#! /bin/sh

########################################################################
##
## Copyright (C) 2006-2021 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################

# Some tests are commented out because they are known to be broken!
# Search for "# fails"

# ./build-sparse-tests.sh preset
#    creates sparse.tst with preset tests.
#    Use "test sparse.tst" from octave to run the tests.
#
# ./build-sparse-tests.sh random
#    Creates sprandom.tst with randomly generated matrices.
#    Use "test sprandom.tst" from octave to run the tests.

# build-sparse-tests.sh generates tests for real and complex sparse matrices.
# Also, we want to run both fixed tests with known outputs (quick tests)
# and longer tests with unknown outputs (thorough tests).  This requires
# two sets of tests -- one which uses preset matrices and another which
# uses randomly generated matrices.
#
# The tests are mostly identical for each case but the code is different,
# so it is important that the tests be run on all cases.  Because our test
# harness doesn't have support for looping or macros (it is only needed
# for new data types), but sh does, we use sh to generate inline versions of
# the tests for each case.
#
# Our 'macros' use shared variables as parameters.  This allows us to
# for example define A complex and include all the unary ops tests,
# then set A=real(A) and include all the unary ops tests.  Thus the
# same tests work for real and complex.  For binary tests it is even
# more complicated because we want full X sparse, sparse X full and
# sparse X sparse tested.
#
# We use the following macros:
#
#    gen_section
#        place a separator in the test file
#    gen_function
#        define the function definion
#    helper gen_specific
#        specific tests such as error handling and null input
#    helper gen_eat_zeros
#        make sure sparse-scalar ops which generate 0 work
#    gen_specific_tests
#        specific and eat zeros tests
#    helper gen_ordering_tests
#        ordered comparison operators for real valued tests
#    helper gen_sparsesparse_ordering_tests
#        ordered comparison operators for real valued sparse-sparse tests
#    helper gen_elementop_tests
#        element-wise matrix binary operators, including scalar-matrix ops.
#        horizontal/vertical concatenation are here as well.
#    helper gen_sparsesparse_elementop_tests
#        element-wise matrix binary operators, for sparse-sparse ops.
#        horizontal/vertical concatenation are here as well.
#    helper gen_divop_tests
#        left and right matrix division operators of rectangular matrices.
#        Needs QR solvers
#    helper gen_square_divop_tests
#        left and right matrix division operators of square matrices.
#    helper gen_matrixop_tests
#        rectangular matrix binary operators: *
#    helper gen_matrixdiag_tests
#        Tests extract of diag and creation of diagonal matrices using
#        diag and spdiags functions
#    helper gen_matrixreshape_tests
#        Test the reshape function on sparse matrices
#    helper print_mapper_test
#        sub-helper function of gen_mapper_tests to print individual tests
#    helper gen_mapper_tests
#        Tests all of the one argument mapper functions. There are a few
#        specific tests that abs, real and imag return real values.
#    helper gen_unaryop_tests
#        functions and operators which transform a single matrix
#    helper gen_save_tests
#        Tests the load/save functionality for ascii/binary and hdf5 formats
#    gen_scalar_tests
#        element ops for real and complex scalar and sparse
#    gen_rectangular_tests
#        unary, element, and matrix tests for a and full/sparse b
#    gen_square_tests
#        operations which require square matrices: lu, inv, \
#        A square non-singular matrix is defined from the rectangular
#        inputs A and B.
#    gen_assembly_tests
#        test for sparse constructors with 'sum' vs. 'unique'
#    gen_select_tests
#        indexing and assignment tests
#    gen_solver_tests
#        Tests the solve function with triangular/banded, etc matrices

case $1 in
    random) preset=false ;;
    preset) preset=true ;;
    '') preset=true ;;
    *) echo "build-sparse-tests.sh random|preset" && exit 1 ;;
esac

# create initial file
cat <<EOF
## !!! DO NOT EDIT !!!
## THIS IS AN AUTOMATICALLY GENERATED FILE
## modify build-sparse-tests.sh to generate the tests you need.
EOF


# define all functions


# =======================================================
# Section separator

gen_section() {
cat <<EOF

# ==============================================================

EOF
}


# =======================================================
# Specific preset tests

# =======================================================
# If a sparse operation yields zeros, then those elements
# of the returned sparse matrix should be eaten.
gen_eat_zeros() {
cat <<EOF
%% Make sure newly introduced zeros get eaten
%!assert (nnz (sparse ([bf,bf,1]).^realmax), 1)
%!assert (nnz (sparse ([1,bf,bf]).^realmax), 1)
%!assert (nnz (sparse ([bf,bf,bf]).^realmax), 0)

%!assert (nnz (sparse ([bf;bf;1]).^realmax), 1)
%!assert (nnz (sparse ([1;bf;bf]).^realmax), 1)
%!assert (nnz (sparse ([0.5;bf;bf]).^realmax), 0)

%!assert (nnz (sparse ([bf,bf,1])*realmin), 1)
%!assert (nnz (sparse ([1,bf,bf])*realmin), 1)
%!assert (nnz (sparse ([bf,bf,bf])*realmin), 0)

%!assert (nnz (sparse ([bf;bf;1])*realmin), 1)
%!assert (nnz (sparse ([1;bf;bf])*realmin), 1)
%!assert (nnz (sparse ([bf;bf;bf])*realmin), 0)

EOF
}

gen_specific() {
cat <<EOF

%!test # segfault test from edd@debian.org
%! n = 510;
%! sparse (kron ((1:n)', ones (n,1)), kron (ones (n,1), (1:n)'), ones (n));

%% segfault tests from Fabian@isas-berlin.de
%% Note that the last four do not fail, but rather give a warning
%% of a singular matrix, which is consistent with the full matrix
%% behavior.  They are therefore disabled.
%!testif HAVE_UMFPACK
%! assert (inv (sparse ([1,1;1,1+i])), sparse ([1-1i,1i;1i,-1i]), 10*eps);
%#!error inv ( sparse ([1,1;1,1]  ) );
%#!error inv ( sparse ([0,0;0,1]  ) );
%#!error inv ( sparse ([0,0;0,1+i]) );
%#!error inv ( sparse ([0,0;0,0]  ) );

%% error handling in constructor
%!error sparse (1,[2,3],[1,2,3])
%!error sparse ([1,1],[1,1],[1,2],3,3,"invalid")
%!error sparse ([1,3],[1,-4],[3,5],2,2)
%!error sparse ([1,3],[1,-4],[3,5i],2,2)
%!error sparse (-1,-1,1)
EOF
}


gen_specific_tests() {
    gen_section
    gen_specific
    gen_section
    echo '%!shared bf'
    echo '%!test bf=realmin;'
    gen_eat_zeros
    echo '%!test bf=realmin+realmin*1i;'
    gen_eat_zeros
    cat <<EOF
%!assert (nnz (sparse ([-1,realmin,realmin]).^1.5), 1)
%!assert (nnz (sparse ([-1,realmin,realmin,1]).^1.5), 2)

## Make sure scalar v==0 doesn't confuse matters
%!assert (nnz (sparse (1,1,0)), 0)
%!assert (nnz (sparse (eye (3))*0), 0)
%!assert (nnz (sparse (eye (3))-sparse (eye (3))), 0)
%!assert (full (sparse (eye (3))/0), full (eye (3)/0));

EOF
}


# =======================================================
# Main function definition

gen_function() {
    if $preset; then
        cat <<EOF
##
## test_sparse
##
##    run preset sparse tests.  All should pass.
function [passes, tests] = test_sparse
  disp ("writing test output to sptest.log");
  test ("sparse.tst", "normal", "sptest.log");
endfunction

EOF
    else
        cat <<EOF
##
## test_sprandom
##
##  total_passes=0; total_tests=0;
##  for i=1:10
##     [passes,tests] = sprandomtest;
##    total_passes += passes;
##    total_tests += tests;
##  end
##  The test log is appended to sprandomtest.log
function [passes,total] = test_sprandom
  warning ("untested --- fix the source in build-sparse-tests.sh");
  disp ("appending test output to sprandomtest.log");
  fid = fopen ("sprandomtest.log", "at");
  test ("sprandom.tst", "normal", fid);
  ##[passes, total] = test ("sprandomtest", "normal", fid);
  fclose (fid);
endfunction

EOF
    fi

}


# =======================================================
# matrix ops

# test ordered comparisons: uses as,af,bs,bf
gen_ordering_tests() {
    cat <<EOF
%% real values can be ordered (uses as,af)
%!assert (as<=bf, sparse (af<=bf))
%!assert (bf<=as, sparse (bf<=af))

%!assert (as>=bf, sparse (af>=bf))
%!assert (bf>=as, sparse (bf>=af))

%!assert (as<bf, sparse (af<bf))
%!assert (bf<as, sparse (bf<af))

%!assert (as>bf, sparse (af>bf))
%!assert (bf>as, sparse (bf>af))

EOF
}

gen_sparsesparse_ordering_tests() {
    cat <<EOF
%!assert (as<=bs, sparse (af<=bf))
%!assert (as>=bs, sparse (af>=bf))
%!assert (as<bs, sparse (af<bf))
%!assert (as>bs, sparse (af>bf))
EOF
}

# test element-wise binary operations: uses as,af,bs,bf,scalar
gen_elementop_tests() {
    cat <<EOF
%% Elementwise binary tests (uses as,af,bs,bf,scalar)
%!assert (as==bs, sparse (af==bf))
%!assert (bf==as, sparse (bf==af))

%!assert (as!=bf, sparse (af!=bf))
%!assert (bf!=as, sparse (bf!=af))

%!assert (as+bf, af+bf)
%!assert (bf+as, bf+af)

%!assert (as-bf, af-bf)
%!assert (bf-as, bf-af)

%!assert (as.*bf, sparse (af.*bf))
%!assert (bf.*as, sparse (bf.*af))

%!assert (as./bf, sparse (af./bf), 100*eps)
%!assert (bf.\as, sparse (bf.\af), 100*eps)

%!test
%! sv = as.^bf;
%! fv = af.^bf;
%! idx = find (af!=0);
%! assert (sv(:)(idx), sparse (fv(:)(idx)), 100*eps);

EOF
}

gen_sparsesparse_elementop_tests() {
    cat <<EOF
%!assert (as==bs, sparse (af==bf))
%!assert (as!=bs, sparse (af!=bf))
%!assert (as+bs, sparse (af+bf))
%!assert (as-bs, sparse (af-bf))
%!assert (as.*bs, sparse (af.*bf))
%!assert (as./bs, sparse (af./bf), 100*eps)
%!test
%! sv = as.^bs;
%! fv = af.^bf;
%! idx = find (af!=0);
%! assert(sv(:)(idx), sparse (fv(:)(idx)), 100*eps);

EOF
}

# test matrix-matrix left and right division: uses as,af,bs,bf
gen_divop_tests() {
    cat <<EOF
%% Matrix-matrix operators (uses af,as,bs,bf)
%!assert (as/bf, af/bf, 100*eps)
%!assert (af/bs, af/bf, 100*eps)
%!assert (as/bs, sparse (af/bf), 100*eps)
%!assert (bs\af', bf\af', 100*eps)
%!assert (bf\as', bf\af', 100*eps)
%!assert (bs\as', sparse (bf\af'), 100*eps)

EOF
}

# test matrix-matrix left and right division: uses as,af,bs,bf
gen_square_divop_tests() {
    cat <<EOF
%% Matrix-matrix operators (uses af,as,bs,bf)
%!assert (as/bf, af/bf, 100*eps)
%!assert (af/bs, af/bf, 100*eps)
%!assert (as/bs, sparse (af/bf), 100*eps)
%!assert (bs\af', bf\af', 100*eps)
%!assert (bf\as', bf\af', 100*eps)
%!assert (bs\as', sparse (bf\af'), 100*eps)

EOF
}

# test matrix-matrix operations: uses as,af,bs,bf
gen_matrixop_tests() {
    cat <<EOF
%% Matrix-matrix operators (uses af,as,bs,bf)
%!assert (as*bf', af*bf')
%!assert (af*bs', af*bf')
%!assert (as*bs', sparse (af*bf'))

EOF
}

# test diagonal operations
gen_matrixdiag_tests() {
    cat <<EOF
%% Matrix diagonal tests (uses af,as,bf,bs)
%!assert (diag (as), sparse (diag (af)))
%!assert (diag (bs), sparse (diag (bf)))
%!assert (diag (as,1), sparse (diag (af,1)))
%!assert (diag (bs,1), sparse (diag (bf,1)))
%!assert (diag (as,-1), sparse (diag (af,-1)))
%!assert (diag (bs,-1), sparse (diag (bf,-1)))
%!assert (diag (as(:)), sparse (diag (af(:))))
%!assert (diag (as(:),1), sparse (diag (af(:),1)))
%!assert (diag (as(:),-1), sparse (diag (af(:),-1)))
%!assert (diag (as(:)'), sparse (diag (af(:)')))
%!assert (diag (as(:)',1), sparse (diag (af(:)',1)))
%!assert (diag (as(:)',-1), sparse (diag (af(:)',-1)))
%!assert (spdiags (as,[0,1]), [diag(af,0), diag(af,1)])
%!test
%! [tb,tc] = spdiags (as);
%! assert (spdiags (tb,tc,sparse (zeros (size (as)))), as);
%! assert (spdiags (tb,tc,size (as,1),size (as,2)), as);

EOF
}

# test matrix reshape operations
gen_matrixreshape_tests() {
    cat <<EOF
%% Matrix diagonal tests (uses af,as,bf,bs)
%!assert (reshape (as,1,prod(size(as))), sparse (reshape (af,1,prod(size(af)))))
%!assert (reshape (as,prod(size(as)),1), sparse (reshape (af,prod(size(af)),1)))
%!assert (reshape (as,fliplr(size(as))), sparse (reshape (af,fliplr(size(af)))))
%!assert (reshape (bs,1,prod(size(as))), sparse (reshape (bf,1,prod(size(af)))))
%!assert (reshape (bs,prod(size(as)),1), sparse (reshape (bf,prod(size(af)),1)))
%!assert (reshape (bs,fliplr(size(as))), sparse (reshape (bf,fliplr(size(af)))))

EOF
}

# test mapper matrix operations: uses as,af
print_mapper_test() {
echo "%!assert ($1(as), sparse ($1(af)))"
}

print_real_mapper_test() {
    cat <<EOF
%!test
%! wn2s = warning ("query", "Octave:num-to-str");
%! warning ("off", "Octave:num-to-str");
%! if (isreal (af))
%!   if ($2)
%!     assert ($1(as), sparse ($1(af)));
%!   else
%!     assert ($1(as), $1(af));
%!   endif
%! endif
%! warning (wn2s.state, "Octave:num-to-str");

EOF
}

gen_mapper_tests() {
echo "%% Unary matrix tests (uses af,as)"
print_mapper_test abs
print_mapper_test acos
print_mapper_test acosh
print_mapper_test angle
print_mapper_test arg
print_mapper_test asin
print_mapper_test asinh
print_mapper_test atan
print_mapper_test atanh
print_mapper_test ceil
print_mapper_test conj
print_mapper_test cos
print_mapper_test cosh
print_mapper_test exp
print_mapper_test isfinite
print_mapper_test fix
print_mapper_test floor
print_mapper_test imag
print_mapper_test isinf
print_mapper_test isna
print_mapper_test isnan
print_mapper_test log
#print_mapper_test log10   ## fails with different NaN, not a problem
print_mapper_test real
print_mapper_test round
print_mapper_test sign
print_mapper_test sin
print_mapper_test sinh
print_mapper_test sqrt
print_mapper_test tan
print_mapper_test tanh

# Specific tests for certain mapper functions
    cat <<EOF
%!assert (issparse (abs (as))  && isreal (abs (as)))
%!assert (issparse (real (as)) && isreal (real (as)))
%!assert (issparse (imag (as)) && isreal (imag (as)))

EOF
}

gen_real_mapper_tests() {
echo "%% Unary matrix tests (uses af,as)"
print_real_mapper_test erf 1
print_real_mapper_test erfc 1
#print_real_mapper_test gamma 1
print_real_mapper_test isalnum 0
print_real_mapper_test isalpha 0
print_real_mapper_test isascii 0
print_real_mapper_test iscntrl 0
print_real_mapper_test isdigit 0
print_real_mapper_test isgraph 0
print_real_mapper_test islower 0
print_real_mapper_test isprint 0
print_real_mapper_test ispunct 0
print_real_mapper_test isspace 0
print_real_mapper_test isupper 0
print_real_mapper_test isxdigit 0
#print_real_mapper_test gammaln 1

# Specific tests for certain mapper functions
    cat <<EOF

%!test
%! wn2s = warning ("query", "Octave:num-to-str");
%! warning ("off", "Octave:num-to-str");
%! if (isreal (af))
%!   assert (tolower (as), as);
%!   assert (toupper (as), as);
%! endif
%! warning (wn2s.state, "Octave:num-to-str");

EOF
}

# test matrix operations: uses as,af
gen_unaryop_tests() {
    cat <<EOF
%% Unary matrix tests (uses af,as)
%!assert (issparse (as))
%!assert (!issparse (af))
%!assert (! (issparse (af) && iscomplex (af)))
%!assert (! (issparse (af) && isreal (af)))
%!assert (sum (as), sparse (sum (af)))
%!assert (sum (as,1), sparse (sum (af,1)))
%!assert (sum (as,2), sparse (sum (af,2)))
%!assert (cumsum (as), sparse (cumsum (af)))
%!assert (cumsum (as,1), sparse (cumsum (af,1)))
%!assert (cumsum (as,2), sparse (cumsum (af,2)))
%!assert (sumsq (as), sparse (sumsq (af)))
%!assert (sumsq (as,1), sparse (sumsq (af,1)))
%!assert (sumsq (as,2), sparse (sumsq (af,2)))
%!assert (prod (as), sparse (prod (af)))
%!assert (prod (as,1), sparse (prod (af,1)))
%!assert (prod (as,2), sparse (prod (af,2)))
%!assert (cumprod (as), sparse (cumprod (af)))
%!assert (cumprod (as,1), sparse (cumprod (af,1)))
%!assert (cumprod (as,2), sparse (cumprod (af,2)))

%!assert (min (as), sparse (min (af)))
%!assert (full (min (as(:))), min (af(:)))
%!assert (min (as,[],1), sparse (min (af,[],1)))
%!assert (min (as,[],2), sparse (min (af,[],2)))
%!assert (min (as,[],1), sparse (min (af,[],1)))
%!assert (min (as,0), sparse (min (af,0)))
%!assert (min (as,bs), sparse (min (af,bf)))
%!assert (max (as), sparse (max (af)))
%!assert (full (max (as(:))), max (af(:)))
%!assert (max (as,[],1), sparse (max (af,[],1)))
%!assert (max (as,[],2), sparse (max (af,[],2)))
%!assert (max (as,[],1), sparse (max (af,[],1)))
%!assert (max (as,0), sparse (max (af,0)))
%!assert (max (as,bs), sparse (max (af,bf)))

%!assert (as==as)
%!assert (as==af)
%!assert (af==as)
%!test
%! [ii,jj,vv,nr,nc] = find (as);
%! assert (af, full (sparse (ii,jj,vv,nr,nc)));
%!assert (nnz (as), sum (af(:)!=0))
%!assert (nnz (as), nnz (af))
%!assert (issparse (as.'))
%!assert (issparse (as'))
%!assert (issparse (-as))
%!assert (!as, sparse (!af))
%!assert (as.', sparse (af.'))
%!assert (as',  sparse (af'))
%!assert (-as, sparse (-af))
%!assert (!as, sparse (!af))
%!error [i,j] = size (af);as(i-1,j+1);
%!error [i,j] = size (af);as(i+1,j-1);
%!test
%! [Is,Js,Vs] = find (as);
%! [If,Jf,Vf] = find (af);
%! assert (Is, If);
%! assert (Js, Jf);
%! assert (Vs, Vf);
%!error as(0,1)
%!error as(1,0)
%!assert (find (as), find (af))
%!test
%! [i,j,v] = find (as);
%! [m,n] = size (as);
%! x = sparse (i,j,v,m,n);
%! assert (x, as);
%!test
%! [i,j,v,m,n] = find (as);
%! x = sparse (i,j,v,m,n);
%! assert (x, as);
%!assert (issparse (horzcat (as,as)))
%!assert (issparse (vertcat (as,as)))
%!assert (issparse (cat (1,as,as)))
%!assert (issparse (cat (2,as,as)))
%!assert (issparse ([as,as]))
%!assert (issparse ([as;as]))
%!assert (horzcat (as,as), sparse ([af,af]))
%!assert (vertcat (as,as), sparse ([af;af]))
%!assert (horzcat (as,as,as), sparse ([af,af,af]))
%!assert (vertcat (as,as,as), sparse ([af;af;af]))
%!assert ([as,as], sparse ([af,af]))
%!assert ([as;as], sparse ([af;af]))
%!assert ([as,as,as], sparse ([af,af,af]))
%!assert ([as;as;as], sparse ([af;af;af]))
%!assert (cat (2,as,as), sparse ([af,af]))
%!assert (cat (1,as,as), sparse ([af;af]))
%!assert (cat (2,as,as,as), sparse ([af,af,af]))
%!assert (cat (1,as,as,as), sparse ([af;af;af]))
%!assert (issparse ([as,af]))
%!assert (issparse ([af,as]))
%!assert ([as,af], sparse ([af,af]))
%!assert ([as;af], sparse ([af;af]))

EOF
}

# operations which require square matrices.
gen_square_tests() {
# The \ and / operator tests on square matrices
    gen_square_divop_tests

    cat <<EOF
%!testif HAVE_UMFPACK
%! assert(det(bs+speye(size(bs))), det(bf+eye(size(bf))), 100*eps*abs(det(bf+eye(size(bf)))));

%!testif HAVE_UMFPACK
%! [l,u] = lu (sparse ([1,1;1,1]));
%! assert (l*u, [1,1;1,1], 10*eps);

%!testif HAVE_UMFPACK
%! [l,u] = lu (sparse ([1,1;1,1+i]));
%! assert (l, sparse ([1,2,2],[1,1,2],1), 10*eps);
%! assert (u, sparse ([1,1,2],[1,2,2],[1,1,1i]), 10*eps);

%!testif HAVE_UMFPACK   # permuted LU
%! [L,U] = lu (bs);
%! assert (L*U, bs, 1e-10);

%!testif HAVE_UMFPACK   # simple LU + row permutations
%! [L,U,P] = lu (bs);
%! assert (P'*L*U, bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

%!testif HAVE_UMFPACK   # simple LU + row/col permutations
%! [L,U,P,Q] = lu (bs);
%! assert (P'*L*U*Q', bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

%!testif HAVE_UMFPACK   # LU with vector permutations
%! [L,U,P,Q] = lu (bs,'vector');
%! assert (L(P,:)*U(:,Q), bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

%!testif HAVE_UMFPACK   # LU with scaling
%! [L,U,P,Q,R] = lu (bs);
%! assert (R*P'*L*U*Q', bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

%!testif HAVE_UMFPACK   # inverse
%! assert (inv (bs)*bs, sparse (eye (rows (bs))), 1e-10);

%!assert (bf\as', bf\af', 100*eps)
%!assert (bs\af', bf\af', 100*eps)
%!assert (bs\as', sparse (bf\af'), 100*eps)

EOF
}

# Cholesky tests
gen_cholesky_tests() {
    cat <<EOF
%!testif HAVE_CHOLMOD
%! assert (chol (bs)'*chol (bs), bs, 1e-10);
%!testif HAVE_CHOLMOD
%! assert (chol (bs,'lower')*chol (bs,'lower')', bs, 1e-10);
%!testif HAVE_CHOLMOD
%! assert (chol (bs,'lower'), chol (bs)', 1e-10);

%!testif HAVE_CHOLMOD   # Return Partial Cholesky factorization
%! [RS,PS] = chol (bs);
%! assert (RS'*RS, bs, 1e-10);
%! assert (PS, 0);
%! [LS,PS] = chol (bs,'lower');
%! assert (LS*LS', bs, 1e-10);
%! assert (PS, 0);

%!testif HAVE_CHOLMOD   # Permuted Cholesky factorization
%! [RS,PS,QS] = chol (bs);
%! assert (RS'*RS, QS*bs*QS', 1e-10);
%! assert (PS, 0);
%! [LS,PS,QS] = chol (bs,'lower');
%! assert (LS*LS', QS*bs*QS', 1e-10);
%! assert (PS, 0);

EOF
}

# test scalar operations: uses af and real scalar bf; modifies as,bf,bs
gen_scalar_tests() {
    echo '%!test as = sparse (af);'
    echo '%!test bs = bf;'
    gen_elementop_tests
    gen_ordering_tests
    echo '%!test bf = bf+1i;'
    echo '%!test bs = bf;'
    gen_elementop_tests
}

# test matrix operations: uses af and bf; modifies as,bs
gen_rectangular_tests() {
    echo '%!test as = sparse(af);'
    echo '%!test bs = sparse(bf);'
    gen_mapper_tests
    gen_real_mapper_tests
    gen_unaryop_tests
    gen_elementop_tests
    gen_sparsesparse_elementop_tests
    gen_matrixop_tests
    # gen_divop_tests # Disable rectangular \ and / for now
    gen_matrixdiag_tests
    gen_matrixreshape_tests
    cat <<EOF
%!testif HAVE_UMFPACK   # permuted LU
%! [L,U] = lu (bs);
%! assert (L*U, bs, 1e-10);

%!testif HAVE_UMFPACK   # simple LU + row permutations
%! [L,U,P] = lu (bs);
%! assert (P'*L*U, bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

%!testif HAVE_UMFPACK   # simple LU + row/col permutations
%! [L,U,P,Q] = lu (bs);
%! assert (P'*L*U*Q', bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

%!testif HAVE_UMFPACK   # LU with vector permutations
%! [L,U,P,Q] = lu (bs,'vector');
%! assert (L (P,:)*U (:,Q), bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

%!testif HAVE_UMFPACK   # LU with scaling
%! [L,U,P,Q,R] = lu (bs);
%! assert (R*P'*L*U*Q', bs, 1e-10);
%! ## triangularity
%! [i,j,v] = find (L);
%! assert (i-j>=0);
%! [i,j,v] = find (U);
%! assert (j-i>=0);

EOF
}


# =======================================================
# sparse assembly tests

gen_assembly_tests() {
cat <<EOF
%%Assembly tests
%!test
%! m = max ([m;r(:)]);
%! n = max ([n;c(:)]);
%! funiq = fsum = zeros (m,n);
%! funiq(r(:) + m*(c(:)-1) ) = ones (size (r(:)));
%! funiq = sparse (funiq);
%! for k=1:length (r)
%!   fsum(r(k),c(k)) += 1;
%! endfor
%! fsum = sparse (fsum);
%!assert (sparse (r,c,1), sparse (fsum(1:max(r), 1:max(c))))
%!assert (sparse (r,c,1,"sum"), sparse (fsum(1:max (r),1:max (c))))
%!assert (sparse (r,c,1,"unique"), sparse (funiq(1:max (r),1:max (c))))
%!assert (sparse (r,c,1,m,n), sparse (fsum))
%!assert (sparse (r,c,1,m,n,"sum"), sparse (fsum))
%!assert (sparse (r,c,1,m,n,"unique"), sparse (funiq))

%!assert (sparse (r,c,1i), sparse (fsum(1:max (r),1:max (c))*1i))
%!assert (sparse (r,c,1i,"sum"), sparse (fsum(1:max (r),1:max (c))*1i))
%!assert (sparse (r,c,1i,"unique"), sparse (funiq(1:max (r),1:max (c))*1i))
%!assert (sparse (r,c,1i,m,n), sparse (fsum*1i))
%!assert (sparse (r,c,1i,m,n,"sum"), sparse (fsum*1i))
%!assert (sparse (r,c,1i,m,n,"unique"), sparse (funiq*1i))

%!test
%! if (issparse (funiq))
%!   assert (sparse (full (1i*funiq)), sparse (1i*funiq));
%! endif

%!assert (sparse (full (funiq)), funiq)


EOF
}

# =======================================================
# sparse selection tests

gen_scalar_select_tests () {
    cat <<EOF
%!assert (sparse (42)([1,1]), sparse ([42,42]))
%!assert (sparse (42*1i)([1,1]), sparse ([42,42].*1i))
EOF
}

gen_select_tests() {
    cat <<EOF
%!test as = sparse (af);

%% Point tests
%!test idx = ridx(:) + rows (as) * (cidx (:)-1);
%!assert (sparse (as(idx)), sparse (af(idx)))
%!assert (as(idx), sparse (af(idx)))
%!assert (as(idx'), sparse (af(idx')))
%!assert (as(flipud (idx(:))), sparse (af(flipud (idx(:)))))
%!assert (as([idx,idx]), sparse (af([idx,idx])))
%!assert (as(reshape ([idx;idx], [1,length(idx),2])), sparse(af(reshape ([idx;idx], [1,length(idx),2]))))

%% Slice tests
%!assert (as(ridx,cidx), sparse (af(ridx,cidx)))
%!assert (as(ridx,:), sparse (af(ridx,:)))
%!assert (as(:,cidx), sparse (af(:,cidx)))
%!assert (as(:,:), sparse (af(:,:)))
%!assert (as((size (as,1):-1:1),:), sparse (af((size (af,1):-1:1),:)))
%!assert (as(:,(size (as,2):-1:1)), sparse (af(:, (size (af,2):-1:1))))

%% Indexing tests
%!assert (full (as([1,1],:)), af([1,1],:))
%!assert (full (as(:,[1,1])), af(:,[1,1]))
%!test
%! [i,j,v] = find (as);
%! assert (as(i(1),j(1))([1,1]), sparse ([v(1), v(1)]));

%% Assignment test
%!test
%! ts = as; ts(:,:) = ts(fliplr (1:size (as,1)),:);
%! tf = af; tf(:,:) = tf(fliplr (1:size (af,1)),:);
%! assert (ts, sparse (tf));
%!test
%! ts = as; ts(fliplr (1:size (as,1)),:) = ts;
%! tf = af; tf(fliplr (1:size (af,1)),:) = tf;
%! assert (ts, sparse (tf));
%!test
%! ts = as; ts(:,fliplr (1:size (as,2))) = ts;
%! tf = af; tf(:,fliplr (1:size (af,2))) = tf;
%! assert (ts, sparse (tf));
%!test
%! ts(fliplr (1:size (as,1))) = as(:,1);
%! tf(fliplr (1:size (af,1))) = af(:,1);
%! assert (ts, sparse (tf));

%% Deletion tests
%!test
%! ts = as; ts(1,:) = []; tf = af; tf(1,:) = [];
%! assert (ts, sparse (tf));
%!test
%! ts = as; ts(:,1) = []; tf = af; tf(:,1) = [];
%! assert (ts, sparse (tf));

%% Test "end" keyword
%!assert (full (as(end)), af(end))
%!assert (full (as(1,end)), af(1,end))
%!assert (full (as(end,1)), af(end,1))
%!assert (full (as(end,end)), af(end,end))
%!assert (as(2:end,2:end), sparse (af(2:end,2:end)))
%!assert (as(1:end-1,1:end-1), sparse (af(1:end-1,1:end-1)))
EOF
}

# =======================================================
# sparse save and load tests

gen_save_tests() {
    cat <<EOF
%!test # save ascii
%! savefile = tempname ();
%! as_save = as;
%! save ("-text", savefile, "bf", "as_save", "af");
%! clear as_save;
%! load (savefile, "as_save");
%! unlink (savefile);
%! assert (as_save, sparse (af));
%!test # save binary
%! savefile = tempname ();
%! as_save = as;
%! save ("-binary", savefile, "bf", "as_save", "af");
%! clear as_save;
%! load (savefile, "as_save");
%! unlink (savefile);
%! assert (as_save, sparse (af));
%!testif HAVE_HDF5   # save hdf5
%! savefile = tempname ();
%! as_save = as;
%! save ("-hdf5", savefile, "bf", "as_save", "af");
%! clear as_save;
%! load (savefile, "as_save");
%! unlink (savefile);
%! assert (as_save, sparse (af));
## FIXME: We should skip (or mark as a known bug) the test for
## saving sparse matrices to MAT files when using 64-bit indexing since
## that is not implemented yet.
%!test # save matlab
%! savefile = tempname ();
%! as_save = as;
%! save ("-mat", savefile, "bf", "as_save", "af");
%! clear as_save;
%! load (savefile, "as_save");
%! unlink (savefile);
%! assert (as_save, sparse (af));
EOF
}

# =============================================================
# Specific solver tests for matrices that will test all of the solver
# code. Uses alpha and beta
gen_solver_tests() {

if $preset; then
  cat <<EOF
%! n=8;
%! lf=diag (1:n); lf(n-1,1)=0.5*alpha; lf(n,2)=0.25*alpha; ls=sparse (lf);
%! uf=diag (1:n); uf(1,n-1)=2*alpha; uf(2,n)=alpha; us=sparse (uf);
%! ts=spdiags (ones (n,3),-1:1,n,n) + diag (1:n); tf = full (ts);
EOF
else
  cat <<EOF
%! n = floor (lognrnd (8,2)+1)';
%! ls = tril (sprandn (8,8,0.2),-1).*alpha + n*speye (8); lf = full (ls);
%! us = triu (sprandn (8,8,0.2),1).*alpha + n*speye (8); uf = full (us);
%! ts = spdiags (randn (8,3),-1:1,8,8).*alpha; tf = full (ts);
EOF
fi

cat <<EOF
%! df = diag (1:n).* alpha; ds = sparse (df);
%! pdf = df(randperm (n), randperm (n));
%! pds = sparse (pdf);
%! plf = lf(randperm (n), randperm (n));
%! pls = sparse (plf);
%! puf = uf(randperm (n), randperm (n));
%! pus = sparse (puf);
%! bs = spdiags (repmat ([1:n]',1,4),-2:1,n,n).*alpha;
%! bf = full (bs);
%! cf = lf + lf'; cs = sparse (cf);
%! bcf = bf + bf'; bcs = sparse (bcf);
%! tcf = tf + tf'; tcs = sparse (tcf);
%! xf = diag (1:n) + fliplr (diag (1:n)).*beta;
%! xs = sparse (xf);
%!assert (ds\xf, df\xf, 1e-10)
%!assert (ds\xs, sparse (df\xf), 1e-10)
%!assert (pds\xf, pdf\xf, 1e-10)
%!assert (pds\xs, sparse (pdf\xf), 1e-10)
%!assert (ls\xf, lf\xf, 1e-10)
%!assert (sparse (ls\xs), sparse (lf\xf), 1e-10)
%!testif HAVE_UMFPACK
%! assert (pls\xf, plf\xf, 1e-10);
%!testif HAVE_UMFPACK
%! assert (sparse (pls\xs), sparse (plf\xf), 1e-10);
%!assert (us\xf, uf\xf, 1e-10)
%!assert (sparse (us\xs), sparse (uf\xf), 1e-10)
%!testif HAVE_UMFPACK
%! assert (pus\xf, puf\xf, 1e-10);
%!testif HAVE_UMFPACK
%! assert (sparse (pus\xs), sparse (puf\xf), 1e-10);
%!assert (bs\xf, bf\xf, 1e-10)
%!assert (sparse (bs\xs), sparse (bf\xf), 1e-10)
%!testif HAVE_UMFPACK
%! assert (cs\xf, cf\xf, 1e-10);
%!testif HAVE_UMFPACK
%! assert (sparse (cs\xs), sparse (cf\xf), 1e-10);
%!testif HAVE_UMFPACK
%! assert (bcs\xf, bcf\xf, 1e-10);
%!testif HAVE_UMFPACK
%! assert (sparse (bcs\xs), sparse (bcf\xf), 1e-10);
%!assert (ts\xf, tf\xf, 1e-10)
%!assert (sparse (ts\xs), sparse (tf\xf), 1e-10)
%!assert (tcs\xf, tcf\xf, 1e-10)
%!assert (sparse (tcs\xs), sparse (tcf\xf), 1e-10)

EOF

cat <<EOF
%% QR solver tests

%!function f (a, sz, feps)
%! b = randn (sz);
%! x = a \ b;
%! assert (a * x, b, feps);
%! b = randn (sz) + 1i*randn (sz);
%! x = a \ b;
%! assert (a * x, b, feps);
%! b = sprandn (sz(1),sz(2),0.2);
%! x = a \ b;
%! assert (sparse (a * x), b, feps);
%! b = sprandn (sz(1),sz(2),0.2) + 1i*sprandn (sz(1),sz(2),0.2);
%! x = a \ b;
%! assert (sparse (a * x), b, feps);
%!endfunction
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! a = alpha*sprandn (10,11,0.2) + speye (10,11);
%! f (a,[10,2],1e-10);
%! ## Test this by forcing matrix_type, as can't get a certain
%! ## result for over-determined systems.
%! a = alpha*sprandn (10,10,0.2) + speye (10,10);
%! matrix_type (a, "Singular");
%! f (a,[10,2],1e-10);

%% Rectanguar solver tests that don't use QR

%!test
%! ds = alpha * spdiags ([1:11]',0,10,11);
%! df = full (ds);
%! xf = beta * ones (10,2);
%! xs = speye (10,10);
%!assert (ds\xf, df\xf, 100*eps)
%!assert (ds\xs, sparse (df\xs), 100*eps)
%!test
%! pds = ds([2,1,3:10],:);
%! pdf = full (pds);
%!assert (pds\xf, pdf\xf, 100*eps)
%!assert (pds\xs, sparse (pdf\xs), 100*eps)
%!test
%! ds = alpha * spdiags ([1:11]',0,11,10);
%! df = full (ds);
%! xf = beta * ones (11,2);
%! xs = speye (11,11);
%!assert (ds\xf, df\xf, 100*eps)
%!assert (ds\xs, sparse (df\xs), 100*eps)
%!test
%! pds = ds([2,1,3:11],:);
%! pdf = full (pds);
%!assert (pds\xf, pdf\xf, 100*eps)
%!assert (pds\xs, sparse (pdf\xs), 100*eps)
%!test
%! us = alpha*[[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]];
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! assert (us*(us\xf), xf, 100*eps);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! assert (us*(us\xs), xs, 100*eps);
%!test
%! pus = us(:,[2,1,3:12]);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! assert (pus*(pus\xf), xf, 100*eps);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! assert (pus*(pus\xs), xs, 100*eps);
%!test
%! us = alpha*[speye(11,9),[1;sparse(8,1);1;0]];
%!testif HAVE_CXSPARSE
%! [c,r] = qr (us, xf);
%! assert (us\xf, r\c, 100*eps);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! [c,r] = qr (us, xs);
%! r = matrix_type (r, "Singular"); ## Force Matrix Type
%! assert (us\xs, r\c, 100*eps);
%!test
%! pus = us(:,[1:8,10,9]);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! [c,r] = qr (pus, xf);
%! r = matrix_type (r, "Singular"); ## Force Matrix Type
%! assert (pus\xf, r\c, 100*eps);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! [c,r] = qr (pus, xs);
%! r = matrix_type (r, "Singular"); ## Force Matrix Type
%! assert (pus\xs, r\c, 100*eps);
%!test
%! ls = alpha*[speye(9,11);[1, sparse(1,8),1,0]];
%! xf = beta * ones (10,2);
%! xs = speye (10,10);
%!assert (ls*(ls\xf), xf, 100*eps)
%!assert (ls*(ls\xs), xs, 100*eps)
%!test
%! pls = ls([1:8,10,9],:);
%!assert (pls*(pls\xf), xf, 100*eps)
%!assert (pls*(pls\xs), xs, 100*eps)
%!test
%! ls = alpha*[speye(10,10), sparse(10,1);[1;1], sparse(2,9),[1;1]];
%! xf = beta * ones (12,2);
%! xs = speye (12,12);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! [c,r] = qr (ls, xf);
%! assert (ls\xf, r\c, 100*eps);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! [c,r] = qr (ls, xs);
%! r = matrix_type (r, "Singular"); ## Force Matrix Type
%! assert (ls\xs, r\c, 100*eps);
%!test
%! pls = ls(:,[1:8,10,9]);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! [c,r] = qr (pls, xf);
%! r = matrix_type (r, "Singular"); ## Force Matrix Type
%! assert (pls\xf, r\c, 100*eps);
%!testif HAVE_UMFPACK, HAVE_CXSPARSE
%! [c,r] = qr (pls, xs);
%! r = matrix_type (r, "Singular"); ## Force Matrix Type
%! assert (pls\xs, r\c, 100*eps);

EOF
}


# =============================================================
# Putting it all together: defining the combined tests


# initial function
gen_function
gen_section

# specific tests
if $preset; then
    gen_specific_tests
    gen_section
fi

# scalar operations
echo '%!shared as,af,bs,bf'
if $preset; then
    echo '%!test af=[1+1i,2-1i,0,0;0,0,0,3+2i;0,0,0,4];'
    echo '%!test bf=3;'
else
    cat <<EOF
%!test
%! % generate m,n from 1 to <5000
%! m = floor (lognrnd (8,2)+1);
%! n = floor (lognrnd (8,2)+1);
%! as = sprandn (m,n,0.3);
%! af = full (as + 1i*sprandn (as));
%! bf = randn;
EOF
fi

gen_scalar_tests
gen_section

# rectangular operations
if $preset; then
    echo '%!test af=[1+1i,2-1i,0,0;0,0,0,3+2i;0,0,0,4];'
    echo '%!test bf=[0,1-1i,0,0;2+1i,0,0,0;3-1i,2+3i,0,0];'
else
    cat <<EOF
%!test
%! m = floor (lognrnd (8,2)+1);
%! n = floor (lognrnd (8,2)+1);
%! as = sprandn (m,n,0.3);
%! af = full (as + 1i*sprandn (as));
%! bs = sprandn (m,n,0.3);
%! bf = full (bs + 1i*sprandn (bs));
EOF
fi

gen_rectangular_tests
gen_section
gen_save_tests
gen_section
echo '%!test bf = real (bf);'
gen_rectangular_tests
gen_section
gen_sparsesparse_ordering_tests
gen_section
echo '%!test af = real (af);'
gen_rectangular_tests
gen_section
gen_save_tests
gen_section
echo '%!test bf = bf+1i*(bf!=0);'
gen_rectangular_tests
gen_section

# square operations
if $preset; then
    echo '%!test af = [1+1i,2-1i,0,0;0,0,0,3+2i;0,0,0,4];'
    echo '%! as = sparse (af);'
    echo '%!test bf = [0,1-1i,0,0;2+1i,0,0,0;3-1i,2+3i,0,0];'
else
    cat <<EOF
%!test
%! m = floor (lognrnd (8,2)+1);
%! n = floor (lognrnd (8,2)+1);
%! as = sprandn (m,n,0.3);
%! af = full (as + 1i*sprandn (as));
%! bs = sprandn (m,n,0.3);
%! bf = full (bs + 1i*sprandn (bs));
EOF
fi

cat <<EOF
%!test ;# invertible matrix
%! bf = af'*bf+max (abs ([af(:);bf(:)]))*sparse (eye (columns (as)));
%! bs = sparse (bf);

EOF

gen_square_tests
gen_section
echo '%!test bf = real (bf);'
echo '%! bs = sparse (bf);'
gen_square_tests
gen_section
echo '%!test af = real (af);'
echo '%! as = sparse (af);'
gen_square_tests
gen_section
echo '%!test bf = bf+1i*(bf!=0);'
echo '%! bs = sparse (bf);'
gen_square_tests
gen_section

# cholesky tests
if $preset; then
  echo '%!test bf = [5,0,1+1i,0;0,5,0,1-2i;1-1i,0,5,0;0,1+2i,0,5];'
  echo '%! bs = sparse (bf);'
else
  echo '# This has a small chance of failing to create a positive definite matrix'
  echo '%!test n = floor (lognrnd (8,2)+1)'
  echo '%! bs = n*speye (n,n) + sprandn (n,n,0.3);'
  echo '%! bf = full (bs);'
fi

gen_cholesky_tests
gen_section
echo '%!test bf = real (bf);'
echo '%! bs = sparse (bf);'
gen_cholesky_tests
gen_section

# assembly tests
echo '%!shared r,c,m,n,fsum,funiq'
if $use_preset; then
    cat <<EOF
%!test
%! r = [1,1,2,1,2,3];
%! c = [2,1,1,1,2,1];
%! m = n = 0;
EOF
else
    cat <<EOF
%!test
%! % generate m,n from 1 to <5000
%! m = floor (lognrnd (8,2)+1);
%! n = floor (lognrnd (8,2)+1);
%! nz = ceil ((m+n)/2);
%! r = floor (rand (5,nz)*n)+1;
%! c = floor (rand (5,nn)*m)+1;
EOF
fi
gen_assembly_tests #includes real and complex tests
gen_section

# slicing tests
echo '%!shared ridx,cidx,idx,as,af'
if $use_preset; then
    cat <<EOF
%!test
%! af = [1+1i,2-1i,0,0;0,0,0,3+2i;0,0,0,4];
%! ridx = [1,3];
%! cidx = [2,3];
EOF
else
    cat <<EOF
%!test
%! % generate m,n from 1 to <5000
%! m = floor (lognrnd (8,2)+1);
%! n = floor (lognrnd (8,2)+1);
%! as = sprandn (m,n,0.3);
%! af = full (as + 1i*sprandn (as));
%! ridx = ceil (m*rand (1,ceil (rand*m));
%! cidx = ceil (n*rand (1,ceil (rand*n));
EOF
fi
gen_scalar_select_tests
gen_select_tests
echo '%!test af = real (af);'
gen_select_tests
gen_section
echo '%!shared alpha,beta,df,pdf,lf,plf,uf,puf,bf,cf,bcf,tf,tcf,xf,ds,pds,ls,pls,us,pus,bs,cs,bcs,ts,tcs,xs'
echo '%!test alpha=1; beta=1;'
gen_solver_tests
echo '%!test alpha=1; beta=1i;'
gen_solver_tests
echo '%!test alpha=1i; beta=1;'
gen_solver_tests
echo '%!test alpha=1i; beta=1i;'
gen_solver_tests
gen_section
