1 /* ----------------------------------------------------------------------
2 * Project: CMSIS DSP Library
3 * Title: arm_mat_cholesky_f16.c
4 * Description: Floating-point Cholesky decomposition
5 *
6 * $Date: 23 April 2021
7 * $Revision: V1.9.0
8 *
9 * Target Processor: Cortex-M and Cortex-A cores
10 * -------------------------------------------------------------------- */
11 /*
12 * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
13 *
14 * SPDX-License-Identifier: Apache-2.0
15 *
16 * Licensed under the Apache License, Version 2.0 (the License); you may
17 * not use this file except in compliance with the License.
18 * You may obtain a copy of the License at
19 *
20 * www.apache.org/licenses/LICENSE-2.0
21 *
22 * Unless required by applicable law or agreed to in writing, software
23 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
24 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
25 * See the License for the specific language governing permissions and
26 * limitations under the License.
27 */
28
29 #include "dsp/matrix_functions_f16.h"
30 #include "dsp/matrix_utils.h"
31
32 #if defined(ARM_FLOAT16_SUPPORTED)
33
34 /**
35 @ingroup groupMatrix
36 */
37
38 /**
39 @addtogroup MatrixChol
40 @{
41 */
42
43 /**
44 * @brief Floating-point Cholesky decomposition of positive-definite matrix.
45 * @param[in] pSrc points to the instance of the input floating-point matrix structure.
46 * @param[out] pDst points to the instance of the output floating-point matrix structure.
47 * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
48 * @return execution status
49 - \ref ARM_MATH_SUCCESS : Operation successful
50 - \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed
51 - \ref ARM_MATH_DECOMPOSITION_FAILURE : Input matrix cannot be decomposed
52 * @par
53 * If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition.
54 * The decomposition of A is returning a lower triangular matrix U such that A = L L^t
55 */
56
57 #if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)
58
59 #include "arm_helium_utils.h"
60
arm_mat_cholesky_f16(const arm_matrix_instance_f16 * pSrc,arm_matrix_instance_f16 * pDst)61 arm_status arm_mat_cholesky_f16(
62 const arm_matrix_instance_f16 * pSrc,
63 arm_matrix_instance_f16 * pDst)
64 {
65
66 arm_status status; /* status of matrix inverse */
67
68
69 #ifdef ARM_MATH_MATRIX_CHECK
70
71 /* Check for matrix mismatch condition */
72 if ((pSrc->numRows != pSrc->numCols) ||
73 (pDst->numRows != pDst->numCols) ||
74 (pSrc->numRows != pDst->numRows) )
75 {
76 /* Set status as ARM_MATH_SIZE_MISMATCH */
77 status = ARM_MATH_SIZE_MISMATCH;
78 }
79 else
80
81 #endif /* #ifdef ARM_MATH_MATRIX_CHECK */
82
83 {
84 int i,j,k;
85 int n = pSrc->numRows;
86 _Float16 invSqrtVj;
87 float16_t *pA,*pG;
88 int kCnt;
89
90 mve_pred16_t p0;
91
92 f16x8_t acc, acc0, acc1, acc2, acc3;
93 f16x8_t vecGi;
94 f16x8_t vecGj,vecGj0,vecGj1,vecGj2,vecGj3;
95
96
97 pA = pSrc->pData;
98 pG = pDst->pData;
99
100 for(i=0 ;i < n ; i++)
101 {
102 for(j=i ; j+3 < n ; j+=4)
103 {
104 acc0 = vdupq_n_f16(0.0f16);
105 acc0[0]=pA[(j + 0) * n + i];
106
107 acc1 = vdupq_n_f16(0.0f16);
108 acc1[0]=pA[(j + 1) * n + i];
109
110 acc2 = vdupq_n_f16(0.0f16);
111 acc2[0]=pA[(j + 2) * n + i];
112
113 acc3 = vdupq_n_f16(0.0f16);
114 acc3[0]=pA[(j + 3) * n + i];
115
116 kCnt = i;
117 for(k=0; k < i ; k+=8)
118 {
119 p0 = vctp16q(kCnt);
120
121 vecGi=vldrhq_z_f16(&pG[i * n + k],p0);
122
123 vecGj0=vldrhq_z_f16(&pG[(j + 0) * n + k],p0);
124 vecGj1=vldrhq_z_f16(&pG[(j + 1) * n + k],p0);
125 vecGj2=vldrhq_z_f16(&pG[(j + 2) * n + k],p0);
126 vecGj3=vldrhq_z_f16(&pG[(j + 3) * n + k],p0);
127
128 acc0 = vfmsq_m(acc0, vecGi, vecGj0, p0);
129 acc1 = vfmsq_m(acc1, vecGi, vecGj1, p0);
130 acc2 = vfmsq_m(acc2, vecGi, vecGj2, p0);
131 acc3 = vfmsq_m(acc3, vecGi, vecGj3, p0);
132
133 kCnt -= 8;
134 }
135 pG[(j + 0) * n + i] = vecAddAcrossF16Mve(acc0);
136 pG[(j + 1) * n + i] = vecAddAcrossF16Mve(acc1);
137 pG[(j + 2) * n + i] = vecAddAcrossF16Mve(acc2);
138 pG[(j + 3) * n + i] = vecAddAcrossF16Mve(acc3);
139 }
140
141 for(; j < n ; j++)
142 {
143
144 kCnt = i;
145 acc = vdupq_n_f16(0.0f16);
146 acc[0] = pA[j * n + i];
147
148 for(k=0; k < i ; k+=8)
149 {
150 p0 = vctp16q(kCnt);
151
152 vecGi=vldrhq_z_f16(&pG[i * n + k],p0);
153 vecGj=vldrhq_z_f16(&pG[j * n + k],p0);
154
155 acc = vfmsq_m(acc, vecGi, vecGj,p0);
156
157 kCnt -= 8;
158 }
159 pG[j * n + i] = vecAddAcrossF16Mve(acc);
160 }
161
162 if ((_Float16)pG[i * n + i] <= 0.0f16)
163 {
164 return(ARM_MATH_DECOMPOSITION_FAILURE);
165 }
166
167 invSqrtVj = 1.0f16/(_Float16)sqrtf((float32_t)pG[i * n + i]);
168 SCALE_COL_F16(pDst,i,invSqrtVj,i);
169 }
170
171 status = ARM_MATH_SUCCESS;
172
173 }
174
175
176 /* Return to application */
177 return (status);
178 }
179
180 #else
arm_mat_cholesky_f16(const arm_matrix_instance_f16 * pSrc,arm_matrix_instance_f16 * pDst)181 arm_status arm_mat_cholesky_f16(
182 const arm_matrix_instance_f16 * pSrc,
183 arm_matrix_instance_f16 * pDst)
184 {
185
186 arm_status status; /* status of matrix inverse */
187
188
189 #ifdef ARM_MATH_MATRIX_CHECK
190
191 /* Check for matrix mismatch condition */
192 if ((pSrc->numRows != pSrc->numCols) ||
193 (pDst->numRows != pDst->numCols) ||
194 (pSrc->numRows != pDst->numRows) )
195 {
196 /* Set status as ARM_MATH_SIZE_MISMATCH */
197 status = ARM_MATH_SIZE_MISMATCH;
198 }
199 else
200
201 #endif /* #ifdef ARM_MATH_MATRIX_CHECK */
202
203 {
204 int i,j,k;
205 int n = pSrc->numRows;
206 float16_t invSqrtVj;
207 float16_t *pA,*pG;
208
209 pA = pSrc->pData;
210 pG = pDst->pData;
211
212
213 for(i=0 ; i < n ; i++)
214 {
215 for(j=i ; j < n ; j++)
216 {
217 pG[j * n + i] = pA[j * n + i];
218
219 for(k=0; k < i ; k++)
220 {
221 pG[j * n + i] = (_Float16)pG[j * n + i] - (_Float16)pG[i * n + k] * (_Float16)pG[j * n + k];
222 }
223 }
224
225 if ((_Float16)pG[i * n + i] <= 0.0f16)
226 {
227 return(ARM_MATH_DECOMPOSITION_FAILURE);
228 }
229
230 /* The division is done in float32 for accuracy reason and
231 because doing it in f16 would not have any impact on the performances.
232 */
233 invSqrtVj = 1.0f/sqrtf((float32_t)pG[i * n + i]);
234 SCALE_COL_F16(pDst,i,invSqrtVj,i);
235
236 }
237
238 status = ARM_MATH_SUCCESS;
239
240 }
241
242
243 /* Return to application */
244 return (status);
245 }
246
247 #endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
248
249 /**
250 @} end of MatrixChol group
251 */
252 #endif /* #if defined(ARM_FLOAT16_SUPPORTED) */
253