Merge pull request #427 from v923z/qr2

add qr implementation

code/numpy/linalg/linalg.c

@@ -364,7 +364,140 @@ static mp_obj_t linalg_norm(size_t n_args, const mp_obj_t *pos_args, mp_map_t *k
 }
 
 MP_DEFINE_CONST_FUN_OBJ_KW(linalg_norm_obj, 1, linalg_norm);
-// MP_DEFINE_CONST_FUN_OBJ_1(linalg_norm_obj, linalg_norm);
+
+#if ULAB_MAX_DIMS > 1
+//| def qr(m: ulab.numpy.ndarray) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]:
+//|     """
+//|     :param m: a matrix
+//|     :return tuple (Q, R):
+//|
+//|     Computes the QR decomposition of a matrix"""
+//|     ...
+//|
+
+static mp_obj_t linalg_qr(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } },
+        { MP_QSTR_mode, MP_ARG_OBJ, { .u_rom_obj = MP_ROM_QSTR(MP_QSTR_complete) } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+
+    if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("operation is defined for ndarrays only"));
+    }
+    ndarray_obj_t *source = MP_OBJ_TO_PTR(args[0].u_obj);
+    if(source->ndim != 2) {
+        mp_raise_ValueError(translate("operation is defined for 2D arrays only"));
+    }
+
+    size_t m = source->shape[ULAB_MAX_DIMS - 2]; // rows
+    size_t n = source->shape[ULAB_MAX_DIMS - 1]; // columns
+
+    ndarray_obj_t *Q = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, m, m), NDARRAY_FLOAT);
+    ndarray_obj_t *R = ndarray_new_dense_ndarray(2, source->shape, NDARRAY_FLOAT);
+
+    mp_float_t *qarray = (mp_float_t *)Q->array;
+    mp_float_t *rarray = (mp_float_t *)R->array;
+
+    // simply copy the entries of source to a float array
+    mp_float_t (*func)(void *) = ndarray_get_float_function(source->dtype);
+    uint8_t *sarray = (uint8_t *)source->array;
+
+    for(size_t i = 0; i < m; i++) {
+        for(size_t j = 0; j < n; j++) {
+            *rarray++ = func(sarray);
+            sarray += source->strides[ULAB_MAX_DIMS - 1];
+        }
+        sarray -= n * source->strides[ULAB_MAX_DIMS - 1];
+        sarray += source->strides[ULAB_MAX_DIMS - 2];
+    }
+    rarray -= m * n;
+
+    // start with the unit matrix
+    for(size_t i = 0; i < m; i++) {
+        qarray[i * (m + 1)] = 1.0;
+    }
+
+    for(size_t j = 0; j < n; j++) { // columns
+        for(size_t i = m - 1; i > j; i--) { // rows
+            mp_float_t c, s;
+            // Givens matrix: note that numpy uses a strange form of the rotation
+            // [[c  s],
+            //  [s -c]]
+            if(MICROPY_FLOAT_C_FUN(fabs)(rarray[i * n + j]) < LINALG_EPSILON) { // r[i, j]
+                c = (rarray[(i - 1) * n + j] >= 0.0) ? 1.0 : -1.0; // r[i-1, j]
+                s = 0.0;
+            } else if(MICROPY_FLOAT_C_FUN(fabs)(rarray[(i - 1) * n + j]) < LINALG_EPSILON) { // r[i-1, j]
+                c = 0.0;
+                s = (rarray[i * n + j] >= 0.0) ? -1.0 : 1.0; // r[i, j]
+            } else {
+                mp_float_t t, u;
+                if(MICROPY_FLOAT_C_FUN(fabs)(rarray[(i - 1) * n + j]) > MICROPY_FLOAT_C_FUN(fabs)(rarray[i * n + j])) { // r[i-1, j], r[i, j]
+                    t = rarray[i * n + j] / rarray[(i - 1) * n + j]; // r[i, j]/r[i-1, j]
+                    u = MICROPY_FLOAT_C_FUN(sqrt)(1 + t * t);
+                    c = -1.0 / u;
+                    s = c * t;
+                } else {
+                    t = rarray[(i - 1) * n + j] / rarray[i * n + j]; // r[i-1, j]/r[i, j]
+                    u = MICROPY_FLOAT_C_FUN(sqrt)(1 + t * t);
+                    s = -1.0 / u;
+                    c = s * t;
+                }
+            }
+
+            mp_float_t r1, r2;
+            // update R: multiply with the rotation matrix from the left
+            for(size_t k = 0; k < n; k++) {
+                r1 = rarray[(i - 1) * n + k]; // r[i-1, k]
+                r2 = rarray[i * n + k]; // r[i, k]
+                rarray[(i - 1) * n + k] = c * r1 + s * r2; // r[i-1, k]
+                rarray[i * n + k] = s * r1 - c * r2; // r[i, k]
+            }
+
+            // update Q: multiply with the transpose of the rotation matrix from the right
+            for(size_t k = 0; k < m; k++) {
+                r1 = qarray[k * m + (i - 1)];
+                r2 = qarray[k * m + i];
+                qarray[k * m + (i - 1)] = c * r1 + s * r2;
+                qarray[k * m + i] = s * r1 - c * r2;
+            }
+        }
+    }
+
+    mp_obj_tuple_t *tuple = MP_OBJ_TO_PTR(mp_obj_new_tuple(2, NULL));
+    GET_STR_DATA_LEN(args[1].u_obj, mode, len);
+    if(memcmp(mode, "complete", 8) == 0) {
+        tuple->items[0] = MP_OBJ_FROM_PTR(Q);
+        tuple->items[1] = MP_OBJ_FROM_PTR(R);
+    } else if(memcmp(mode, "reduced", 7) == 0) {
+        size_t k = MAX(m, n) - MIN(m, n);
+        ndarray_obj_t *q = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, m, m - k), NDARRAY_FLOAT);
+        ndarray_obj_t *r = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, m - k, n), NDARRAY_FLOAT);
+        mp_float_t *qa = (mp_float_t *)q->array;
+        mp_float_t *ra = (mp_float_t *)r->array;
+        for(size_t i = 0; i < m; i++) {
+            memcpy(qa, qarray, (m - k) * q->itemsize);
+            qa += (m - k);
+            qarray += m;
+        }
+        for(size_t i = 0; i < m - k; i++) {
+            memcpy(ra, rarray, n * r->itemsize);
+            ra += n;
+            rarray += n;
+        }
+        tuple->items[0] = MP_OBJ_FROM_PTR(q);
+        tuple->items[1] = MP_OBJ_FROM_PTR(r);
+    } else {
+        mp_raise_ValueError(translate("mode must be complete, or reduced"));
+    }
+    return tuple;
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(linalg_qr_obj, 1, linalg_qr);
+#endif
 
 STATIC const mp_rom_map_elem_t ulab_linalg_globals_table[] = {
     { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_linalg) },
@@ -381,6 +514,9 @@ STATIC const mp_rom_map_elem_t ulab_linalg_globals_table[] = {
         #if ULAB_LINALG_HAS_INV
         { MP_ROM_QSTR(MP_QSTR_inv), (mp_obj_t)&linalg_inv_obj },
         #endif
+        #if ULAB_LINALG_HAS_QR
+        { MP_ROM_QSTR(MP_QSTR_qr), (mp_obj_t)&linalg_qr_obj },
+        #endif
     #endif
     #if ULAB_LINALG_HAS_NORM
     { MP_ROM_QSTR(MP_QSTR_norm), (mp_obj_t)&linalg_norm_obj },

code/numpy/linalg/linalg.h

@@ -23,4 +23,5 @@ MP_DECLARE_CONST_FUN_OBJ_1(linalg_det_obj);
 MP_DECLARE_CONST_FUN_OBJ_1(linalg_eig_obj);
 MP_DECLARE_CONST_FUN_OBJ_1(linalg_inv_obj);
 MP_DECLARE_CONST_FUN_OBJ_KW(linalg_norm_obj);
+MP_DECLARE_CONST_FUN_OBJ_KW(linalg_qr_obj);
 #endif

code/ulab.c

@@ -33,7 +33,7 @@
 #include "user/user.h"
 #include "utils/utils.h"
 
-#define ULAB_VERSION 3.2.0
+#define ULAB_VERSION 3.3.0
 #define xstr(s) str(s)
 #define str(s) #s
 #define ULAB_VERSION_STRING xstr(ULAB_VERSION) xstr(-) xstr(ULAB_MAX_DIMS) xstr(D)

code/ulab.h

@@ -371,6 +371,10 @@
 #define ULAB_LINALG_HAS_NORM            (1)
 #endif
 
+#ifndef ULAB_LINALG_HAS_QR
+#define ULAB_LINALG_HAS_QR              (1)
+#endif
+
 // the FFT module; functions of the fft module still have
 // to be defined separately
 #ifndef ULAB_NUMPY_HAS_FFT_MODULE

docs/ulab-change-log.md

@@ -1,3 +1,15 @@
+Thu, 22 Jul 2021
+
+version 3.3.0
+
+    add QR decomposition
+
+Tue, 13 Jul 2021
+
+version 3.2.0
+
+    add flatiter/flat to ndarray methods
+
 Tue, 22 Jun 2021
 
 version 3.1.1