REGRESSION - Linear Regression

REGRESSION is a collection of software for linear regression. The most common task for such routines is to solve an overdetermined system of linear equations.

In particular, many routines will produce a least-squares solution. That is, given an M by N matrix A, and an M vector B, the routines will seek an N vector X so which minimizes the L2 norm (square root of the sum of the squares of the components) of the residual

        R = A * X - B
      

The code is in a very provisional state. Many routines have not been carefully proofread or debugged or tested yet.

Reference:

Helmuth Spaeth,
Mathematical Algorithms for Linear Regression,
Academic Press, 1991,
ISBN 0-12-656460-4.

A set of 60 data files are also available in the REGRESSION data directory.

Files you may copy include:

• regression.f90, the source code;
• regression_prb.f90, sample calling program;
• regression_prb.out, the results file.

The list of routines includes:

• A328_LI minimizes the L-infinity norm of A*x-b.
• A478_L1 minimizes the L1 norm of A*x-b using the modified simplex method.
• A478_L1_COL is used by A478_L1.
• A495_LI minimizes the L-Infinity norm of A*x-b using a simplex method.
• A495_LI_COL adds a multiple of one vector to another.
• ABD_LI minimizes the L-infinity norm of A*x-b using a simplex method.
• AFK_L1 minimizes the L1 norm of A*x-b.
• AFK_L1_CALBET is used by AFK_L1 to compute the solution.
• AFK_L1_UPDATE updates the LU decomposition of a matrix.
• AVLLSQ carries out average linear regression.
• BLOD_L1 minimizes the L1 norm of A*x-b.
• BLOD_L1_CRIT returns three sums of entries of U.
• BLOD_L1_GET1 is used by BLOD_L1.
• BLOD_L1_GET2 is used by BLOD_L1.
• BLOD_L1_MED3 is used by BLOD_L1.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_IS_DIGIT returns .TRUE. if a character is a decimal digit.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• C01M generates a new combination from an old one efficiently.
• CON_L1 minimizes the L1 norm of A * X - B subject to linear constraints.
• CON_L1_COL adds a multiple of one vector to another.
• CON_L2 minimizes the L2 norm of A * X - B subject to linear constraints.
• CON_LI minimizes the L-infinity norm of A * X - B subject to linear constraints.
• CON_LI_COL adds a multiple of one vector to another.
• CWLR_L1 minimizes the L1 norm of A*x-b using clustering techniques.
• CWLR_L2 minimizes the L2 norm of A*x-b using clustering techniques.
• CWLR_LI minimizes the L-infinity norm of A*X-B.
• DIGIT_INC increments a decimal digit.
• DIGIT_TO_CH returns the character representation of a decimal digit.
• EXAMPLE_MULTI_SIZE returns values for a multiple system file.
• EXAMPLE_PRINT prints data from an example file.
• EXAMPLE_READ reads data from an example file.
• EXAMPLE_SIZE returns the values of M and N in an example file.
• FILE_NAME_INC generates the next filename in a series.
• G1 computes an orthogonal rotation matrix.
• GEN generates a random matrix A and right hand side B.
• GET_UNIT returns a free FORTRAN unit number.
• GIVR_L2 minimizes the L2 norm of A*x-b using fast Givens rotations.
• HFTI minimizes the L2 norm of A*x-b using Householder transformations.
• H12 constructs or applies a Householder transformation.
• I_LOG_10 returns the integer part of the logarithm base 10 of ABS(X).
• I_RANDOM returns a random integer in a given range.
• I_SWAP switches two integer values.
• I_TO_S_ZERO converts an integer to a string, with zero padding.
• ICMGS uses modifed Gram Schmidt on a problem with nonzero intercept.
• INEXCL computes auxilliary arrays F, T and R used to control exchanges.
• IVEC_IDENTITY sets an integer vector to the identity vector A(I)=I.
• IVEC_PRINT prints an integer vector.
• LDP_L2 implements least distance programming algorithm.
• MGS minimizes the L2 norm of A*x-b using the modified Gram-Schmidt method.
• NGL minimizes the L2 norm of A*x-b using the normal equations.
• NN_L1 minimizes the L1 norm of A * X - B with linear constraints and X >=0.
• NN_L2 minimizes the L2 norm of A * X - B with linear constraints and X >=0.
• NN_LI minimizes the L-infinity norm of A * X - B with linear constraints and X >=0.
• NPART_ENUM enumerates the number of partitions of N with NPART parts.
• NPART_RSF_LEX_RANDOM returns a random RSF NPART partition.
• NPART_RSF_LEX_UNRANK unranks an RSF NPART partition in the lex ordering.
• NPART_TABLE tabulates the number of partitions of N having NPART parts.
• ORTH_L1 carries out orthogonal regression in the L1 norm.
• ORTH_L2 carries out orthogonal regression in the L2 norm.
• ORTH_LI carries out orthogonal regression in the L-infinity norm.
• ORTH_LM is a least squares solver for linear manifolds.
• ORTH_LP carries out orthogonal regression in the LP norm.
• PERM_RANDOM2 selects a random permutation of N objects.
• PYTHAG computes SQRT ( A**2 + B**2 ) carefully.
• QRBD uses the QR algorithm for the singular values of a bidiagonal matrix.
• R_DIFF computes the difference ( X - Y ) of two real numbers.
• R_NEXT "reads" real numbers from a string, one at a time.
• R_RANDOM returns a random real in a given range.
• R_SWAP switches two real values.
• RANDOM_PARTITION generates a random partition.
• RANDOM_PARTITION2 generates a random partition with occupancy constraints.
• REGR_LP minimizes the LP norm of A*x-b for P > 1.
• RESIDUAL calculates the residual vector A*X-B and related information.
• RMAT_CHOLESKY_FACTOR computes the Cholesky factor of a symmetric matrix.
• RMAT_CHOLESKY_SOLVE solves a Cholesky factored linear system A * x = b.
• RMAT_DIAG_ADD_SCALAR adds a scalar to the diagonal of a matrix.
• RMAT_INDICATOR sets the indicator matrix.
• RMAT_L_SOLVE solves a lower triangular linear system.
• RMAT_LT_SOLVE solves a transposed lower triangular linear system.
• RMAT_PRINT prints a real matrix.
• ROBUST carries out robust regression, with eight choices for the method.
• RR_L1 carries out ridge regression in the L1 norm.
• RR_L2 carries out ridge regression in the L2 norm.
• RR_LI carries out ridge regression in the L2 norm.
• RVEC_NORM_LI returns the L-infinity norm of a vector.
• RVEC_NORM_L1 returns the L1 norm of a vector.
• RVEC_NORM_LP returns the LP norm of a vector.
• RVEC_NORM_L2 returns the L2 norm of a vector.
• RVEC_BIN bins a real vector, returning the population of each bin.
• RVEC_IDENTITY sets a real vector to the identity vector A(I)=I.
• RVEC_PRINT prints a real vector.
• S_TO_I reads an integer value from a string.
• S_TO_R reads a real number from a string.
• SCR selects M by NA submatrices from an M by N matrix.
• SCRF_L1 minimizes the L1 norm of A*X-B using NA variables out of N.
• SVD computes the singular value decomposition for a real matrix.
• SVDR minimizes the L2 norm of A*x-b using the singular value decomposition.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UNIFORM_01_SAMPLE is a portable random number generator.
• URAND returns a uniformly distributed pseudo random number.

Back to the FORTRAN software page.