tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/MatrixFunctions/arm_mat_inverse_f32.c

   1 /* ----------------------------------------------------------------------
   2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
   3 *
   4 * $Date:        1. March 2013
   5 * $Revision:    V1.4.1
   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 till 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 *pInT3, *pInT4;                      /* 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 coluimns, 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 absolut 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     pInT2 = 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         *pInT2++ = 0.0f;
 171         j--;
 172       }
 173
 174       /* Writing all ones in the diagonal of the destination matrix */
 175       *pInT2++ = 1.0f;
 176
 177       /* Writing all zeroes in upper triangle of the destination matrix */
 178       j = rowCnt - 1u;
 179       while(j > 0u)
 180       {
 181         *pInT2++ = 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       pInT3 = pOut + (l * numCols);
 210
 211       /* Temporary variable to hold the pivot value */
 212       in = *pInT1;
 213
 214       /* Destination pointer modifier */
 215       k = 1u;
 216
 217      /* Grab the most significant value from column l */
 218       maxC = 0;
 219       for (i = 0; i < numRows; i++)
 220       {
 221         maxC = *pInT1 > 0 ? (*pInT1 > maxC ? *pInT1 : maxC) : (-*pInT1 > maxC ? -*pInT1 : maxC);
 222         pInT1 += numCols;
 223       }
 224
 225       /* Update the status if the matrix is singular */
 226       if(maxC == 0.0f)
 227       {
 228         status = ARM_MATH_SINGULAR;
 229         break;
 230       }
 231
 232       /* Restore pInT1  */
 233       pInT1 -= numRows * numCols;
 234
 235       /* Check if the pivot element is the most significant of the column */
 236       if( (in > 0.0f ? in : -in) != maxC)
 237       {
 238         /* Loop over the number rows present below */
 239         i = numRows - (l + 1u);
 240
 241         while(i > 0u)
 242         {
 243           /* Update the input and destination pointers */
 244           pInT2 = pInT1 + (numCols * l);
 245           pInT4 = pInT3 + (numCols * k);
 246
 247           /* Look for the most significant element to
 248            * replace in the rows below */
 249           if((*pInT2 > 0.0f ? *pInT2: -*pInT2) == maxC)
 250           {
 251             /* Loop over number of columns
 252              * to the right of the pilot element */
 253             j = numCols - l;
 254
 255             while(j > 0u)
 256             {
 257               /* Exchange the row elements of the input matrix */
 258               Xchg = *pInT2;
 259               *pInT2++ = *pInT1;
 260               *pInT1++ = Xchg;
 261
 262               /* Decrement the loop counter */
 263               j--;
 264             }
 265
 266             /* Loop over number of columns of the destination matrix */
 267             j = numCols;
 268
 269             while(j > 0u)
 270             {
 271               /* Exchange the row elements of the destination matrix */
 272               Xchg = *pInT4;
 273               *pInT4++ = *pInT3;
 274               *pInT3++ = Xchg;
 275
 276               /* Decrement the loop counter */
 277               j--;
 278             }
 279
 280             /* Flag to indicate whether exchange is done or not */
 281             flag = 1u;
 282
 283             /* Break after exchange is done */
 284             break;
 285           }
 286
 287           /* Update the destination pointer modifier */
 288           k++;
 289
 290           /* Decrement the loop counter */
 291           i--;
 292         }
 293       }
 294
 295       /* Update the status if the matrix is singular */
 296       if((flag != 1u) && (in == 0.0f))
 297       {
 298         status = ARM_MATH_SINGULAR;
 299
 300         break;
 301       }
 302
 303       /* Points to the pivot row of input and destination matrices */
 304       pPivotRowIn = pIn + (l * numCols);
 305       pPivotRowDst = pOut + (l * numCols);
 306
 307       /* Temporary pointers to the pivot row pointers */
 308       pInT1 = pPivotRowIn;
 309       pInT2 = pPivotRowDst;
 310
 311       /* Pivot element of the row */
 312       in = *pPivotRowIn;
 313
 314       /* Loop over number of columns
 315        * to the right of the pilot element */
 316       j = (numCols - l);
 317
 318       while(j > 0u)
 319       {
 320         /* Divide each element of the row of the input matrix
 321          * by the pivot element */
 322         in1 = *pInT1;
 323         *pInT1++ = in1 / in;
 324
 325         /* Decrement the loop counter */
 326         j--;
 327       }
 328
 329       /* Loop over number of columns of the destination matrix */
 330       j = numCols;
 331
 332       while(j > 0u)
 333       {
 334         /* Divide each element of the row of the destination matrix
 335          * by the pivot element */
 336         in1 = *pInT2;
 337         *pInT2++ = in1 / in;
 338
 339         /* Decrement the loop counter */
 340         j--;
 341       }
 342
 343       /* Replace the rows with the sum of that row and a multiple of row i
 344        * so that each new element in column i above row i is zero.*/
 345
 346       /* Temporary pointers for input and destination matrices */
 347       pInT1 = pIn;
 348       pInT2 = pOut;
 349
 350       /* index used to check for pivot element */
 351       i = 0u;
 352
 353       /* Loop over number of rows */
 354       /*  to be replaced by the sum of that row and a multiple of row i */
 355       k = numRows;
 356
 357       while(k > 0u)
 358       {
 359         /* Check for the pivot element */
 360         if(i == l)
 361         {
 362           /* If the processing element is the pivot element,
 363              only the columns to the right are to be processed */
 364           pInT1 += numCols - l;
 365
 366           pInT2 += numCols;
 367         }
 368         else
 369         {
 370           /* Element of the reference row */
 371           in = *pInT1;
 372
 373           /* Working pointers for input and destination pivot rows */
 374           pPRT_in = pPivotRowIn;
 375           pPRT_pDst = pPivotRowDst;
 376
 377           /* Loop over the number of columns to the right of the pivot element,
 378              to replace the elements in the input matrix */
 379           j = (numCols - l);
 380
 381           while(j > 0u)
 382           {
 383             /* Replace the element by the sum of that row
 384                and a multiple of the reference row  */
 385             in1 = *pInT1;
 386             *pInT1++ = in1 - (in * *pPRT_in++);
 387
 388             /* Decrement the loop counter */
 389             j--;
 390           }
 391
 392           /* Loop over the number of columns to
 393              replace the elements in the destination matrix */
 394           j = numCols;
 395
 396           while(j > 0u)
 397           {
 398             /* Replace the element by the sum of that row
 399                and a multiple of the reference row  */
 400             in1 = *pInT2;
 401             *pInT2++ = in1 - (in * *pPRT_pDst++);
 402
 403             /* Decrement the loop counter */
 404             j--;
 405           }
 406
 407         }
 408
 409         /* Increment the temporary input pointer */
 410         pInT1 = pInT1 + l;
 411
 412         /* Decrement the loop counter */
 413         k--;
 414
 415         /* Increment the pivot index */
 416         i++;
 417       }
 418
 419       /* Increment the input pointer */
 420       pIn++;
 421
 422       /* Decrement the loop counter */
 423       loopCnt--;
 424
 425       /* Increment the index modifier */
 426       l++;
 427     }
 428
 429
 430 #else
 431
 432   /* Run the below code for Cortex-M0 */
 433
 434   float32_t Xchg, in = 0.0f;                     /* Temporary input values  */
 435   uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l;      /* loop counters */
 436   arm_status status;                             /* status of matrix inverse */
 437
 438 #ifdef ARM_MATH_MATRIX_CHECK
 439
 440   /* Check for matrix mismatch condition */
 441   if((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols)
 442      || (pSrc->numRows != pDst->numRows))
 443   {
 444     /* Set status as ARM_MATH_SIZE_MISMATCH */
 445     status = ARM_MATH_SIZE_MISMATCH;
 446   }
 447   else
 448 #endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
 449   {
 450
 451     /*--------------------------------------------------------------------------------------------------------------
 452          * Matrix Inverse can be solved using elementary row operations.
 453          *
 454          *      Gauss-Jordan Method:
 455          *
 456          *         1. First combine the identity matrix and the input matrix separated by a bar to form an
 457          *        augmented matrix as follows:
 458          *                                      _  _          _     _      _   _         _             _
 459          *                                         |  |  a11  a12  | | | 1   0  |   |       |  X11 X12  |
 460          *                                         |  |            | | |        |   |   =   |           |
 461          *                                         |_ |_ a21  a22 _| | |_0   1 _|  _|       |_ X21 X21 _|
 462          *
 463          *              2. In our implementation, pDst Matrix is used as identity matrix.
 464          *
 465          *              3. Begin with the first row. Let i = 1.
 466          *
 467          *          4. Check to see if the pivot for row i is zero.
 468          *                 The pivot is the element of the main diagonal that is on the current row.
 469          *                 For instance, if working with row i, then the pivot element is aii.
 470          *                 If the pivot is zero, exchange that row with a row below it that does not
 471          *                 contain a zero in column i. If this is not possible, then an inverse
 472          *                 to that matrix does not exist.
 473          *
 474          *          5. Divide every element of row i by the pivot.
 475          *
 476          *          6. For every row below and  row i, replace that row with the sum of that row and
 477          *                 a multiple of row i so that each new element in column i below row i is zero.
 478          *
 479          *          7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
 480          *                 for every element below and above the main diagonal.
 481          *
 482          *              8. Now an identical matrix is formed to the left of the bar(input matrix, src).
 483          *                 Therefore, the matrix to the right of the bar is our solution(dst matrix, dst).
 484          *----------------------------------------------------------------------------------------------------------------*/
 485
 486     /* Working pointer for destination matrix */
 487     pInT2 = pOut;
 488
 489     /* Loop over the number of rows */
 490     rowCnt = numRows;
 491
 492     /* Making the destination matrix as identity matrix */
 493     while(rowCnt > 0u)
 494     {
 495       /* Writing all zeroes in lower triangle of the destination matrix */
 496       j = numRows - rowCnt;
 497       while(j > 0u)
 498       {
 499         *pInT2++ = 0.0f;
 500         j--;
 501       }
 502
 503       /* Writing all ones in the diagonal of the destination matrix */
 504       *pInT2++ = 1.0f;
 505
 506       /* Writing all zeroes in upper triangle of the destination matrix */
 507       j = rowCnt - 1u;
 508       while(j > 0u)
 509       {
 510         *pInT2++ = 0.0f;
 511         j--;
 512       }
 513
 514       /* Decrement the loop counter */
 515       rowCnt--;
 516     }
 517
 518     /* Loop over the number of columns of the input matrix.
 519        All the elements in each column are processed by the row operations */
 520     loopCnt = numCols;
 521
 522     /* Index modifier to navigate through the columns */
 523     l = 0u;
 524     //for(loopCnt = 0u; loopCnt < numCols; loopCnt++)
 525     while(loopCnt > 0u)
 526     {
 527       /* Check if the pivot element is zero..
 528        * If it is zero then interchange the row with non zero row below.
 529        * If there is no non zero element to replace in the rows below,
 530        * then the matrix is Singular. */
 531
 532       /* Working pointer for the input matrix that points
 533        * to the pivot element of the particular row  */
 534       pInT1 = pIn + (l * numCols);
 535
 536       /* Working pointer for the destination matrix that points
 537        * to the pivot element of the particular row  */
 538       pInT3 = pOut + (l * numCols);
 539
 540       /* Temporary variable to hold the pivot value */
 541       in = *pInT1;
 542
 543       /* Destination pointer modifier */
 544       k = 1u;
 545
 546       /* Check if the pivot element is zero */
 547       if(*pInT1 == 0.0f)
 548       {
 549         /* Loop over the number rows present below */
 550         for (i = (l + 1u); i < numRows; i++)
 551         {
 552           /* Update the input and destination pointers */
 553           pInT2 = pInT1 + (numCols * l);
 554           pInT4 = pInT3 + (numCols * k);
 555
 556           /* Check if there is a non zero pivot element to
 557            * replace in the rows below */
 558           if(*pInT2 != 0.0f)
 559           {
 560             /* Loop over number of columns
 561              * to the right of the pilot element */
 562             for (j = 0u; j < (numCols - l); j++)
 563             {
 564               /* Exchange the row elements of the input matrix */
 565               Xchg = *pInT2;
 566               *pInT2++ = *pInT1;
 567               *pInT1++ = Xchg;
 568             }
 569
 570             for (j = 0u; j < numCols; j++)
 571             {
 572               Xchg = *pInT4;
 573               *pInT4++ = *pInT3;
 574               *pInT3++ = Xchg;
 575             }
 576
 577             /* Flag to indicate whether exchange is done or not */
 578             flag = 1u;
 579
 580             /* Break after exchange is done */
 581             break;
 582           }
 583
 584           /* Update the destination pointer modifier */
 585           k++;
 586         }
 587       }
 588
 589       /* Update the status if the matrix is singular */
 590       if((flag != 1u) && (in == 0.0f))
 591       {
 592         status = ARM_MATH_SINGULAR;
 593
 594         break;
 595       }
 596
 597       /* Points to the pivot row of input and destination matrices */
 598       pPivotRowIn = pIn + (l * numCols);
 599       pPivotRowDst = pOut + (l * numCols);
 600
 601       /* Temporary pointers to the pivot row pointers */
 602       pInT1 = pPivotRowIn;
 603       pInT2 = pPivotRowDst;
 604
 605       /* Pivot element of the row */
 606       in = *(pIn + (l * numCols));
 607
 608       /* Loop over number of columns
 609        * to the right of the pilot element */
 610       for (j = 0u; j < (numCols - l); j++)
 611       {
 612         /* Divide each element of the row of the input matrix
 613          * by the pivot element */
 614         *pInT1 = *pInT1 / in;
 615         pInT1++;
 616       }
 617       for (j = 0u; j < numCols; j++)
 618       {
 619         /* Divide each element of the row of the destination matrix
 620          * by the pivot element */
 621         *pInT2 = *pInT2 / in;
 622         pInT2++;
 623       }
 624
 625       /* Replace the rows with the sum of that row and a multiple of row i
 626        * so that each new element in column i above row i is zero.*/
 627
 628       /* Temporary pointers for input and destination matrices */
 629       pInT1 = pIn;
 630       pInT2 = pOut;
 631
 632       for (i = 0u; i < numRows; i++)
 633       {
 634         /* Check for the pivot element */
 635         if(i == l)
 636         {
 637           /* If the processing element is the pivot element,
 638              only the columns to the right are to be processed */
 639           pInT1 += numCols - l;
 640           pInT2 += numCols;
 641         }
 642         else
 643         {
 644           /* Element of the reference row */
 645           in = *pInT1;
 646
 647           /* Working pointers for input and destination pivot rows */
 648           pPRT_in = pPivotRowIn;
 649           pPRT_pDst = pPivotRowDst;
 650
 651           /* Loop over the number of columns to the right of the pivot element,
 652              to replace the elements in the input matrix */
 653           for (j = 0u; j < (numCols - l); j++)
 654           {
 655             /* Replace the element by the sum of that row
 656                and a multiple of the reference row  */
 657             *pInT1 = *pInT1 - (in * *pPRT_in++);
 658             pInT1++;
 659           }
 660           /* Loop over the number of columns to
 661              replace the elements in the destination matrix */
 662           for (j = 0u; j < numCols; j++)
 663           {
 664             /* Replace the element by the sum of that row
 665                and a multiple of the reference row  */
 666             *pInT2 = *pInT2 - (in * *pPRT_pDst++);
 667             pInT2++;
 668           }
 669
 670         }
 671         /* Increment the temporary input pointer */
 672         pInT1 = pInT1 + l;
 673       }
 674       /* Increment the input pointer */
 675       pIn++;
 676
 677       /* Decrement the loop counter */
 678       loopCnt--;
 679       /* Increment the index modifier */
 680       l++;
 681     }
 682
 683
 684 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
 685
 686     /* Set status as ARM_MATH_SUCCESS */
 687     status = ARM_MATH_SUCCESS;
 688
 689     if((flag != 1u) && (in == 0.0f))
 690     {
 691       status = ARM_MATH_SINGULAR;
 692     }
 693   }
 694   /* Return to application */
 695   return (status);
 696 }
 697
 698 /**
 699  * @} end of MatrixInv group
 700  */