def eigenvalues(a):
-    _assertRank2(a)
-    _assertSquareness(a)
-    t =_commonType(a)
-    real_t = _array_type[0][_array_precision[t]]
-    a = _fastCopyAndTranspose(t, a)
-    n = a.shape[0]
-    dummy = zeros((1,), t)
-    if _array_kind[t] == 1: # Complex routines take different arguments
-        lapack_routine = lapack_lite.zgeev
-        w = zeros((n,), t)
-        rwork = zeros((n,),real_t)
-        lwork = 1
-        work = zeros((lwork,), t)
-        results = lapack_routine('N', 'N', n, a, n, w,
-                                 dummy, 1, dummy, 1, work, -1, rwork, 0)
-        lwork = int(abs(work[0]))
-        work = zeros((lwork,), t)
-        results = lapack_routine('N', 'N', n, a, n, w,
-                                 dummy, 1, dummy, 1, work, lwork, rwork, 0)
-    else:
-        lapack_routine = lapack_lite.dgeev
-        wr = zeros((n,), t)
-        wi = zeros((n,), t)
-        lwork = 1
-        work = zeros((lwork,), t)
-        results = lapack_routine('N', 'N', n, a, n, wr, wi,
-                                 dummy, 1, dummy, 1, work, -1, 0)
-        lwork = int(work[0])
-        work = zeros((lwork,), t)
-        results = lapack_routine('N', 'N', n, a, n, wr, wi,
-                                 dummy, 1, dummy, 1, work, lwork, 0)
-        if logical_and.reduce(equal(wi, 0.)):
-            w = wr
-        else:
-            w = wr+1j*wi
-    if results['info'] > 0:
-        raise LinAlgError, 'Eigenvalues did not converge'
-    return w
-
-
-def Heigenvalues(a, UPLO='L'):
-    _assertRank2(a)
-    _assertSquareness(a)
-    t =_commonType(a)
-    real_t = _array_type[0][_array_precision[t]]
-    a = _castCopyAndTranspose(t, a)
-    n = a.shape[0]
-    liwork = 5*n+3
-    iwork = zeros((liwork,),'i')
-    if _array_kind[t] == 1: # Complex routines take different arguments
-        lapack_routine = lapack_lite.zheevd
-        w = zeros((n,), real_t)
-        lwork = 1
-        work = zeros((lwork,), t)
-        lrwork = 1
-        rwork = zeros((lrwork,),real_t)
-        results = lapack_routine('N', UPLO, n, a, n,w, work, -1, rwork, -1, iwork, liwork,  0)
-        lwork = int(abs(work[0]))
-        work = zeros((lwork,), t)
-        lrwork = int(rwork[0])
-        rwork = zeros((lrwork,),real_t)
-        results = lapack_routine('N', UPLO, n, a, n,w, work, lwork, rwork, lrwork, iwork, liwork,  0)
-    else:
-        lapack_routine = lapack_lite.dsyevd
-        w = zeros((n,), t)
-        lwork = 1
-        work = zeros((lwork,), t)
-        results = lapack_routine('N', UPLO, n, a, n,w, work, -1, iwork, liwork, 0)
-        lwork = int(work[0])
-        work = zeros((lwork,), t)
-        results = lapack_routine('N', UPLO, n, a, n,w, work, lwork, iwork, liwork, 0)
-    if results['info'] > 0:
-        raise LinAlgError, 'Eigenvalues did not converge'
-    return w
-
-def _convertarray(a):
-    if issubclass(a.dtype, complexfloating):
-        if a.dtypechar == 'D':
-            a = _fastCT(a)
-        else:
-            a = _fastCT(a.astype('D'))
-    else:
-        if a.dtypechar == 'd':
-            a = _fastCT(a)
-        else:
-            a = _fastCT(a.astype('d'))
-    return a, a.dtypechar
-
-# Eigenvectors
-
-def eig(a):
-    """eig(a) returns u,v  where u is the eigenvalues and
-v is a matrix of eigenvectors with vector v[:,i] corresponds to
-eigenvalue u[i].  Satisfies the equation dot(a, v[:,i]) = u[i]*v[:,i]
-"""
-    a = asarray(a)    
-    _assertRank2(a)
-    _assertSquareness(a)
-    a,t = _convertarray(a) # convert to float_ or complex_ type
-    wrap = a.__array_wrap__
-    real_t = 'd'
-    n = a.shape[0]
-    dummy = zeros((1,), t)
-    if t == 'D': # Complex routines take different arguments
-        lapack_routine = lapack_lite.zgeev
-        w = zeros((n,), t)
-        v = zeros((n,n), t)
-        lwork = 1
-        work = zeros((lwork,),t)
-        rwork = zeros((2*n,),real_t)
-        results = lapack_routine('N', 'V', n, a, n, w,
-                                  dummy, 1, v, n, work, -1, rwork, 0)
-        lwork = int(abs(work[0]))
-        work = zeros((lwork,),t)
-        results = lapack_routine('N', 'V', n, a, n, w,
-                                  dummy, 1, v, n, work, lwork, rwork, 0)
-    else:
-        lapack_routine = lapack_lite.dgeev
-        wr = zeros((n,), t)
-        wi = zeros((n,), t)
-        vr = zeros((n,n), t)
-        lwork = 1
-        work = zeros((lwork,),t)
-        results = lapack_routine('N', 'V', n, a, n, wr, wi,
-                                  dummy, 1, vr, n, work, -1, 0)
-        lwork = int(work[0])
-        work = zeros((lwork,),t)
-        results = lapack_routine('N', 'V', n, a, n, wr, wi,
-                                  dummy, 1, vr, n, work, lwork, 0)
-        if logical_and.reduce(equal(wi, 0.)):
-            w = wr
-            v = vr
-        else:
-            w = wr+1j*wi
-            v = array(vr,Complex)
-            ind = nonzero(
-                          equal(
-                              equal(wi,0.0) # true for real e-vals
-                                       ,0)          # true for complex e-vals
-                                 )                  # indices of complex e-vals
-            for i in range(len(ind)/2):
-                v[ind[2*i]] = vr[ind[2*i]] + 1j*vr[ind[2*i+1]]
-                v[ind[2*i+1]] = vr[ind[2*i]] - 1j*vr[ind[2*i+1]]
-    if results['info'] > 0:
-        raise LinAlgError, 'Eigenvalues did not converge'
-    return w,wrap(v.transpose())
-
-
-def eigh(a, UPLO='L'):
-    _assertRank2(a)
-    _assertSquareness(a)
-    t =_commonType(a)
-    real_t = _array_type[0][_array_precision[t]]
-    a = _castCopyAndTranspose(t, a)
-    wrap = a.__array_wrap__
-    n = a.shape[0]
-    liwork = 5*n+3
-    iwork = zeros((liwork,),'i')
-    if _array_kind[t] == 1: # Complex routines take different arguments
-        lapack_routine = lapack_lite.zheevd
-        w = zeros((n,), real_t)
-        lwork = 1
-        work = zeros((lwork,), t)
-        lrwork = 1
-        rwork = zeros((lrwork,),real_t)
-        results = lapack_routine('V', UPLO, n, a, n,w, work, -1, rwork, -1, iwork, liwork,  0)
-        lwork = int(abs(work[0]))
-        work = zeros((lwork,), t)
-        lrwork = int(rwork[0])
-        rwork = zeros((lrwork,),real_t)
-        results = lapack_routine('V', UPLO, n, a, n,w, work, lwork, rwork, lrwork, iwork, liwork,  0)
-    else:
-        lapack_routine = lapack_lite.dsyevd
-        w = zeros((n,), t)
-        lwork = 1
-        work = zeros((lwork,),t)
-        results = lapack_routine('V', UPLO, n, a, n,w, work, -1, iwork, liwork, 0)
-        lwork = int(work[0])
-        work = zeros((lwork,),t)
-        results = lapack_routine('V', UPLO, n, a, n,w, work, lwork, iwork, liwork, 0)
-    if results['info'] > 0:
-        raise LinAlgError, 'Eigenvalues did not converge'
-    return w,wrap(a.transpose())
-
-
-# Singular value decomposition
-
-def svd(a, full_matrices = 1):
-    _assertRank2(a)
-    n = a.shape[1]
-    m = a.shape[0]
-    t =_commonType(a)
-    real_t = _array_type[0][_array_precision[t]]
-    a = _fastCopyAndTranspose(t, a)
-    wrap = a.__array_wrap__
-    if full_matrices:
-        nu = m
-        nvt = n
-        option = 'A'
-    else:
-        nu = min(n,m)
-        nvt = min(n,m)
-        option = 'S'
-    s = zeros((min(n,m),), real_t)
-    u = zeros((nu, m), t)
-    vt = zeros((n, nvt), t)
-    iwork = zeros((8*min(m,n),), 'i')
-    if _array_kind[t] == 1: # Complex routines take different arguments
-        lapack_routine = lapack_lite.zgesdd
-        rwork = zeros((5*min(m,n)*min(m,n) + 5*min(m,n),), real_t)
-        lwork = 1
-        work = zeros((lwork,), t)
-        results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
-                                 work, -1, rwork, iwork, 0)
-        lwork = int(abs(work[0]))
-        work = zeros((lwork,), t)
-        results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
-                                 work, lwork, rwork, iwork, 0)
-    else:
-        lapack_routine = lapack_lite.dgesdd
-        lwork = 1
-        work = zeros((lwork,), t)
-        results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
-                                 work, -1, iwork, 0)
-        lwork = int(work[0])
-        work = zeros((lwork,), t)
-        results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
-                                 work, lwork, iwork, 0)
-    if results['info'] > 0:
-        raise LinAlgError, 'SVD did not converge'
-    return wrap(transpose(u)), s, \
-           wrap(transpose(vt)) # why copy here?
-
-
-# Generalized inverse
-
-def generalized_inverse(a, rcond = 1.e-10):
-    a = array(a, copy=0)
-    if a.dtypechar in typecodes['Complex']:
-        a = conjugate(a)
-    u, s, vt = svd(a, 0)
-    m = u.shape[0]
-    n = vt.shape[1]
-    cutoff = rcond*maximum.reduce(s)
-    for i in range(min(n,m)):
-        if s[i] > cutoff:
-            s[i] = 1./s[i]
-        else:
-            s[i] = 0.;
-    wrap = a.__array_wrap__
-    return wrap(dot(transpose(vt),                        
-                       multiply(s[:, NewAxis],transpose(u))))
-
-# Determinant
-
-def determinant(a):
-    _assertRank2(a)
-    _assertSquareness(a)
-    t =_commonType(a)
-    a = _fastCopyAndTranspose(t, a)
-    n = a.shape[0]
-    if _array_kind[t] == 1:
-        lapack_routine = lapack_lite.zgetrf
-    else:
-        lapack_routine = lapack_lite.dgetrf
-    pivots = zeros((n,), 'i')
-    results = lapack_routine(n, n, a, n, pivots, 0)
-    sign = add.reduce(not_equal(pivots,
-                                                arrayrange(1, n+1))) % 2
-    return (1.-2.*sign)*multiply.reduce(diagonal(a),axis=-1)
-
-# Linear Least Squares
-
-def linear_least_squares(a, b, rcond=1.e-10):
-    """returns x,resids,rank,s
-where x minimizes 2-norm(|b - Ax|)
-      resids is the sum square residuals
-      rank is the rank of A
-      s is the rank of the singular values of A in descending order
-
-If b is a matrix then x is also a matrix with corresponding columns.
-If the rank of A is less than the number of columns of A or greater than
-the number of rows, then residuals will be returned as an empty array
-otherwise resids = sum((b-dot(A,x)**2).
-Singular values less than s[0]*rcond are treated as zero.
-"""
-    a = asarray(a)
-    b = asarray(b)
-    one_eq = len(b.shape) == 1
-    if one_eq:
-        b = b[:, NewAxis]
-    _assertRank2(a, b)
-    m  = a.shape[0]
-    n  = a.shape[1]
-    n_rhs = b.shape[1]
-    ldb = max(n,m)
-    if m != b.shape[0]:
-        raise LinAlgError, 'Incompatible dimensions'
-    t =_commonType(a, b)
-    real_t = _array_type[0][_array_precision[t]]
-    bstar = zeros((ldb,n_rhs),t)
-    bstar[:b.shape[0],:n_rhs] = b.copy()
-    a,bstar = _castCopyAndTranspose(t, a, bstar)
-    s = zeros((min(m,n),),real_t)
-    nlvl = max( 0, int( math.log( float(min( m,n ))/2. ) ) + 1 )
-    iwork = zeros((3*min(m,n)*nlvl+11*min(m,n),), 'i')
-    if _array_kind[t] == 1: # Complex routines take different arguments
-        lapack_routine = lapack_lite.zgelsd
-        lwork = 1
-        rwork = zeros((lwork,), real_t)
-        work = zeros((lwork,),t)
-        results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
-                        0,work,-1,rwork,iwork,0 )
-        lwork = int(abs(work[0]))
-        rwork = zeros((lwork,),real_t)
-        a_real = zeros((m,n),real_t)
-        bstar_real = zeros((ldb,n_rhs,),real_t)
-        results = lapack_lite.dgelsd( m, n, n_rhs, a_real, m, bstar_real,ldb , s, rcond,
-                        0,rwork,-1,iwork,0 )
-        lrwork = int(rwork[0])
-        work = zeros((lwork,), t)
-        rwork = zeros((lrwork,), real_t)
-        results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
-                        0,work,lwork,rwork,iwork,0 )
-    else:
-        lapack_routine = lapack_lite.dgelsd
-        lwork = 1
-        work = zeros((lwork,), t)
-        results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
-                        0,work,-1,iwork,0 )
-        lwork = int(work[0])
-        work = zeros((lwork,), t)
-        results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
-                        0,work,lwork,iwork,0 )
-    if results['info'] > 0:
-        raise LinAlgError, 'SVD did not converge in Linear Least Squares'
-    resids = array([],t)
-    if one_eq:
-        x = ravel(bstar)[:n].copy()
-        if (results['rank']==n) and (m>n):
-            resids = array([sum((ravel(bstar)[n:])**2)])
-    else:
-        x = transpose(bstar)[:n,:].copy()
-        if (results['rank']==n) and (m>n):
-            resids = sum((transpose(bstar)[n:,:])**2).copy()
-    return x,resids,results['rank'],s[:min(n,m)].copy()
-
-def singular_value_decomposition(A, full_matrices=0):
-    return svd(A, 0)
-
-def eigenvectors(A):
-    w, v = eig(A)
-    return w, transpose(v)
-
-def Heigenvectors(A):
-    w, v = eigh(A)
-    return w, transpose(v)
-
-inv = inverse
-solve = solve_linear_equations
-cholesky = cholesky_decomposition
-eigvals = eigenvalues
-eigvalsh = Heigenvalues
-pinv = generalized_inverse
-det = determinant
-lstsq = linear_least_squares
-
-if __name__ == '__main__':
-    def test(a, b):
-
-        print "All numbers printed should be (almost) zero:"
-
-        x = solve_linear_equations(a, b)
-        check = b - matrixmultiply(a, x)
-        print check
-
-
-        a_inv = inverse(a)
-        check = matrixmultiply(a, a_inv)-identity(a.shape[0])
-        print check
-
-
-        ev = eigenvalues(a)
-
-        evalues, evectors = eig(a)
-        check = ev-evalues
-        print check
-
-        evectors = transpose(evectors)
-        check = matrixmultiply(a, evectors)-evectors*evalues
-        print check
-
-
-        u, s, vt = svd(a,0)
-        check = a - matrixmultiply(u*s, vt)
-        print check
-
-
-        a_ginv = generalized_inverse(a)
-        check = matrixmultiply(a, a_ginv)-identity(a.shape[0])
-        print check
-
-
-        det = determinant(a)
-        check = det-multiply.reduce(evalues)
-        print check
-
-        x, residuals, rank, sv = linear_least_squares(a, b)
-        check = b - matrixmultiply(a, x)
-        print check
-        print rank-a.shape[0]
-        print sv-s
-
-    a = array([[1.,2.], [3.,4.]])
-    b = array([2., 1.])
-    test(a, b)
-
-    a = a+0j
-    b = b+0j
-    test(a, b)
-
-