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Pseudoinverse
5-347
5Pseudoinverse
Purpose Compute the Moore-Penrose pseudoinverse of a matrix.
Library Math Functions / Matrices and Linear Algebra / Matrix Inverses
Description The Pseudoinverse block computes the Moore-Penrose pseudoinverse of input
matrix A.
[U,S,V] = svd(A,0) % Equivalent MATLAB code
The pseudoinverse of A is the matrix A
+
such that
where U and V are orthogonal matrices, and S is a diagonal matrix. The
pseudoinverse has the following properties:
•AA
+
= (AA
+
)
*
•A
+
A = (A
+
A)
*
•AA
+
A = A
•A
+
AA
+
= A
+
The output is always sample-based.
Dialog Box
References
Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.
Supported
Data Types
A
+
VS
+
U
*
=
Double-precision floating point
- Blockset 1
- How to Contact The MathWorks: 2
- Contents 3
- Working with Signals 4
- DSP Function Reference 10
- Introduction 11
- 1 Introduction 12
- Welcome to the DSP Blockset 12
- What Is the DSP Blockset? 13
- Frame-Based Operations 13
- Matrix Support 14
- Statistical Operations 15
- Linear Algebra 15
- Parametric Estimation 15
- Real-Time Code Generation 15
- What Is in the DSP Blockset? 16
- Installation 17
- How to Use This Guide 19
- Signal Dimension Nomenclature 20
- Sampling Nomenclature 21
- R12 Related Products 23
- DSP Blockset 25
- The Simulink Environment 27
- Simulink on PC Platforms 27
- Simulink on UNIX Platforms 28
- The Simulink Libraries 29
- Model Definition 29
- parameters. They also both 31
- Model Simulation 32
- 0.1 for Time 33
- [1 5] or 33
- Learning More About Simulink 34
- Fixed-step option in the 35
- Using dspstartup.m 36
- Customizing dspstartup.m 36
- Performance-Related Settings 37
- Simulink and the DSP Blockset 38
- Parameters 38
- Miscellaneous Settings 39
- Signal Concepts 43
- Source Blocks 49
- Nonsource Blocks 50
- Error: Continuous sample 50
- Multichannel Signals 51
- Accelerating Simulations 55
- Sample Rates and Frame Rates 57
- 0, as explained in 58
- Red = fastest sample rate 59
- Direct Rate Conversion 61
- Sample time and Samples per 63
- Changing Frame Status 71
- Creating Signals 73
- •Sample time 77
- Constructing Signals 82
- Number of inputs = 2 85
- Signal = 5*ones(10,1) 87
- Initial 93
- Signal = randn(3,2,10) 95
- Select = Rows 95
- - Starting column index = 1 96
- 3 Working with Signals 100
- Deconstructing Signals 101
- Importing Signals 102
- Importing WAV Files 111
- Exporting Signals 112
- Using the To Workspace Block 116
- Stereo check box. See the 119
- Viewing Signals 120
- Example: Displaying Matrices 123
- = 0:pi/64:pi 124
- •Ending column offset = 1 124
- Delay and Latency 125
- Reducing Computational Delay 125
- Zero Algorithmic Delay 127
- Basic Algorithmic Delay 129
- Predicting Tasking Latency 132
- Type = Fixed-step 135
- Mode = SingleTasking 135
- DSP Operations 137
- 4 DSP Operations 138
- Overview 138
- Filters 139
- Multirate Filters 145
- Transforms 146
- Example: Using the FFT Block 146
- Example: Using the IFFT Block 148
- Power Spectrum Estimation 151
- Example: LU Solver 153
- Example: LU Inverse 155
- Statistics 157
- Example: Sliding Windows 158
- Running Operations 159
- DSP Blockset Demos Overview 160
- Communications Demos 161
- Filtering Demos 161
- DSP Block Reference 163
- 5 DSP Block Reference 164
- About Tunable Parameters 165
- About Supported Data Types 165
- Block Library List 171
- Analytic Signal IDCT 179
- Complex Cepstrum IFFT 179
- DCT Real Cepstrum 179
- Analog Filter Design 180
- Supported 183
- Data Types 183
- See Also 183
- Analytic Signal 184
- Autocorrelation 186
- Dialog Box 187
- Autocorrelation LPC 188
- Backward Substitution 192
- Biquadratic Filter 194
- Sample-Based Operation 198
- Sample-based input 199
- Frame-based output 199
- Frame-Based Operation 200
- Latency Zero Latency 201
- Nonzero Latency 202
- Burg AR Estimator 205
- Burg Method 207
- Check Signal Attributes 211
- Library DSP Sources 218
- These diagrams apply 220
- Initial frequency (Hertz), f 221
- Unidirectional 221
- Sweep time, T 221
- Bidirectional 221
- Sweep time, 2 221
- Block Computation Methods 222
- Quadratic, or Logarithmic 224
- 1 second), the Target 226
- Sweep time (1.5 seconds) 229
- Target frequency parameter 230
- AMPLITUDE 231
- Cholesky Factorization 235
- Cholesky Inverse 237
- Cholesky Solver 239
- Complex Cepstrum 241
- Complex Exponential 243
- Constant Diagonal Matrix 244
- parameter 246
- Constant Ramp 247
- Contiguous Copy 248
- Convert 1-D to 2-D 250
- Convert 2-D to 1-D 252
- ∗) as a guide to wiring 253
- ∗ symbol 253
- Convolution 257
- Correlation 259
- 5Counter 261
- Free-Running Operation 263
- Covariance AR Estimator 268
- Covariance Method 270
- Create Diagonal Matrix 272
- Cumulative Sum 273
- Power Inputs 275
- Voltage Inputs 275
- Library Transforms 279
- Delay Line 281
- 5Detrend 285
- Difference 286
- Digital Filter Design 288
- Initial Conditions 292
- Discrete Impulse 295
- Output Sequence (K=4) 298
- Downsample 299
- ) appears in the output as 303
- DSP Constant 305
- 5DSP Constant 305
- Dyadic Analysis Filter Bank 308
- Dyadic Synthesis Filter Bank 316
- Edge Detector 323
- Event-Count Comparator 325
- Extract Diagonal 327
- Extract Triangular Matrix 328
- Valid Block Inputs 331
- Dimension Along 331
- Which Block 331
- Computes DFT 331
- Twiddle factor computation 335
- Parameter Setting 335
- Sine and Cosine Computation 335
- Effect on Block Performance 335
- Speed 3N/4 1536 bytes 336
- Memory N/4 + 1 516 bytes 336
- Look under mask. Look under 337
- Filter Realization Wizard 340
- 5Filter Realization Wizard 340
- Fixed-Point Options 341
- Example 1: Direct Form II 342
- Example 3: Nth Order Sections 344
- Example 4: ARMA Lattice 345
- FIR Decimation 350
- Examples Example 1 353
- FIR Interpolation 357
- FIR Rate Conversion 364
- Forward Substitution 370
- Frame Status Conversion 372
- From Wave Device 374
- 5From Wave Device 374
- Buffering 375
- From Wave File 379
- Histogram 381
- Running Operation 382
- Identity Matrix 387
- Skip normaliza 391
- Conjugate Symmetric Input 392
- Inputs in Bit-Reversed Order 393
- Inherit Complexity 396
- Integer Delay 398
- Delay: [2 0 5] 404
- Initial conditions: 0 404
- Kalman Adaptive Filter 406
- LDL Factorization 411
- LDL Inverse 414
- LDL Solver 416
- Least Squares Polynomial Fit 418
- Levinson-Durbin 421
- Applications 422
- LMS Adaptive Filter 425
- LU Factorization 429
- LU Inverse 431
- LU Solver 432
- Magnitude FFT 434
- Matrix 1-Norm 437
- Matrix Multiply 439
- Matrix Product 441
- Matrix Scaling 443
- Matrix Square 445
- Matrix Sum 447
- Matrix Viewer 449
- Library Statistics 455
- Value Mode 455
- Index Mode 455
- Value and Index Mode 456
- Running Mode 456
- Basic Operation 460
- Modified Covariance Method 473
- Multiphase Clock 476
- Multiport Selector 479
- 5Multiport Selector 479
- N-Sample Enable 482
- N-Sample Switch 484
- 5N-Sample Switch 484
- Normalization 486
- Overlap-Add FFT Filter 488
- Overlap-Save FFT Filter 491
- Library Signal Operations 494
- Permute Matrix 496
- 5Permute Matrix 496
- Polynomial Evaluation 500
- Polynomial Stability Test 502
- Pseudoinverse 504
- QR Factorization 506
- QR Solver 508
- Register size parameter, and 510
- Clear input check box) 510
- Example 2 512
- Random Source 515
- Sample Period 518
- Real Cepstrum 522
- Reciprocal Condition 524
- Maintain input frame rate 527
- Initial condition 528
- RLS Adaptive Filter 532
- Sample and Hold 540
- Short-Time FFT 542
- Signal From Workspace 545
- Signal To Workspace 549
- Output Dimension Summary 550
- Sine Wave 555
- Singular Value Decomposition 562
- Spectrum Scope 566
- Standard Deviation 575
- Submatrix 579
- N/2 by the 581
- •Starting column offset = 1 582
- SVD Solver 587
- Time Scope 589
- 5Time Scope 589
- Library DSP Sinks 589
- Filter Type 590
- Filter Update Rate 592
- Time-Varying Lattice Filter 595
- Toeplitz 599
- 5Toeplitz 599
- To Wave Device 601
- 5To Wave Device 601
- To Wave File 606
- 5To Wave File 606
- Transpose 608
- Triggered Delay Line 610
- Trigger Event 613
- Initial and Final Conditions 613
- Triggered To Workspace 617
- 5Triggered To Workspace 617
- Unbuffer 620
- Uniform Decoder 623
- Uniform Encoder 627
- The Two Unwrap Modes 632
- Tolerance parameter) 634
- Tolerance parameter = π 634
- Unwrap Method 636
- Definition of Phase Unwrap 636
- Method” on page 5-479 637
- 0 pi 2pi 3pi 4pi 5pi 6pi 638
- Upsample 641
- Variable Fractional Delay 648
- Interpolation Modes 649
- Variable Integer Delay 653
- Variable Selector 661
- 5Variable Selector 661
- Variance 664
- Vector Scope 668
- Display Properties 672
- Axis Properties 673
- Line Properties 675
- Scope Window 678
- Display Properties Dialog Box 681
- Line Properties Dialog Box 684
- Wavelet Analysis 686
- Filter Coefficients 687
- Tree Structure 687
- Wavelet Synthesis 692
- Window Function 698
- Window Sampling 699
- Window Type 699
- Yule-Walker AR Estimator 703
- Yule-Walker Method 706
- Zero Pad 709
- 6 DSP Function Reference 713
- Syntax dsp_links 714
- Syntax dsplib 715
- 6dspstartup 716
- Syntax dspstartup 716
- Syntax liblinks 718
- Numerics 720
- RTWOptions parameter 2-15 733
- SaveOutput parameter 2-13 733
- SaveTime parameter 2-13 733
- Solver parameter 2-15 735
- StopTime parameter 2-15 735
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