SVD_DEMO
Demonstration of the Singular Value Decomposition

SVD_DEMO is an executable MATLAB program, using double precision arithmetic, which demonstrates the computation of the singular value decomposition and a few of its properties.

The singular value decomposition has uses in solving overdetermined or underdetermined linear systems, linear least squares problems, data compression, the pseudoinverse matrix, reduced order modeling, and the accurate computation of matrix rank and null space,

Usage:

svd_demo ( m, n, [seed] )

runs the program, generating a random matrix of order M rows by N columns. If SEED is supplied, it is used as the seed for the random number generator. Otherwise, a value is generated internally by the program.

Related Data and Programs:

LAPACK is a FORTRAN90 library of linear algebra routines, which includes routines to carry out the singular value decomposition.

LINPACK is a MATLAB library of linear algebra routines, which includes routines to carry out the singular value decomposition.

SVD_BASIS is an interactive executable MATLAB program which computes a reduced basis for a collection of data vectors using the SVD.

SVD_DEMO is also available in a C++ version and a FORTRAN90 version.

TOMS358 is a FORTRAN77 routine which computes the singular value decomposition for a complex matrix.

Reference:

1. Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Danny Sorensen,
   LAPACK User's Guide,
   Third Edition,
   SIAM, 1999,
   ISBN: 0898714478,
   LC: QA76.73.F25L36
2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
3. Gene Golub, Charles VanLoan,
   Matrix Computations, Third Edition,
   Johns Hopkins, 1996,
   ISBN: 0-8018-4513-X,
   LC: QA188.G65.
4. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.
5. Lloyd Trefethen, David Bau,
   Numerical Linear Algebra,
   SIAM, 1997,
   ISBN: 0-89871-361-7,
   LC: QA184.T74.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• svd_demo_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• svd_demo_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• svd_demo.m, the main program.
• get_seed.m returns a seed for the random number generator.
• i4_uniform.m returns a pseudorandom I4.
• pseudo_inverse.m computes the pseudoinverse.
• pseudo_linear_solve_test.m uses the pseudoinverse for linear systems.
• pseudo_product_test.m examines the products A*A+ and A+*A.
• r4_uniform_01.m returns a unit pseudorandom R4.
• r8mat_dif_fro.m returns the Frobenius norm of the difference of two R8MAT's.
• r8mat_norm_fro.m returns the Frobenius norm of an R8MAT.
• r8mat_print.m prints an R8MAT.
• r8mat_print_some.m prints some of an R8MAT.
• r8mat_uniform_01.m returns a unit pseudorandom R8MAT.
• r8vec_norm_l2.m returns the L2 norm of an R8VEC.
• r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
• rank_one_print_test.m prints the sums of rank one matrices.
• rank_one_test.m compares A to the sum of rank one matrices.
• svd_product_test.m tests that A = U * S * V.
• timestamp.m prints the current YMDHMS date as a time stamp.

Examples and Tests:

• svd_demo_5_3.out, the output from the command "svd_demo 5 3".
• svd_demo_5_5.out, the output from the command "svd_demo 5 5".
• svd_demo_5_8.out, the output from the command "svd_demo 5 8".

You can go up one level to the MATLAB source codes.