B = sqrt(X) returnsthe square root of each element of the array X.For the elements of X that are negative or complex, sqrt(X) producescomplex results.
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The sqrt function’s domain includesnegative and complex numbers, which can lead to unexpected resultsif used unintentionally. For negative and complex numbers z= u + i*w, the complex square root sqrt(z) returns
sqrt(r)*(cos(phi/2) + 1i*sin(phi/2))
where r = abs(z) is the radius and phi= angle(z) is the phase angle on the closed interval -pi.
If you want negative and complex numbers to return error messagesrather than return complex results, use realsqrt instead.
Examples
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Square Root of Vector Elements
Open Live Script
Create a row vector containing both negative and positive values.
X = -2:2
X = 1×5 -2 -1 0 1 2
Compute the square root of each element of X.
Y = sqrt(X)
Y = 1×5 complex 0.0000 + 1.4142i 0.0000 + 1.0000i 0.0000 + 0.0000i 1.0000 + 0.0000i 1.4142 + 0.0000i
Input Arguments
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X — Input array scalar | vector | matrix | multidimensional array
Input array, specified as a numeric scalar, vector, matrix,or multidimensional array.
Data Types: single | doubleComplex Number Support: Yes
More About
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IEEE Compliance
For real inputs, sqrt has a few behaviors that differ from those recommended in the IEEE®-754 Standard. In particular, negative inputs produce complex results instead of NaN.
|
sqrt(-0) |
0 |
-0 |
|
sqrt(X) for X |
0+sqrt(-X)*i |
NaN |
Tips
Extended Capabilities
Tall Arrays Calculate with arrays that have more rows than fit in memory.
This function fully supports tall arrays. Formore information, see Tall Arrays.
C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Simulation produces an error. Generated standalonecode returns NaN when the input value x isreal, but the output should be complex. To get the complex result,make the input value complex by passing in complex(x).
If you generate code for standalone targets and the input to sqrt in your MATLAB code is not a constant, the value that the generated code returns for sqrt(-0) is identical to the value that the standard library function of your C/C++ compiler returns. If the standard library function complies with the IEEE-754 Standard, the generated code returns -0.
GPU Code Generation Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.
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Usage notes and limitations:
Simulation produces an error. Generated standalone code returns NaN when the input value x is real, but the output should be complex. To get the complex result, make the input value complex by passing in complex(x).
Thread-Based Environment Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
If the output of the function running on the GPU can be complex, then you must explicitly specify its input arguments as complex. For more information, see Work with Complex Numbers on a GPU (Parallel Computing Toolbox).
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Distributed ArraysPartition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
See Also
nthroot | sqrtm | realsqrt
Introduced before R2006a
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