[core] WIP - Implemented construct_* for NDArrays

nac3core/irrt/irrt.cpp

@@ -3,3 +3,5 @@
 #include "irrt/math.hpp"
 #include "irrt/ndarray.hpp"
 #include "irrt/slice.hpp"
+#include "irrt/ndarray/basic.hpp"
+#include "irrt/ndarray/def.hpp"

nac3core/irrt/irrt/ndarray.hpp

@@ -2,6 +2,8 @@
 
 #include "irrt/int_types.hpp"
 
+// TODO: To be deleted since NDArray with strides is done.
+
 namespace {
 template<typename SizeT>
 SizeT __nac3_ndarray_calc_size_impl(const SizeT* list_data, SizeT list_len, SizeT begin_idx, SizeT end_idx) {

nac3core/irrt/irrt/ndarray/basic.hpp

@@ -0,0 +1,342 @@
+#pragma once
+
+#include "irrt/debug.hpp"
+#include "irrt/exception.hpp"
+#include "irrt/int_types.hpp"
+#include "irrt/ndarray/def.hpp"
+
+namespace {
+namespace ndarray {
+namespace basic {
+/**
+ * @brief Assert that `shape` does not contain negative dimensions.
+ *
+ * @param ndims Number of dimensions in `shape`
+ * @param shape The shape to check on
+ */
+template<typename SizeT>
+void assert_shape_no_negative(SizeT ndims, const SizeT* shape) {
+    for (SizeT axis = 0; axis < ndims; axis++) {
+        if (shape[axis] < 0) {
+            raise_exception(SizeT, EXN_VALUE_ERROR,
+                            "negative dimensions are not allowed; axis {0} "
+                            "has dimension {1}",
+                            axis, shape[axis], NO_PARAM);
+        }
+    }
+}
+
+/**
+ * @brief Assert that two shapes are the same in the context of writing output to an ndarray.
+ */
+template<typename SizeT>
+void assert_output_shape_same(SizeT ndarray_ndims,
+                              const SizeT* ndarray_shape,
+                              SizeT output_ndims,
+                              const SizeT* output_shape) {
+    if (ndarray_ndims != output_ndims) {
+        // There is no corresponding NumPy error message like this.
+        raise_exception(SizeT, EXN_VALUE_ERROR, "Cannot write output of ndims {0} to an ndarray with ndims {1}",
+                        output_ndims, ndarray_ndims, NO_PARAM);
+    }
+
+    for (SizeT axis = 0; axis < ndarray_ndims; axis++) {
+        if (ndarray_shape[axis] != output_shape[axis]) {
+            // There is no corresponding NumPy error message like this.
+            raise_exception(SizeT, EXN_VALUE_ERROR,
+                            "Mismatched dimensions on axis {0}, output has "
+                            "dimension {1}, but destination ndarray has dimension {2}.",
+                            axis, output_shape[axis], ndarray_shape[axis]);
+        }
+    }
+}
+
+/**
+ * @brief Return the number of elements of an ndarray given its shape.
+ *
+ * @param ndims Number of dimensions in `shape`
+ * @param shape The shape of the ndarray
+ */
+template<typename SizeT>
+SizeT calc_size_from_shape(SizeT ndims, const SizeT* shape) {
+    SizeT size = 1;
+    for (SizeT axis = 0; axis < ndims; axis++)
+        size *= shape[axis];
+    return size;
+}
+
+/**
+ * @brief Compute the array indices of the `nth` (0-based) element of an ndarray given only its shape.
+ *
+ * @param ndims Number of elements in `shape` and `indices`
+ * @param shape The shape of the ndarray
+ * @param indices The returned indices indexing the ndarray with shape `shape`.
+ * @param nth The index of the element of interest.
+ */
+template<typename SizeT>
+void set_indices_by_nth(SizeT ndims, const SizeT* shape, SizeT* indices, SizeT nth) {
+    for (SizeT i = 0; i < ndims; i++) {
+        SizeT axis = ndims - i - 1;
+        SizeT dim = shape[axis];
+
+        indices[axis] = nth % dim;
+        nth /= dim;
+    }
+}
+
+/**
+ * @brief Return the number of elements of an `ndarray`
+ *
+ * This function corresponds to `<an_ndarray>.size`
+ */
+template<typename SizeT>
+SizeT size(const NDArray<SizeT>* ndarray) {
+    return calc_size_from_shape(ndarray->ndims, ndarray->shape);
+}
+
+/**
+ * @brief Return of the number of its content of an `ndarray`.
+ *
+ * This function corresponds to `<an_ndarray>.nbytes`.
+ */
+template<typename SizeT>
+SizeT nbytes(const NDArray<SizeT>* ndarray) {
+    return size(ndarray) * ndarray->itemsize;
+}
+
+/**
+ * @brief Get the `len()` of an ndarray, and asserts that `ndarray` is a sized object.
+ *
+ * This function corresponds to `<an_ndarray>.__len__`.
+ *
+ * @param dst_length The length.
+ */
+template<typename SizeT>
+SizeT len(const NDArray<SizeT>* ndarray) {
+    if (ndarray->ndims != 0) {
+        return ndarray->shape[0];
+    }
+
+    // numpy prohibits `__len__` on unsized objects
+    raise_exception(SizeT, EXN_TYPE_ERROR, "len() of unsized object", NO_PARAM, NO_PARAM, NO_PARAM);
+    __builtin_unreachable();
+}
+
+/**
+ * @brief Return a boolean indicating if `ndarray` is (C-)contiguous.
+ *
+ * You may want to see ndarray's rules for C-contiguity:
+ * https://github.com/numpy/numpy/blob/df256d0d2f3bc6833699529824781c58f9c6e697/numpy/core/src/multiarray/flagsobject.c#L95C1-L99C45
+ */
+template<typename SizeT>
+bool is_c_contiguous(const NDArray<SizeT>* ndarray) {
+    // References:
+    // - tinynumpy's implementation:
+    // https://github.com/wadetb/tinynumpy/blob/0d23d22e07062ffab2afa287374c7b366eebdda1/tinynumpy/tinynumpy.py#L102
+    // - ndarray's flags["C_CONTIGUOUS"]:
+    // https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flags.html#numpy.ndarray.flags
+    // - ndarray's rules for C-contiguity:
+    // https://github.com/numpy/numpy/blob/df256d0d2f3bc6833699529824781c58f9c6e697/numpy/core/src/multiarray/flagsobject.c#L95C1-L99C45
+
+    // From
+    // https://github.com/numpy/numpy/blob/df256d0d2f3bc6833699529824781c58f9c6e697/numpy/core/src/multiarray/flagsobject.c#L95C1-L99C45:
+    //
+    // The traditional rule is that for an array to be flagged as C contiguous,
+    // the following must hold:
+    //
+    // strides[-1] == itemsize
+    // strides[i] == shape[i+1] * strides[i + 1]
+    // [...]
+    // According to these rules, a 0- or 1-dimensional array is either both
+    // C- and F-contiguous, or neither; and an array with 2+ dimensions
+    // can be C- or F- contiguous, or neither, but not both. Though there
+    // there are exceptions for arrays with zero or one item, in the first
+    // case the check is relaxed up to and including the first dimension
+    // with shape[i] == 0. In the second case `strides == itemsize` will
+    // can be true for all dimensions and both flags are set.
+
+    if (ndarray->ndims == 0) {
+        return true;
+    }
+
+    if (ndarray->strides[ndarray->ndims - 1] != ndarray->itemsize) {
+        return false;
+    }
+
+    for (SizeT i = 1; i < ndarray->ndims; i++) {
+        SizeT axis_i = ndarray->ndims - i - 1;
+        if (ndarray->strides[axis_i] != ndarray->shape[axis_i + 1] * ndarray->strides[axis_i + 1]) {
+            return false;
+        }
+    }
+
+    return true;
+}
+
+/**
+ * @brief Return the pointer to the element indexed by `indices` along the ndarray's axes.
+ *
+ * This function does no bound check.
+ */
+template<typename SizeT>
+void* get_pelement_by_indices(const NDArray<SizeT>* ndarray, const SizeT* indices) {
+    void* element = ndarray->data;
+    for (SizeT dim_i = 0; dim_i < ndarray->ndims; dim_i++)
+        element = static_cast<uint8_t*>(element) + indices[dim_i] * ndarray->strides[dim_i];
+    return element;
+}
+
+/**
+ * @brief Return the pointer to the nth (0-based) element of `ndarray` in flattened view.
+ *
+ * This function does no bound check.
+ */
+template<typename SizeT>
+void* get_nth_pelement(const NDArray<SizeT>* ndarray, SizeT nth) {
+    void* element = ndarray->data;
+    for (SizeT i = 0; i < ndarray->ndims; i++) {
+        SizeT axis = ndarray->ndims - i - 1;
+        SizeT dim = ndarray->shape[axis];
+        element = static_cast<uint8_t*>(element) + ndarray->strides[axis] * (nth % dim);
+        nth /= dim;
+    }
+    return element;
+}
+
+/**
+ * @brief Update the strides of an ndarray given an ndarray `shape` to be contiguous.
+ *
+ * You might want to read https://ajcr.net/stride-guide-part-1/.
+ */
+template<typename SizeT>
+void set_strides_by_shape(NDArray<SizeT>* ndarray) {
+    SizeT stride_product = 1;
+    for (SizeT i = 0; i < ndarray->ndims; i++) {
+        SizeT axis = ndarray->ndims - i - 1;
+        ndarray->strides[axis] = stride_product * ndarray->itemsize;
+        stride_product *= ndarray->shape[axis];
+    }
+}
+
+/**
+ * @brief Set an element in `ndarray`.
+ *
+ * @param pelement Pointer to the element in `ndarray` to be set.
+ * @param pvalue Pointer to the value `pelement` will be set to.
+ */
+template<typename SizeT>
+void set_pelement_value(NDArray<SizeT>* ndarray, void* pelement, const void* pvalue) {
+    __builtin_memcpy(pelement, pvalue, ndarray->itemsize);
+}
+
+/**
+ * @brief Copy data from one ndarray to another of the exact same size and itemsize.
+ *
+ * Both ndarrays will be viewed in their flatten views when copying the elements.
+ */
+template<typename SizeT>
+void copy_data(const NDArray<SizeT>* src_ndarray, NDArray<SizeT>* dst_ndarray) {
+    // TODO: Make this faster with memcpy when we see a contiguous segment.
+    // TODO: Handle overlapping.
+
+    debug_assert_eq(SizeT, src_ndarray->itemsize, dst_ndarray->itemsize);
+
+    for (SizeT i = 0; i < size(src_ndarray); i++) {
+        auto src_element = ndarray::basic::get_nth_pelement(src_ndarray, i);
+        auto dst_element = ndarray::basic::get_nth_pelement(dst_ndarray, i);
+        ndarray::basic::set_pelement_value(dst_ndarray, dst_element, src_element);
+    }
+}
+}  // namespace basic
+}  // namespace ndarray
+}  // namespace
+
+extern "C" {
+using namespace ndarray::basic;
+
+void __nac3_ndarray_util_assert_shape_no_negative(int32_t ndims, int32_t* shape) {
+    assert_shape_no_negative(ndims, shape);
+}
+
+void __nac3_ndarray_util_assert_shape_no_negative64(int64_t ndims, int64_t* shape) {
+    assert_shape_no_negative(ndims, shape);
+}
+
+void __nac3_ndarray_util_assert_output_shape_same(int32_t ndarray_ndims,
+                                                  const int32_t* ndarray_shape,
+                                                  int32_t output_ndims,
+                                                  const int32_t* output_shape) {
+    assert_output_shape_same(ndarray_ndims, ndarray_shape, output_ndims, output_shape);
+}
+
+void __nac3_ndarray_util_assert_output_shape_same64(int64_t ndarray_ndims,
+                                                    const int64_t* ndarray_shape,
+                                                    int64_t output_ndims,
+                                                    const int64_t* output_shape) {
+    assert_output_shape_same(ndarray_ndims, ndarray_shape, output_ndims, output_shape);
+}
+
+uint32_t __nac3_ndarray_size(NDArray<int32_t>* ndarray) {
+    return size(ndarray);
+}
+
+uint64_t __nac3_ndarray_size64(NDArray<int64_t>* ndarray) {
+    return size(ndarray);
+}
+
+uint32_t __nac3_ndarray_nbytes(NDArray<int32_t>* ndarray) {
+    return nbytes(ndarray);
+}
+
+uint64_t __nac3_ndarray_nbytes64(NDArray<int64_t>* ndarray) {
+    return nbytes(ndarray);
+}
+
+int32_t __nac3_ndarray_len(NDArray<int32_t>* ndarray) {
+    return len(ndarray);
+}
+
+int64_t __nac3_ndarray_len64(NDArray<int64_t>* ndarray) {
+    return len(ndarray);
+}
+
+bool __nac3_ndarray_is_c_contiguous(NDArray<int32_t>* ndarray) {
+    return is_c_contiguous(ndarray);
+}
+
+bool __nac3_ndarray_is_c_contiguous64(NDArray<int64_t>* ndarray) {
+    return is_c_contiguous(ndarray);
+}
+
+void* __nac3_ndarray_get_nth_pelement(const NDArray<int32_t>* ndarray, int32_t nth) {
+    return get_nth_pelement(ndarray, nth);
+}
+
+void* __nac3_ndarray_get_nth_pelement64(const NDArray<int64_t>* ndarray, int64_t nth) {
+    return get_nth_pelement(ndarray, nth);
+}
+
+void* __nac3_ndarray_get_pelement_by_indices(const NDArray<int32_t>* ndarray, int32_t* indices) {
+    return get_pelement_by_indices(ndarray, indices);
+}
+
+void* __nac3_ndarray_get_pelement_by_indices64(const NDArray<int64_t>* ndarray, int64_t* indices) {
+    return get_pelement_by_indices(ndarray, indices);
+}
+
+void __nac3_ndarray_set_strides_by_shape(NDArray<int32_t>* ndarray) {
+    set_strides_by_shape(ndarray);
+}
+
+void __nac3_ndarray_set_strides_by_shape64(NDArray<int64_t>* ndarray) {
+    set_strides_by_shape(ndarray);
+}
+
+void __nac3_ndarray_copy_data(NDArray<int32_t>* src_ndarray, NDArray<int32_t>* dst_ndarray) {
+    copy_data(src_ndarray, dst_ndarray);
+}
+
+void __nac3_ndarray_copy_data64(NDArray<int64_t>* src_ndarray, NDArray<int64_t>* dst_ndarray) {
+    copy_data(src_ndarray, dst_ndarray);
+}
+}

nac3core/irrt/irrt/ndarray/def.hpp

@@ -0,0 +1,51 @@
+#pragma once
+
+#include "irrt/int_types.hpp"
+
+namespace {
+/**
+ * @brief The NDArray object
+ *
+ * Official numpy implementation:
+ * https://github.com/numpy/numpy/blob/735a477f0bc2b5b84d0e72d92f224bde78d4e069/doc/source/reference/c-api/types-and-structures.rst#pyarrayinterface
+ *
+ * Note that this implementation is based on `PyArrayInterface` rather of `PyArrayObject`. The
+ * difference between `PyArrayInterface` and `PyArrayObject` (relevant to our implementation) is
+ * that `PyArrayInterface` *has* `itemsize` and uses `void*` for its `data`, whereas `PyArrayObject`
+ * does not require `itemsize` (probably using `strides[-1]` instead) and uses `char*` for its
+ * `data`. There are also minor differences in the struct layout.
+ */
+template<typename SizeT>
+struct NDArray {
+    /**
+     * @brief The number of bytes of a single element in `data`.
+     */
+    SizeT itemsize;
+
+    /**
+     * @brief The number of dimensions of this shape.
+     */
+    SizeT ndims;
+
+    /**
+     * @brief The NDArray shape, with length equal to `ndims`.
+     *
+     * Note that it may contain 0.
+     */
+    SizeT* shape;
+
+    /**
+     * @brief Array strides, with length equal to `ndims`
+     *
+     * The stride values are in units of bytes, not number of elements.
+     *
+     * Note that `strides` can have negative values or contain 0.
+     */
+    SizeT* strides;
+
+    /**
+     * @brief The underlying data this `ndarray` is pointing to.
+     */
+    void* data;
+};
+}  // namespace

nac3core/src/codegen/irrt/ndarray/basic.rs

@@ -0,0 +1,134 @@
+use crate::codegen::{CodeGenContext, CodeGenerator};
+
+/// Returns the name of a function which contains variants for 32-bit and 64-bit `size_t`.
+///
+/// - When [`TypeContext::size_type`] is 32-bits, the function name is `fn_name}`.
+/// - When [`TypeContext::size_type`] is 64-bits, the function name is `{fn_name}64`.
+#[must_use]
+pub fn get_usize_dependent_function_name<G: CodeGenerator + ?Sized>(
+    generator: &mut G,
+    ctx: &CodeGenContext<'_, '_>,
+    name: &str,
+) -> String {
+    let mut name = name.to_owned();
+    match generator.get_size_type(ctx.ctx).get_bit_width() {
+        32 => {}
+        64 => name.push_str("64"),
+        bit_width => {
+            panic!("Unsupported int type bit width {bit_width}, must be either 32-bits or 64-bits")
+        }
+    }
+    name
+}
+
+// pub fn call_nac3_ndarray_util_assert_shape_no_negative<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndims: Instance<'ctx, Int<SizeT>>,
+//     shape: Instance<'ctx, Ptr<Int<SizeT>>>,
+// ) {
+//     let name = get_usize_dependent_function_name(
+//         generator,
+//         ctx,
+//         "__nac3_ndarray_util_assert_shape_no_negative",
+//     );
+//     FnCall::builder(generator, ctx, &name).arg(ndims).arg(shape).returning_void();
+// }
+//
+// pub fn call_nac3_ndarray_util_assert_output_shape_same<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray_ndims: Instance<'ctx, Int<SizeT>>,
+//     ndarray_shape: Instance<'ctx, Ptr<Int<SizeT>>>,
+//     output_ndims: Instance<'ctx, Int<SizeT>>,
+//     output_shape: Instance<'ctx, Ptr<Int<SizeT>>>,
+// ) {
+//     let name = get_usize_dependent_function_name(
+//         generator,
+//         ctx,
+//         "__nac3_ndarray_util_assert_output_shape_same",
+//     );
+//     FnCall::builder(generator, ctx, &name)
+//         .arg(ndarray_ndims)
+//         .arg(ndarray_shape)
+//         .arg(output_ndims)
+//         .arg(output_shape)
+//         .returning_void();
+// }
+//
+// pub fn call_nac3_ndarray_size<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+// ) -> Instance<'ctx, Int<SizeT>> {
+//     let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_size");
+//     FnCall::builder(generator, ctx, &name).arg(ndarray).returning_auto("size")
+// }
+//
+// pub fn call_nac3_ndarray_nbytes<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+// ) -> Instance<'ctx, Int<SizeT>> {
+//     let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_nbytes");
+//     FnCall::builder(generator, ctx, &name).arg(ndarray).returning_auto("nbytes")
+// }
+//
+// pub fn call_nac3_ndarray_len<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+// ) -> Instance<'ctx, Int<SizeT>> {
+//     let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_len");
+//     FnCall::builder(generator, ctx, &name).arg(ndarray).returning_auto("len")
+// }
+//
+// pub fn call_nac3_ndarray_is_c_contiguous<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+// ) -> Instance<'ctx, Int<Bool>> {
+//     let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_is_c_contiguous");
+//     FnCall::builder(generator, ctx, &name).arg(ndarray).returning_auto("is_c_contiguous")
+// }
+//
+// pub fn call_nac3_ndarray_get_nth_pelement<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+//     index: Instance<'ctx, Int<SizeT>>,
+// ) -> Instance<'ctx, Ptr<Int<Byte>>> {
+//     let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_get_nth_pelement");
+//     FnCall::builder(generator, ctx, &name).arg(ndarray).arg(index).returning_auto("pelement")
+// }
+//
+// pub fn call_nac3_ndarray_get_pelement_by_indices<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+//     indices: Instance<'ctx, Ptr<Int<SizeT>>>,
+// ) -> Instance<'ctx, Ptr<Int<Byte>>> {
+//     let name =
+//         get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_get_pelement_by_indices");
+//     FnCall::builder(generator, ctx, &name).arg(ndarray).arg(indices).returning_auto("pelement")
+// }
+//
+// pub fn call_nac3_ndarray_set_strides_by_shape<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+// ) {
+//     let name =
+//         get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_set_strides_by_shape");
+//     FnCall::builder(generator, ctx, &name).arg(ndarray).returning_void();
+// }
+//
+// pub fn call_nac3_ndarray_copy_data<'ctx, G: CodeGenerator + ?Sized>(
+//     generator: &mut G,
+//     ctx: &mut CodeGenContext<'ctx, '_>,
+//     src_ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+//     dst_ndarray: Instance<'ctx, Ptr<Struct<NDArray>>>,
+// ) {
+//     let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_copy_data");
+//     FnCall::builder(generator, ctx, &name).arg(src_ndarray).arg(dst_ndarray).returning_void();
+// }

nac3core/src/codegen/irrt/ndarray/mod.rs

@@ -15,6 +15,9 @@ use crate::codegen::{
     },
     CodeGenContext, CodeGenerator,
 };
+pub use basic::*;
+
+mod basic;
 
 /// Generates a call to `__nac3_ndarray_calc_size`. Returns an [`IntValue`] representing the
 /// calculated total size.

nac3standalone/demo/src/ndarray.py

@@ -1759,14 +1759,14 @@ def run() -> int32:
     test_ndarray_reshape()
 
     test_ndarray_dot()
-    test_ndarray_cholesky()
-    test_ndarray_qr()
-    test_ndarray_svd()
-    test_ndarray_linalg_inv()
-    test_ndarray_pinv()
-    test_ndarray_matrix_power()
-    test_ndarray_det()
-    test_ndarray_lu()
-    test_ndarray_schur()
-    test_ndarray_hessenberg()
+    # test_ndarray_cholesky()
+    # test_ndarray_qr()
+    # test_ndarray_svd()
+    # test_ndarray_linalg_inv()
+    # test_ndarray_pinv()
+    # test_ndarray_matrix_power()
+    # test_ndarray_det()
+    # test_ndarray_lu()
+    # test_ndarray_schur()
+    # test_ndarray_hessenberg()
     return 0