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bfc108	1	/* ----------------------------------------------------------------------
Q	2	* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
	3	*
	4	* $Date: 19. March 2015
	5	* $Revision: V.1.4.5
	6	*
	7	* Project: CMSIS DSP Library
	8	* Title: arm_mat_inverse_f32.c
	9	*
	10	* Description: Floating-point matrix inverse.
	11	*
	12	* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
	13	*
	14	* Redistribution and use in source and binary forms, with or without
	15	* modification, are permitted provided that the following conditions
	16	* are met:
	17	* - Redistributions of source code must retain the above copyright
	18	* notice, this list of conditions and the following disclaimer.
	19	* - Redistributions in binary form must reproduce the above copyright
	20	* notice, this list of conditions and the following disclaimer in
	21	* the documentation and/or other materials provided with the
	22	* distribution.
	23	* - Neither the name of ARM LIMITED nor the names of its contributors
	24	* may be used to endorse or promote products derived from this
	25	* software without specific prior written permission.
	26	*
	27	* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
	28	* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
	29	* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
	30	* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
	31	* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
	32	* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
	33	* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
	34	* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
	35	* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	36	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
	37	* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
	38	* POSSIBILITY OF SUCH DAMAGE.
	39	* -------------------------------------------------------------------- */
	40
	41	#include "arm_math.h"
	42
	43	/**
	44	* @ingroup groupMatrix
	45	*/
	46
	47	/**
	48	* @defgroup MatrixInv Matrix Inverse
	49	*
	50	* Computes the inverse of a matrix.
	51	*
	52	* The inverse is defined only if the input matrix is square and non-singular (the determinant
	53	* is non-zero). The function checks that the input and output matrices are square and of the
	54	* same size.
	55	*
	56	* Matrix inversion is numerically sensitive and the CMSIS DSP library only supports matrix
	57	* inversion of floating-point matrices.
	58	*
	59	* \par Algorithm
	60	* The Gauss-Jordan method is used to find the inverse.
	61	* The algorithm performs a sequence of elementary row-operations until it
	62	* reduces the input matrix to an identity matrix. Applying the same sequence
	63	* of elementary row-operations to an identity matrix yields the inverse matrix.
	64	* If the input matrix is singular, then the algorithm terminates and returns error status
	65	* <code>ARM_MATH_SINGULAR</code>.
	66	* \image html MatrixInverse.gif "Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method"
	67	*/
	68
	69	/**
	70	* @addtogroup MatrixInv
	71	* @{
	72	*/
	73
	74	/**
	75	* @brief Floating-point matrix inverse.
	76	* @param[in] *pSrc points to input matrix structure
	77	* @param[out] *pDst points to output matrix structure
	78	* @return The function returns
	79	* <code>ARM_MATH_SIZE_MISMATCH</code> if the input matrix is not square or if the size
	80	* of the output matrix does not match the size of the input matrix.
	81	* If the input matrix is found to be singular (non-invertible), then the function returns
	82	* <code>ARM_MATH_SINGULAR</code>. Otherwise, the function returns <code>ARM_MATH_SUCCESS</code>.
	83	*/
	84
	85	arm_status arm_mat_inverse_f32(
	86	const arm_matrix_instance_f32 * pSrc,
	87	arm_matrix_instance_f32 * pDst)
	88	{
	89	float32_t pIn = pSrc->pData; / input data matrix pointer */
	90	float32_t pOut = pDst->pData; / output data matrix pointer */
	91	float32_t pInT1, pInT2; /* Temporary input data matrix pointer */
	92	float32_t pOutT1, pOutT2; /* Temporary output data matrix pointer */
	93	float32_t pPivotRowIn, pPRT_in, pPivotRowDst, pPRT_pDst; /* Temporary input and output data matrix pointer */
	94	uint32_t numRows = pSrc->numRows; /* Number of rows in the matrix */
	95	uint32_t numCols = pSrc->numCols; /* Number of Cols in the matrix */
	96
	97	#ifndef ARM_MATH_CM0_FAMILY
	98	float32_t maxC; /* maximum value in the column */
	99
	100	/* Run the below code for Cortex-M4 and Cortex-M3 */
	101
	102	float32_t Xchg, in = 0.0f, in1; /* Temporary input values */
	103	uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l; /* loop counters */
	104	arm_status status; /* status of matrix inverse */
	105
	106	#ifdef ARM_MATH_MATRIX_CHECK
	107
	108
	109	/* Check for matrix mismatch condition */
	110	if((pSrc->numRows != pSrc->numCols) \|\| (pDst->numRows != pDst->numCols)
	111	\|\| (pSrc->numRows != pDst->numRows))
	112	{
	113	/* Set status as ARM_MATH_SIZE_MISMATCH */
	114	status = ARM_MATH_SIZE_MISMATCH;
	115	}
	116	else
	117	#endif /* #ifdef ARM_MATH_MATRIX_CHECK */
	118
	119	{
	120
	121	/*--------------------------------------------------------------------------------------------------------------
	122	* Matrix Inverse can be solved using elementary row operations.
	123	*
	124	* Gauss-Jordan Method:
	125	*
	126	* 1. First combine the identity matrix and the input matrix separated by a bar to form an
	127	* augmented matrix as follows:
	128	* _ _ _ _
	129	* \| a11 a12 \| 1 0 \| \| X11 X12 \|
	130	* \| \| \| = \| \|
	131	* \|_ a21 a22 \| 0 1 _\| \|_ X21 X21 _\|
	132	*
	133	* 2. In our implementation, pDst Matrix is used as identity matrix.
	134	*
	135	* 3. Begin with the first row. Let i = 1.
	136	*
	137	* 4. Check to see if the pivot for column i is the greatest of the column.
	138	* The pivot is the element of the main diagonal that is on the current row.
	139	* For instance, if working with row i, then the pivot element is aii.
	140	* If the pivot is not the most significant of the columns, exchange that row with a row
	141	* below it that does contain the most significant value in column i. If the most
	142	* significant value of the column is zero, then an inverse to that matrix does not exist.
	143	* The most significant value of the column is the absolute maximum.
	144	*
	145	* 5. Divide every element of row i by the pivot.
	146	*
	147	* 6. For every row below and row i, replace that row with the sum of that row and
	148	* a multiple of row i so that each new element in column i below row i is zero.
	149	*
	150	* 7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
	151	* for every element below and above the main diagonal.
	152	*
	153	* 8. Now an identical matrix is formed to the left of the bar(input matrix, pSrc).
	154	* Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst).
	155	----------------------------------------------------------------------------------------------------------------/
	156
	157	/* Working pointer for destination matrix */
	158	pOutT1 = pOut;
	159
	160	/* Loop over the number of rows */
	161	rowCnt = numRows;
	162
	163	/* Making the destination matrix as identity matrix */
	164	while(rowCnt > 0u)
	165	{
	166	/* Writing all zeroes in lower triangle of the destination matrix */
	167	j = numRows - rowCnt;
	168	while(j > 0u)
	169	{
	170	*pOutT1++ = 0.0f;
	171	j--;
	172	}
	173
	174	/* Writing all ones in the diagonal of the destination matrix */
	175	*pOutT1++ = 1.0f;
	176
	177	/* Writing all zeroes in upper triangle of the destination matrix */
	178	j = rowCnt - 1u;
	179	while(j > 0u)
	180	{
	181	*pOutT1++ = 0.0f;
	182	j--;
	183	}
	184
	185	/* Decrement the loop counter */
	186	rowCnt--;
	187	}
	188
	189	/* Loop over the number of columns of the input matrix.
	190	All the elements in each column are processed by the row operations */
	191	loopCnt = numCols;
	192
	193	/* Index modifier to navigate through the columns */
	194	l = 0u;
	195
	196	while(loopCnt > 0u)
	197	{
	198	/* Check if the pivot element is zero..
	199	* If it is zero then interchange the row with non zero row below.
	200	* If there is no non zero element to replace in the rows below,
	201	* then the matrix is Singular. */
	202
	203	/* Working pointer for the input matrix that points
	204	* to the pivot element of the particular row */
	205	pInT1 = pIn + (l * numCols);
	206
	207	/* Working pointer for the destination matrix that points
	208	* to the pivot element of the particular row */
	209	pOutT1 = pOut + (l * numCols);
	210
	211	/* Temporary variable to hold the pivot value */
	212	in = *pInT1;
	213
	214	/* Grab the most significant value from column l */
	215	maxC = 0;
	216	for (i = l; i < numRows; i++)
	217	{
	218	maxC = pInT1 > 0 ? (pInT1 > maxC ? pInT1 : maxC) : (-pInT1 > maxC ? -*pInT1 : maxC);
	219	pInT1 += numCols;
	220	}
	221
	222	/* Update the status if the matrix is singular */
	223	if(maxC == 0.0f)
	224	{
	225	return ARM_MATH_SINGULAR;
	226	}
	227
	228	/* Restore pInT1 */
	229	pInT1 = pIn;
	230
	231	/* Destination pointer modifier */
	232	k = 1u;
	233
	234	/* Check if the pivot element is the most significant of the column */
	235	if( (in > 0.0f ? in : -in) != maxC)
	236	{
	237	/* Loop over the number rows present below */
	238	i = numRows - (l + 1u);
	239
	240	while(i > 0u)
	241	{
	242	/* Update the input and destination pointers */
	243	pInT2 = pInT1 + (numCols * l);
	244	pOutT2 = pOutT1 + (numCols * k);
	245
	246	/* Look for the most significant element to
	247	* replace in the rows below */
	248	if((pInT2 > 0.0f ? pInT2: -*pInT2) == maxC)
	249	{
	250	/* Loop over number of columns
	251	* to the right of the pilot element */
	252	j = numCols - l;
	253
	254	while(j > 0u)
	255	{
	256	/* Exchange the row elements of the input matrix */
	257	Xchg = *pInT2;
	258	pInT2++ = pInT1;
	259	*pInT1++ = Xchg;
	260
	261	/* Decrement the loop counter */
	262	j--;
	263	}
	264
	265	/* Loop over number of columns of the destination matrix */
	266	j = numCols;
	267
	268	while(j > 0u)
	269	{
	270	/* Exchange the row elements of the destination matrix */
	271	Xchg = *pOutT2;
	272	pOutT2++ = pOutT1;
	273	*pOutT1++ = Xchg;
	274
	275	/* Decrement the loop counter */
	276	j--;
	277	}
	278
	279	/* Flag to indicate whether exchange is done or not */
	280	flag = 1u;
	281
	282	/* Break after exchange is done */
	283	break;
	284	}
	285
	286	/* Update the destination pointer modifier */
	287	k++;
	288
	289	/* Decrement the loop counter */
	290	i--;
	291	}
	292	}
	293
	294	/* Update the status if the matrix is singular */
	295	if((flag != 1u) && (in == 0.0f))
	296	{
	297	return ARM_MATH_SINGULAR;
	298	}
	299
	300	/* Points to the pivot row of input and destination matrices */
	301	pPivotRowIn = pIn + (l * numCols);
	302	pPivotRowDst = pOut + (l * numCols);
	303
	304	/* Temporary pointers to the pivot row pointers */
	305	pInT1 = pPivotRowIn;
	306	pInT2 = pPivotRowDst;
	307
	308	/* Pivot element of the row */
	309	in = *pPivotRowIn;
	310
	311	/* Loop over number of columns
	312	* to the right of the pilot element */
	313	j = (numCols - l);
	314
	315	while(j > 0u)
	316	{
	317	/* Divide each element of the row of the input matrix
	318	* by the pivot element */
	319	in1 = *pInT1;
	320	*pInT1++ = in1 / in;
	321
	322	/* Decrement the loop counter */
	323	j--;
	324	}
	325
	326	/* Loop over number of columns of the destination matrix */
	327	j = numCols;
	328
	329	while(j > 0u)
	330	{
	331	/* Divide each element of the row of the destination matrix
	332	* by the pivot element */
	333	in1 = *pInT2;
	334	*pInT2++ = in1 / in;
	335
	336	/* Decrement the loop counter */
	337	j--;
	338	}
	339
	340	/* Replace the rows with the sum of that row and a multiple of row i
	341	* so that each new element in column i above row i is zero.*/
	342
	343	/* Temporary pointers for input and destination matrices */
	344	pInT1 = pIn;
	345	pInT2 = pOut;
	346
	347	/* index used to check for pivot element */
	348	i = 0u;
	349
	350	/* Loop over number of rows */
	351	/* to be replaced by the sum of that row and a multiple of row i */
	352	k = numRows;
	353
	354	while(k > 0u)
	355	{
	356	/* Check for the pivot element */
	357	if(i == l)
	358	{
	359	/* If the processing element is the pivot element,
	360	only the columns to the right are to be processed */
	361	pInT1 += numCols - l;
	362
	363	pInT2 += numCols;
	364	}
	365	else
	366	{
	367	/* Element of the reference row */
	368	in = *pInT1;
	369
	370	/* Working pointers for input and destination pivot rows */
	371	pPRT_in = pPivotRowIn;
	372	pPRT_pDst = pPivotRowDst;
	373
	374	/* Loop over the number of columns to the right of the pivot element,
	375	to replace the elements in the input matrix */
	376	j = (numCols - l);
	377
	378	while(j > 0u)
	379	{
	380	/* Replace the element by the sum of that row
	381	and a multiple of the reference row */
	382	in1 = *pInT1;
	383	pInT1++ = in1 - (in *pPRT_in++);
	384
	385	/* Decrement the loop counter */
	386	j--;
	387	}
	388
	389	/* Loop over the number of columns to
	390	replace the elements in the destination matrix */
	391	j = numCols;
	392
	393	while(j > 0u)
	394	{
	395	/* Replace the element by the sum of that row
	396	and a multiple of the reference row */
	397	in1 = *pInT2;
	398	pInT2++ = in1 - (in *pPRT_pDst++);
	399
	400	/* Decrement the loop counter */
	401	j--;
	402	}
	403
	404	}
	405
	406	/* Increment the temporary input pointer */
	407	pInT1 = pInT1 + l;
	408
	409	/* Decrement the loop counter */
	410	k--;
	411
	412	/* Increment the pivot index */
	413	i++;
	414	}
	415
	416	/* Increment the input pointer */
	417	pIn++;
	418
	419	/* Decrement the loop counter */
	420	loopCnt--;
	421
	422	/* Increment the index modifier */
	423	l++;
	424	}
	425
	426
	427	#else
	428
	429	/* Run the below code for Cortex-M0 */
	430
	431	float32_t Xchg, in = 0.0f; /* Temporary input values */
	432	uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l; /* loop counters */
	433	arm_status status; /* status of matrix inverse */
	434
	435	#ifdef ARM_MATH_MATRIX_CHECK
	436
	437	/* Check for matrix mismatch condition */
	438	if((pSrc->numRows != pSrc->numCols) \|\| (pDst->numRows != pDst->numCols)
	439	\|\| (pSrc->numRows != pDst->numRows))
	440	{
	441	/* Set status as ARM_MATH_SIZE_MISMATCH */
	442	status = ARM_MATH_SIZE_MISMATCH;
	443	}
	444	else
	445	#endif /* #ifdef ARM_MATH_MATRIX_CHECK */
	446	{
	447
	448	/*--------------------------------------------------------------------------------------------------------------
	449	* Matrix Inverse can be solved using elementary row operations.
	450	*
	451	* Gauss-Jordan Method:
	452	*
	453	* 1. First combine the identity matrix and the input matrix separated by a bar to form an
	454	* augmented matrix as follows:
	455	* _ _ _ _ _ _ _ _
	456	* \| \| a11 a12 \| \| \| 1 0 \| \| \| X11 X12 \|
	457	* \| \| \| \| \| \| \| = \| \|
	458	* \|_ \|_ a21 a22 _\| \| \|_0 1 _\| _\| \|_ X21 X21 _\|
	459	*
	460	* 2. In our implementation, pDst Matrix is used as identity matrix.
	461	*
	462	* 3. Begin with the first row. Let i = 1.
	463	*
	464	* 4. Check to see if the pivot for row i is zero.
	465	* The pivot is the element of the main diagonal that is on the current row.
	466	* For instance, if working with row i, then the pivot element is aii.
	467	* If the pivot is zero, exchange that row with a row below it that does not
	468	* contain a zero in column i. If this is not possible, then an inverse
	469	* to that matrix does not exist.
	470	*
	471	* 5. Divide every element of row i by the pivot.
	472	*
	473	* 6. For every row below and row i, replace that row with the sum of that row and
	474	* a multiple of row i so that each new element in column i below row i is zero.
	475	*
	476	* 7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
	477	* for every element below and above the main diagonal.
	478	*
	479	* 8. Now an identical matrix is formed to the left of the bar(input matrix, src).
	480	* Therefore, the matrix to the right of the bar is our solution(dst matrix, dst).
	481	----------------------------------------------------------------------------------------------------------------/
	482
	483	/* Working pointer for destination matrix */
	484	pOutT1 = pOut;
	485
	486	/* Loop over the number of rows */
	487	rowCnt = numRows;
	488
	489	/* Making the destination matrix as identity matrix */
	490	while(rowCnt > 0u)
	491	{
	492	/* Writing all zeroes in lower triangle of the destination matrix */
	493	j = numRows - rowCnt;
	494	while(j > 0u)
	495	{
	496	*pOutT1++ = 0.0f;
	497	j--;
	498	}
	499
	500	/* Writing all ones in the diagonal of the destination matrix */
	501	*pOutT1++ = 1.0f;
	502
	503	/* Writing all zeroes in upper triangle of the destination matrix */
	504	j = rowCnt - 1u;
	505	while(j > 0u)
	506	{
	507	*pOutT1++ = 0.0f;
	508	j--;
	509	}
	510
	511	/* Decrement the loop counter */
	512	rowCnt--;
	513	}
	514
	515	/* Loop over the number of columns of the input matrix.
	516	All the elements in each column are processed by the row operations */
	517	loopCnt = numCols;
	518
	519	/* Index modifier to navigate through the columns */
	520	l = 0u;
	521	//for(loopCnt = 0u; loopCnt < numCols; loopCnt++)
	522	while(loopCnt > 0u)
	523	{
	524	/* Check if the pivot element is zero..
	525	* If it is zero then interchange the row with non zero row below.
	526	* If there is no non zero element to replace in the rows below,
	527	* then the matrix is Singular. */
	528
	529	/* Working pointer for the input matrix that points
	530	* to the pivot element of the particular row */
	531	pInT1 = pIn + (l * numCols);
	532
	533	/* Working pointer for the destination matrix that points
	534	* to the pivot element of the particular row */
	535	pOutT1 = pOut + (l * numCols);
	536
	537	/* Temporary variable to hold the pivot value */
	538	in = *pInT1;
	539
	540	/* Destination pointer modifier */
	541	k = 1u;
	542
	543	/* Check if the pivot element is zero */
	544	if(*pInT1 == 0.0f)
	545	{
	546	/* Loop over the number rows present below */
	547	for (i = (l + 1u); i < numRows; i++)
	548	{
	549	/* Update the input and destination pointers */
	550	pInT2 = pInT1 + (numCols * l);
	551	pOutT2 = pOutT1 + (numCols * k);
	552
	553	/* Check if there is a non zero pivot element to
	554	* replace in the rows below */
	555	if(*pInT2 != 0.0f)
	556	{
	557	/* Loop over number of columns
	558	* to the right of the pilot element */
	559	for (j = 0u; j < (numCols - l); j++)
	560	{
	561	/* Exchange the row elements of the input matrix */
	562	Xchg = *pInT2;
	563	pInT2++ = pInT1;
	564	*pInT1++ = Xchg;
	565	}
	566
	567	for (j = 0u; j < numCols; j++)
	568	{
	569	Xchg = *pOutT2;
	570	pOutT2++ = pOutT1;
	571	*pOutT1++ = Xchg;
	572	}
	573
	574	/* Flag to indicate whether exchange is done or not */
	575	flag = 1u;
	576
	577	/* Break after exchange is done */
	578	break;
	579	}
	580
	581	/* Update the destination pointer modifier */
	582	k++;
	583	}
	584	}
	585
	586	/* Update the status if the matrix is singular */
	587	if((flag != 1u) && (in == 0.0f))
	588	{
	589	return ARM_MATH_SINGULAR;
	590	}
	591
	592	/* Points to the pivot row of input and destination matrices */
	593	pPivotRowIn = pIn + (l * numCols);
	594	pPivotRowDst = pOut + (l * numCols);
	595
	596	/* Temporary pointers to the pivot row pointers */
	597	pInT1 = pPivotRowIn;
	598	pOutT1 = pPivotRowDst;
	599
	600	/* Pivot element of the row */
	601	in = (pIn + (l numCols));
	602
	603	/* Loop over number of columns
	604	* to the right of the pilot element */
	605	for (j = 0u; j < (numCols - l); j++)
	606	{
	607	/* Divide each element of the row of the input matrix
	608	* by the pivot element */
	609	pInT1 = pInT1 / in;
	610	pInT1++;
	611	}
	612	for (j = 0u; j < numCols; j++)
	613	{
	614	/* Divide each element of the row of the destination matrix
	615	* by the pivot element */
	616	pOutT1 = pOutT1 / in;
	617	pOutT1++;
	618	}
	619
	620	/* Replace the rows with the sum of that row and a multiple of row i
	621	* so that each new element in column i above row i is zero.*/
	622
	623	/* Temporary pointers for input and destination matrices */
	624	pInT1 = pIn;
	625	pOutT1 = pOut;
	626
	627	for (i = 0u; i < numRows; i++)
	628	{
	629	/* Check for the pivot element */
	630	if(i == l)
	631	{
	632	/* If the processing element is the pivot element,
	633	only the columns to the right are to be processed */
	634	pInT1 += numCols - l;
	635	pOutT1 += numCols;
	636	}
	637	else
	638	{
	639	/* Element of the reference row */
	640	in = *pInT1;
	641
	642	/* Working pointers for input and destination pivot rows */
	643	pPRT_in = pPivotRowIn;
	644	pPRT_pDst = pPivotRowDst;
	645
	646	/* Loop over the number of columns to the right of the pivot element,
	647	to replace the elements in the input matrix */
	648	for (j = 0u; j < (numCols - l); j++)
	649	{
	650	/* Replace the element by the sum of that row
	651	and a multiple of the reference row */
	652	pInT1 = pInT1 - (in * *pPRT_in++);
	653	pInT1++;
	654	}
	655	/* Loop over the number of columns to
	656	replace the elements in the destination matrix */
	657	for (j = 0u; j < numCols; j++)
	658	{
	659	/* Replace the element by the sum of that row
	660	and a multiple of the reference row */
	661	pOutT1 = pOutT1 - (in * *pPRT_pDst++);
	662	pOutT1++;
	663	}
	664
	665	}
	666	/* Increment the temporary input pointer */
	667	pInT1 = pInT1 + l;
	668	}
	669	/* Increment the input pointer */
	670	pIn++;
	671
	672	/* Decrement the loop counter */
	673	loopCnt--;
	674	/* Increment the index modifier */
	675	l++;
	676	}
	677
	678
	679	#endif /* #ifndef ARM_MATH_CM0_FAMILY */
	680
	681	/* Set status as ARM_MATH_SUCCESS */
	682	status = ARM_MATH_SUCCESS;
	683
	684	if((flag != 1u) && (in == 0.0f))
	685	{
	686	pIn = pSrc->pData;
	687	for (i = 0; i < numRows * numCols; i++)
	688	{
	689	if (pIn[i] != 0.0f)
	690	break;
	691	}
	692
	693	if (i == numRows * numCols)
	694	status = ARM_MATH_SINGULAR;
	695	}
	696	}
	697	/* Return to application */
	698	return (status);
	699	}
	700
	701	/**
	702	* @} end of MatrixInv group
	703	*/