1 /* ----------------------------------------------------------------------
2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
4 * $Date: 17. January 2013
7 * Project: CMSIS DSP Library
10 * Description: Variance of the elements of a floating-point vector.
12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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48 * @defgroup variance Variance
50 * Calculates the variance of the elements in the input vector.
51 * The underlying algorithm is used:
54 * Result = (sumOfSquares - sum<sup>2</sup> / blockSize) / (blockSize - 1)
56 * where, sumOfSquares = pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]
58 * sum = pSrc[0] + pSrc[1] + pSrc[2] + ... + pSrc[blockSize-1]
61 * There are separate functions for floating point, Q31, and Q15 data types.
65 * @addtogroup variance
71 * @brief Variance of the elements of a floating-point vector.
72 * @param[in] *pSrc points to the input vector
73 * @param[in] blockSize length of the input vector
74 * @param[out] *pResult variance value returned here
86 float32_t sum = 0.0f; /* Temporary result storage */
87 float32_t sumOfSquares = 0.0f; /* Sum of squares */
88 float32_t in; /* input value */
89 uint32_t blkCnt; /* loop counter */
91 #ifndef ARM_MATH_CM0_FAMILY
93 /* Run the below code for Cortex-M4 and Cortex-M3 */
95 float32_t meanOfSquares, mean, squareOfMean; /* Temporary variables */
98 blkCnt = blockSize >> 2u;
100 /* First part of the processing with loop unrolling. Compute 4 outputs at a time.
101 ** a second loop below computes the remaining 1 to 3 samples. */
104 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
105 /* Compute Sum of squares of the input samples
106 * and then store the result in a temporary variable, sum. */
109 sumOfSquares += in * in;
112 sumOfSquares += in * in;
115 sumOfSquares += in * in;
118 sumOfSquares += in * in;
120 /* Decrement the loop counter */
124 /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
125 ** No loop unrolling is used. */
126 blkCnt = blockSize % 0x4u;
130 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
131 /* Compute Sum of squares of the input samples
132 * and then store the result in a temporary variable, sum. */
135 sumOfSquares += in * in;
137 /* Decrement the loop counter */
141 /* Compute Mean of squares of the input samples
142 * and then store the result in a temporary variable, meanOfSquares. */
143 meanOfSquares = sumOfSquares / ((float32_t) blockSize - 1.0f);
145 /* Compute mean of all input values */
146 mean = sum / (float32_t) blockSize;
148 /* Compute square of mean */
149 squareOfMean = (mean * mean) * (((float32_t) blockSize) /
150 ((float32_t) blockSize - 1.0f));
152 /* Compute variance and then store the result to the destination */
153 *pResult = meanOfSquares - squareOfMean;
157 /* Run the below code for Cortex-M0 */
158 float32_t squareOfSum; /* Square of Sum */
160 /* Loop over blockSize number of values */
165 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
166 /* Compute Sum of squares of the input samples
167 * and then store the result in a temporary variable, sumOfSquares. */
169 sumOfSquares += in * in;
171 /* C = (A[0] + A[1] + ... + A[blockSize-1]) */
172 /* Compute Sum of the input samples
173 * and then store the result in a temporary variable, sum. */
176 /* Decrement the loop counter */
180 /* Compute the square of sum */
181 squareOfSum = ((sum * sum) / (float32_t) blockSize);
183 /* Compute the variance */
184 *pResult = ((sumOfSquares - squareOfSum) / (float32_t) (blockSize - 1.0f));
186 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
191 * @} end of variance group