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 * @par
57 * The destination matrix should be set to 0 before calling the functions because
58 * the function may not overwrite all output elements.
59 */
60
61 #if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)
62
63 #include "arm_helium_utils.h"
64
arm_mat_cholesky_f16(const arm_matrix_instance_f16 * pSrc,arm_matrix_instance_f16 * pDst)65 ARM_DSP_ATTRIBUTE arm_status arm_mat_cholesky_f16(
66 const arm_matrix_instance_f16 * pSrc,
67 arm_matrix_instance_f16 * pDst)
68 {
69
70 arm_status status; /* status of matrix inverse */
71
72
73 #ifdef ARM_MATH_MATRIX_CHECK
74
75 /* Check for matrix mismatch condition */
76 if ((pSrc->numRows != pSrc->numCols) ||
77 (pDst->numRows != pDst->numCols) ||
78 (pSrc->numRows != pDst->numRows) )
79 {
80 /* Set status as ARM_MATH_SIZE_MISMATCH */
81 status = ARM_MATH_SIZE_MISMATCH;
82 }
83 else
84
85 #endif /* #ifdef ARM_MATH_MATRIX_CHECK */
86
87 {
88 int i,j,k;
89 int n = pSrc->numRows;
90 _Float16 invSqrtVj;
91 float16_t *pA,*pG;
92 int kCnt;
93
94 mve_pred16_t p0;
95
96 f16x8_t acc, acc0, acc1, acc2, acc3;
97 f16x8_t vecGi;
98 f16x8_t vecGj,vecGj0,vecGj1,vecGj2,vecGj3;
99
100
101 pA = pSrc->pData;
102 pG = pDst->pData;
103
104 for(i=0 ;i < n ; i++)
105 {
106 for(j=i ; j+3 < n ; j+=4)
107 {
108 acc0 = vdupq_n_f16(0.0f16);
109 acc0[0]=pA[(j + 0) * n + i];
110
111 acc1 = vdupq_n_f16(0.0f16);
112 acc1[0]=pA[(j + 1) * n + i];
113
114 acc2 = vdupq_n_f16(0.0f16);
115 acc2[0]=pA[(j + 2) * n + i];
116
117 acc3 = vdupq_n_f16(0.0f16);
118 acc3[0]=pA[(j + 3) * n + i];
119
120 kCnt = i;
121 for(k=0; k < i ; k+=8)
122 {
123 p0 = vctp16q(kCnt);
124
125 vecGi=vldrhq_z_f16(&pG[i * n + k],p0);
126
127 vecGj0=vldrhq_z_f16(&pG[(j + 0) * n + k],p0);
128 vecGj1=vldrhq_z_f16(&pG[(j + 1) * n + k],p0);
129 vecGj2=vldrhq_z_f16(&pG[(j + 2) * n + k],p0);
130 vecGj3=vldrhq_z_f16(&pG[(j + 3) * n + k],p0);
131
132 acc0 = vfmsq_m(acc0, vecGi, vecGj0, p0);
133 acc1 = vfmsq_m(acc1, vecGi, vecGj1, p0);
134 acc2 = vfmsq_m(acc2, vecGi, vecGj2, p0);
135 acc3 = vfmsq_m(acc3, vecGi, vecGj3, p0);
136
137 kCnt -= 8;
138 }
139 pG[(j + 0) * n + i] = vecAddAcrossF16Mve(acc0);
140 pG[(j + 1) * n + i] = vecAddAcrossF16Mve(acc1);
141 pG[(j + 2) * n + i] = vecAddAcrossF16Mve(acc2);
142 pG[(j + 3) * n + i] = vecAddAcrossF16Mve(acc3);
143 }
144
145 for(; j < n ; j++)
146 {
147
148 kCnt = i;
149 acc = vdupq_n_f16(0.0f16);
150 acc[0] = pA[j * n + i];
151
152 for(k=0; k < i ; k+=8)
153 {
154 p0 = vctp16q(kCnt);
155
156 vecGi=vldrhq_z_f16(&pG[i * n + k],p0);
157 vecGj=vldrhq_z_f16(&pG[j * n + k],p0);
158
159 acc = vfmsq_m(acc, vecGi, vecGj,p0);
160
161 kCnt -= 8;
162 }
163 pG[j * n + i] = vecAddAcrossF16Mve(acc);
164 }
165
166 if ((_Float16)pG[i * n + i] <= 0.0f16)
167 {
168 return(ARM_MATH_DECOMPOSITION_FAILURE);
169 }
170
171 invSqrtVj = 1.0f16/(_Float16)sqrtf((float32_t)pG[i * n + i]);
172 SCALE_COL_F16(pDst,i,invSqrtVj,i);
173 }
174
175 status = ARM_MATH_SUCCESS;
176
177 }
178
179
180 /* Return to application */
181 return (status);
182 }
183
184 #else
arm_mat_cholesky_f16(const arm_matrix_instance_f16 * pSrc,arm_matrix_instance_f16 * pDst)185 ARM_DSP_ATTRIBUTE arm_status arm_mat_cholesky_f16(
186 const arm_matrix_instance_f16 * pSrc,
187 arm_matrix_instance_f16 * pDst)
188 {
189
190 arm_status status; /* status of matrix inverse */
191
192
193 #ifdef ARM_MATH_MATRIX_CHECK
194
195 /* Check for matrix mismatch condition */
196 if ((pSrc->numRows != pSrc->numCols) ||
197 (pDst->numRows != pDst->numCols) ||
198 (pSrc->numRows != pDst->numRows) )
199 {
200 /* Set status as ARM_MATH_SIZE_MISMATCH */
201 status = ARM_MATH_SIZE_MISMATCH;
202 }
203 else
204
205 #endif /* #ifdef ARM_MATH_MATRIX_CHECK */
206
207 {
208 int i,j,k;
209 int n = pSrc->numRows;
210 float16_t invSqrtVj;
211 float16_t *pA,*pG;
212
213 pA = pSrc->pData;
214 pG = pDst->pData;
215
216
217 for(i=0 ; i < n ; i++)
218 {
219 for(j=i ; j < n ; j++)
220 {
221 pG[j * n + i] = pA[j * n + i];
222
223 for(k=0; k < i ; k++)
224 {
225 pG[j * n + i] = (_Float16)pG[j * n + i] - (_Float16)pG[i * n + k] * (_Float16)pG[j * n + k];
226 }
227 }
228
229 if ((_Float16)pG[i * n + i] <= 0.0f16)
230 {
231 return(ARM_MATH_DECOMPOSITION_FAILURE);
232 }
233
234 /* The division is done in float32 for accuracy reason and
235 because doing it in f16 would not have any impact on the performances.
236 */
237 invSqrtVj = 1.0f/sqrtf((float32_t)pG[i * n + i]);
238 SCALE_COL_F16(pDst,i,invSqrtVj,i);
239
240 }
241
242 status = ARM_MATH_SUCCESS;
243
244 }
245
246
247 /* Return to application */
248 return (status);
249 }
250
251 #endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
252
253 /**
254 @} end of MatrixChol group
255 */
256 #endif /* #if defined(ARM_FLOAT16_SUPPORTED) */
257
