test_that('basic goedel composition', {
    R <- matrix(c(0.1, 0.6, 1, 0, 0, 0,
                  0, 0.3, 0.7, 0.9, 1, 1,
                  0, 0, 0.6, 0.8, 1, 0,
                  0, 1, 0.5, 0, 0, 0,
                  0, 0, 1, 1, 0, 0), byrow=TRUE, nrow=5)

    S <- matrix(c(0.9, 1, 0.9, 1,
                  1, 1, 1, 1,
                  0.1, 0.2, 0, 0.2,
                  0, 0, 0, 0,
                  0.7, 0.6, 0.5, 0.4,
                  1, 0.9, 0.7, 0.6), byrow=TRUE, nrow=6)

    RS <- matrix(c(0.6, 0.6, 0.6, 0.6,
                   1, 0.9, 0.7, 0.6,
                   0.7, 0.6, 0.5, 0.4,
                   1, 1, 1, 1,
                   0.1, 0.2, 0, 0.2), byrow=TRUE, nrow=5)

    expect_that(compose(R, S, alg='goedel', type='basic'), equals(RS))
})

test_that('basic goguen composition', {
    R <- matrix(c(0.1, 0.6, 1, 0, 0, 0,
                  0, 0.3, 0.7, 0.9, 1, 1,
                  0, 0, 0.6, 0.8, 1, 0,
                  0, 1, 0.5, 0, 0, 0,
                  0, 0, 1, 1, 0, 0), byrow=TRUE, nrow=5)

    S <- matrix(c(0.9, 1, 0.9, 1,
                  1, 1, 1, 1,
                  0.1, 0.2, 0, 0.2,
                  0, 0, 0, 0,
                  0.7, 0.6, 0.5, 0.4,
                  1, 0.9, 0.7, 0.6), byrow=TRUE, nrow=6)

    RS <- matrix(c(0.6, 0.6, 0.6, 0.6,
                   1, 0.9, 0.7, 0.6,
                   0.7, 0.6, 0.5, 0.4,
                   1, 1, 1, 1,
                   0.1, 0.2, 0, 0.2), byrow=TRUE, nrow=5)

    expect_that(compose(R, S, alg='goguen', type='basic'), equals(RS))
})

test_that('basic lukasiewicz composition', {
    R <- matrix(c(0.4, 0.9, 1, 0.9, 1, 0.6,
                  0.9, 0.5, 0, 0, 0, 0.2,
                  0, 0.9, 0.5, 1, 0.9, 1,
                  0.2, 1, 0, 0.2, 0.5, 0,
                  0.3, 1, 0.6, 1, 0.9, 0.9), byrow=TRUE, nrow=5)

    S <- matrix(c(0.1, 0.9, 0.2, 0,
                  0.8, 0.4, 1, 1,
                  0, 0, 0.8, 0.6,
                  0.4, 0, 1, 1,
                  0.9, 0.1, 1, 1,
                  0.2, 0, 0.6, 1), byrow=TRUE, nrow=6)

    RS <- matrix(c(0.9, 0.3, 1, 1,
                   0.3, 0.8, 0.5, 0.5,
                   0.8, 0.3, 1, 1,
                   0.8, 0.4, 1, 1,
                   0.8, 0.4, 1, 1), byrow=TRUE, nrow=5)

    expect_that(compose(R, S, alg='lukas', type='basic'), equals(RS))
})

test_that('lukasiewicz bandler-kohout subproduct composition', {
    R <- matrix(c(0.4, 0.9, 1, 0.9, 1, 0.6,
                  0.9, 0.5, 0, 0, 0, 0.2,
                  0, 0.9, 0.5, 1, 0.9, 1,
                  0.2, 1, 0, 0.2, 0.5, 0,
                  0.3, 1, 0.6, 1, 0.9, 0.9), byrow=TRUE, nrow=5)

    S <- matrix(c(0.1, 0.9, 0.2, 0,
                  0.8, 0.4, 1, 1,
                  0, 0, 0.8, 0.6,
                  0.4, 0, 1, 1,
                  0.9, 0.1, 1, 1,
                  0.2, 0, 0.6, 1), byrow=TRUE, nrow=6)

    RS <- matrix(c(0, 0, 0.8, 0.6,
                   0.2, 0.8, 0.3, 0.1,
                   0.2, 0, 0.6, 1,
                   0.8, 0.4, 1, 0.8,
                   0.3, 0, 0.7, 0.7), byrow=TRUE, nrow=5)

    expect_that(compose(R, S, alg='lukas', type='sub'), equals(RS))
})



test_that('lukasiewicz bandler-kohout superproduct composition', {
    R <- matrix(c(0.4, 0.9, 1, 0.9, 1, 0.6,
                  0.9, 0.5, 0, 0, 0, 0.2,
                  0, 0.9, 0.5, 1, 0.9, 1,
                  0.2, 1, 0, 0.2, 0.5, 0,
                  0.3, 1, 0.6, 1, 0.9, 0.9), byrow=TRUE, nrow=5)

    S <- matrix(c(0.1, 0.9, 0.2, 0,
                  0.8, 0.4, 1, 1,
                  0, 0, 0.8, 0.6,
                  0.4, 0, 1, 1,
                  0.9, 0.1, 1, 1,
                  0.2, 0, 0.6, 1), byrow=TRUE, nrow=6)

    RS <- matrix(c(1, 0.5, 0.9, 0.6,
                   0.1, 0.9, 0, 0,
                   0.9, 0.1, 0.7, 0.9,
                   0.6, 0.3, 0.2, 0,
                   1, 0.4, 0.8, 0.9), byrow=TRUE, nrow=5)


    expect_that(compose(R, S, alg='lukas', type='super'), equals(RS))
})



test_that('lukasiewicz bandler-kohout square composition', {
    R <- matrix(c(0.4, 0.9, 1, 0.9, 1, 0.6,
                  0.9, 0.5, 0, 0, 0, 0.2,
                  0, 0.9, 0.5, 1, 0.9, 1,
                  0.2, 1, 0, 0.2, 0.5, 0,
                  0.3, 1, 0.6, 1, 0.9, 0.9), byrow=TRUE, nrow=5)

    S <- matrix(c(0.1, 0.9, 0.2, 0,
                  0.8, 0.4, 1, 1,
                  0, 0, 0.8, 0.6,
                  0.4, 0, 1, 1,
                  0.9, 0.1, 1, 1,
                  0.2, 0, 0.6, 1), byrow=TRUE, nrow=6)

    RS <- matrix(c(0, 0, 0.8, 0.6,
                   0.1, 0.8, 0, 0,
                   0.2, 0, 0.6, 0.9,
                   0.6, 0.3, 0.2, 0,
                   0.3, 0, 0.7, 0.7), byrow=TRUE, nrow=5)


    expect_that(compose(R, S, alg='lukas', type='square'), equals(RS))
})

test_that('basic goedel composition with e', {
    R <- matrix(c(0.1, 0.6, 1, 0, 0, 0,
                  0, 0.3, 0.7, 0.9, 1, 1,
                  0, 0, 0.6, 0.8, 1, 0,
                  0, 1, 0.5, 0, 0, 0,
                  0, 0, 1, 1, 0, 0), byrow=TRUE, nrow=5)

    S <- matrix(c(0.9, 1, 0.9, 1,
                  1, 1, 1, 1,
                  0.1, 0.2, 0, 0.2,
                  0, 0, 0, 0,
                  0.7, 0.6, 0.5, 0.4,
                  1, 0.9, 0.7, 0.6), byrow=TRUE, nrow=6)

    E <- matrix(c(0, 0, 0, 0,
                  0, 0, 0, 0,
                  0, 0, 0, 0,
                  0, 0, 0, 0,
                  0, 0, 0, 0,
                  0, 0, 0, 0), byrow=TRUE, nrow=6)

    RS <- matrix(c(0.6, 0.6, 0.6, 0.6,
                   1, 0.9, 0.7, 0.6,
                   0.7, 0.6, 0.5, 0.4,
                   1, 1, 1, 1,
                   0.1, 0.2, 0, 0.2), byrow=TRUE, nrow=5)

    expect_that(suppressWarnings(compose(R, S, E, alg='goedel', type='basic')), equals(RS))
})

test_that('basic goedel composition with quantifier', {
    R <- matrix(c(1, 0, 1, 1, 1, 0, 0, 0), nrow=1)

    S <- matrix(c(0, 0, 0, 0, 1, 0, 1, 1,
                  0, 0, 0, 1, 1, 0, 1, 1,
                  0, 0, 1, 1, 1, 0, 1, 1), byrow=FALSE, ncol=3)

    RS1 <- matrix(c(1, 1, 1), nrow=1)
    RS2 <- matrix(c(0, 1, 1), nrow=1)
    RS3 <- matrix(c(0, 0, 1), nrow=1)

    atLeastN <- function(a) {
        function(xx) {
            ifelse(xx < a / length(xx), 0, 1)
        }
    }

    expect_that(suppressWarnings(compose(R, S, alg='goedel', type='basic', q=atLeastN(1))),
                equals(RS1))
    expect_that(suppressWarnings(compose(R, S, alg='goedel', type='basic', q=atLeastN(2))),
                equals(RS2))
    expect_that(suppressWarnings(compose(R, S, alg='goedel', type='basic', q=atLeastN(3))),
                equals(RS3))

    atLeastP <- function(p) {
        function(xx) {
            y <- attr(xx, 'y')
            a <- ceiling(p * sum(y))
            ifelse(xx < a / length(xx), 0, 1)
        }
    }

    expect_that(suppressWarnings(compose(R, S, alg='goedel', type='basic', q=atLeastP(0.3))),
                equals(RS1))
    expect_that(suppressWarnings(compose(R, S, alg='goedel', type='basic', q=atLeastP(0.49))),
                equals(RS2))
    expect_that(suppressWarnings(compose(R, S, alg='goedel', type='basic', q=atLeastP(0.59))),
                equals(RS3))
})


test_that('compose handling of row/col-names', {
    set.seed(334)

    x <- matrix(runif(24, 0, 1), ncol=6)
    y <- matrix(runif(18, 0, 1), nrow=6)
    rownames(x) <- rev(LETTERS[seq_len(nrow(x))])
    colnames(x) <- letters[seq_len(ncol(x))]
    rownames(y) <- letters[seq_len(nrow(y))]
    colnames(y) <- LETTERS[seq_len(ncol(y))]
    res <- compose(x, y)
    expect_equal(colnames(res), colnames(y))
    expect_equal(rownames(res), rownames(x))

    colnames(x) <- rev(letters[seq_len(ncol(x))])
    expect_error(compose(x, y))
})