LINPLUS_C8
Linear Algebra Utilities

LINPLUS_C8 is a FORTRAN90 library which carries out linear algebra operations for complex matrices in a variety of formats.

The routines are primarily organized by the arithmetic type, and the storage format of the matrix they operate on. Some of these formats were defined by LINPACK, while others are new; I just made them up when I had to solve problems involving such matrices. The formats include:

• C83 - Complex double precision tridiagonal;
• C8CI - Complex double precision circulant;
• C8GE - Complex double precision general;
• C8TO - Complex double precision Toeplitz;

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

LINPLUS_C8 is available in a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

R83, a FORTRAN90 library which contains linear algebra routines for R83 matrices (real, 64 bit, tridiagonal 3xN format).

R83_NP, a FORTRAN90 library which contains linear algebra routines for R83_NP matrices (real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).

R83P, a FORTRAN90 library which contains linear algebra routines for R83P matrices (real, 64 bit, tridiagonal periodic format).

R83S, a FORTRAN90 library which contains linear algebra routines for R83S matrices (real, 64 bit, tridiagonal scalar format).

R83T, a FORTRAN90 library which contains linear algebra routines for R83T matrices (real, 64 bit, tridiagonal Mx3 format).

R83V, a FORTRAN90 library which contains linear algebra routines for R83V matrices (real, 64 bit, tridiagonal three vector format).

R8BLT, a FORTRAN90 library which contains linear algebra routines for R8BLT matrices (real, 64 bit, band lower triangular format).

R8BTO, a FORTRAN90 library which contains linear algebra routines for R8BTO matrices (real, 64 bit, block Toeplitz format).

R8BUT, a FORTRAN90 library which contains linear algebra routines for R8BUT matrices (real, 64 bit, band upper triangular format).

R8CC, a FORTRAN90 library which contains linear algebra routines for R8CC matrices (real, 64 bit, Compressed Column (Colptr,Row,Value) format).

R8CI, a FORTRAN90 library which contains linear algebra routines for R8CI matrices (real, 64 bit, circulant format).

R8COL, a FORTRAN90 library which contains utility routines for R8COL's, that is, double precision real MxN arrays, considered as N column vectors, each of length M. The data may be thought of as a matrix of multiple columns, and many operations will be carried out columnwise.

R8GB, a FORTRAN90 library which contains linear algebra routines for R8GB matrices (real, 64 bit, General Banded format).

R8GE, a FORTRAN90 library which contains linear algebra routines for R8GE matrices (real, 64 bit, General format).

R8GE_NP, a FORTRAN90 library which contains nonpivoting linear algebra routines for R8GE_NP matrices (real, 64 bit, General Nonpivoting format).

R8LT, a FORTRAN90 library which contains linear algebra routines for R8LT matrices (real, 64 bit, lower triangular format).

R8LTT, a FORTRAN90 library which contains linear algebra routines for R8LTT matrices (real, 64 bit, lower triangular Toeplitz format).

R8PBU, a FORTRAN90 library which contains linear algebra routines for R8PBU matrices (real, 64 bit, positive definite symmetric band upper format).

R8PO, a FORTRAN90 library which contains linear algebra routines for R8PO matrices (real, 64 bit, positive definite symmetric format).

R8PP, a FORTRAN90 library which contains linear algebra routines for R8PP matrices (real, 64 bit, positive definite symmetric packed format).

R8ROW, a FORTRAN90 library which contains utility routines for R8ROW's, that is, double precision real MxN arrays, considered as M row vectors, each of length N. The data may be thought of as a matrix of multiple rows, and many operations will be carried out rowwise.

R8S3, a FORTRAN90 library which contains linear algebra routines for R8S3 matrices (real, 64 bit, SLAP Triad (I,J,AIJ) format).

R8SM, a FORTRAN90 library which contains linear algebra routines for R8SM (Sherman-Morrison) matrices (real, 64 bit, A-u*v' format).

R8SP, a FORTRAN90 library which contains linear algebra routines for R8SP matrices (real, 64 bit, SLAP Triad (I,J,AIJ) format).

R8SR, a FORTRAN90 library which carries out linear algebra operations for R8SR matrices (real, 64 bit, diagonal + compressed row offdiagonal format).

R8SS, a FORTRAN90 library which carries out linear algebra operations for R8SS matrices (real, 64 bit, symmetric skyline format).

R8STO, a FORTRAN90 library which contains linear algebra routines for R8STO matrices (real, 64 bit, symmetric Toeplitz N format).

R8TO, a FORTRAN90 library which contains linear algebra routines for R8TO matrices (real, 64 bit, Toeplitz 2*N-1 format).

R8UT, a FORTRAN90 library which contains linear algebra routines for R8UT matrices (real, 64 bit, upper triangular format).

R8UTT, a FORTRAN90 library which contains linear algebra routines for R8UTT matrices (real, 64 bit, upper triangular Toeplitz format).

R8VM, a FORTRAN90 library which contains linear algebra routines for R8VM matrices (real, 64 bit, Vandermonde format).

TEST_MAT, a FORTRAN90 library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.

Source Code:

• linplus_c8.f90, the source code;

Examples and Tests:

• linplus_c8_test.f90, the calling program;
• linplus_c8_test.txt, the output file.

List of Routines:

• C8_LE_L2 := X <= Y for the L2 norm on C8 values.
• C8_SWAP swaps two C8's.
• C83_CR_FA decomposes a C83 matrix using cyclic reduction.
• C83_CR_SLS solves several linear systems factored by C83_CR_FA.
• C83_INDICATOR sets up a C83 indicator matrix.
• C83_JAC_SL solves a C83 system using Jacobi iteration.
• C83_MTV multiplies a C8VEC by a C83 matrix.
• C83_MV multiplies a C83 matrix times a C8VEC.
• C83_NP_DET returns the determinant of a C83 system factored by C83_NP_FA.
• C83_NP_FA factors a C83 matrix without pivoting.
• C83_NP_FS factors and solves a C83 system.
• C83_NP_ML computes A * x or x * A, where A has been factored by C83_NP_FA.
• C83_NP_SL solves a C83 system factored by C83_NP_FA.
• C83_PRINT prints a C83 matrix.
• C83_PRINT_SOME prints some of a C83 matrix.
• C83_RANDOM randomizes a C83 matrix.
• C83_TO_C8GE copies a C83 matrix into a C8GE matrix.
• C83_ZEROS zeros a C83 matrix.
• C8CI_EVAL returns the eigenvalues of a C8CI matrix.
• C8CI_MTV multiplies a C8VEC by a C8CI matrix.
• C8CI_MV multiplies a C8CI matrix times a C8VEC.
• C8CI_PRINT prints a C8CI matrix.
• C8CI_PRINT_SOME prints some of a C8CI matrix.
• C8CI_RANDOM randomizes a C8CI matrix.
• C8CI_SL solves a C8CI system.
• C8CI_TO_C8GE copies a C8CI matrix to a C8GE matrix.
• C8CI_ZEROS zeros a C8CI matrix.
• C8GE_PRINT prints a C8GE.
• C8GE_PRINT_SOME prints some of a C8GE.
• C8GE_RANDOM returns a unit pseudorandom C8GE.
• C8GE_ZEROS zeros a C8GE.
• C8TO_MTV multiplies a C8VEC by a C8TO matrix.
• C8TO_MV multiplies a C8TO matrix times a C8VEC.
• C8TO_PRINT prints a C8TO matrix.
• C8TO_PRINT_SOME prints some of a C8TO matrix.
• C8TO_RANDOM randomizes a C8TO matrix.
• C8TO_SL solves a C8TO system.
• C8TO_TO_C8GE copies a C8TO matrix to a C8GE matrix.
• C8TO_ZEROS zeros a C8TO matrix.
• C8VEC_INDICATOR sets a C8VEC to an "indicator" vector.
• C8VEC_PRINT prints a C8VEC.
• C8VEC_PRINT_SOME prints some of a C8VEC.
• C8VEC_SORT_A_L2 ascending sorts a C8VEC by L2 norm.
• C8VEC_UNIFORM_01 returns a unit pseudorandom C8VEC.
• C8VEC_UNITY returns the N roots of unity as a C8VEC.
• SORT_HEAP_EXTERNAL externally sorts a list of items into linear order.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.