R83V
Tridiagonal Matrix Utilities

R83V is a FORTRAN90 library which carries out some basic linear algebra operations on R83V matrices (real 64 bit precision tridiagonal three vector format).

Licensing:

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

Languages:

R83V is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python 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).

R85, a FORTRAN90 library which contains linear algebra routines for R85 matrices (real, 64 bit, pentadiagonal format).

R8BB, a FORTRAN90 library which contains linear algebra routines for R8BB matrices (real, 64 bit, border banded 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).

R8CB, a FORTRAN90 library which contains linear algebra routines for R8CB matrices (real, 64 bit, Compressed Band format).

R8CBB, a FORTRAN90 library which contains linear algebra routines for R8CBB matrices (real, 64 bit, Compressed Border Banded 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).

R8GD, a FORTRAN90 library which contains linear algebra routines for R8GD matrices (real, 64 bit, general diagonal 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 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).

R8NCF, a FORTRAN90 library which contains linear algebra routines for R8NCF matrices (real, 64 bit, nonsymmetric coordinate format).

R8PBL, a FORTRAN90 library which contains linear algebra routines for R8PBL matrices (real, 64 bit, positive definite symmetric band lower 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).

R8RI, a FORTRAN90 library which contains linear algebra routines for R8RI matrices (real, 64 bit, row indexed 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).

R8SD, a FORTRAN90 library which contains linear algebra routines for R8SD matrices (real, 64 bit, symmetric diagonal 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).

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

Source Code:

• r83v.f90, the source code.

Examples and Tests:

• r83v_test.f90, a sample calling program.
• r83v_test.txt, the output file.

List of Routines:

• I4_LOG_10 returns the integer part of the logarithm base 10 of an I4.
• I4_LOG_10_TEST tests I4_LOG_10.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8_UNIFORM_01_TEST tests R8_UNIFORM_01
• R83_INDICATOR sets up an R83 indicator matrix.
• R83_INDICATOR_TEST tests R83_INDICATOR.
• R83_PRINT prints an R83 matrix.
• R83_PRINT_TEST tests R83_PRINT.
• R83_PRINT_SOME prints some of an R83 matrix.
• R83_PRINT_SOME_TEST tests R83_PRINT_SOME.
• R83V_CG uses the conjugate gradient method on an R83V system.
• R83V_CG_TEST tests R83V_CG.
• R83V_COPY copies an R83V matrix.
• R83V_COPY_TEST tests R83V_COPY.
• R83V_CR_FA decomposes an R83V matrix using cyclic reduction.
• R83V_CR_FA_TEST tests R83V_CR_FA.
• R83V_CR_SL solves a real linear system factored by R83V_CR_FA.
• R83V_CR_SL_TEST tests R83V_CR_SL.
• R83V_CR_SLS solves several real linear systems factored by R83V_CR_FA.
• R83V_CR_SLS_TEST tests R83V_CR_SLS.
• R83V_DIF2 returns the DIF2 matrix in R83V format.
• R83V_DIF2_TEST tests R83V_DIF2.
• R83V_FS solves a linear system with R83V matrix.
• R83V_FS_TEST tests R83V_FS_SL.
• R83V_GS_SL solves a R83V system using Gauss-Seidel iteration.
• R83V_GS_SL_TEST tests R83V_GS_SL.
• R83V_INDICATOR sets up an R83V indicator matrix.
• R83V_INDICATOR_TEST tests R83V_INDICATOR.
• R83V_JAC_SL solves a R83V system A*x=b using Jacobi iteration.
• R83V_JAC_SL_TEST tests R83V_JAC_SL.
• R83V_MTV multiplies a vector by an R83V matrix.
• R83V_MTV_TEST tests R83V_MTV.
• R83V_MV multiplies a R83V matrix times a vector.
• R83V_MV_TEST tests R83V_MV.
• R83V_PRINT prints an R83V matrix.
• R83V_PRINT_TEST tests R83V_PRINT.
• R83V_PRINT_SOME prints some of a R83V matrix.
• R83V_PRINT_SOME_TEST tests R83V_PRINT_SOME.
• R83V_RANDOM randomizes an R83V matrix.
• R83V_RANDOM_TEST tests R83V_RANDOM.
• R83V_RES computes the residual R = b-A*x for R83V matrices.
• R83V_RES_TEST tests R83V_RES.
• R83V_TO_R8GE copies an R83V matrix to a R8GE matrix.
• R83V_TO_R8GE_TEST tests R83V_TO_R8GE.
• R83V_TO_R8VEC copies an R83V matrix to an R8VEC.
• R83V_TO_R8VEC_TEST tests R83V_TO_R8VEC.
• R83V_TRANSPOSE makes a transposed copy of an R83V matrix.
• R83V_TRANSPOSE_TEST tests R83V_TRANSPOSE.
• R83V_ZEROS zeros an R83V matrix.
• R83V_ZEROS_TEST tests R83V_ZEROS.
• R8GE_INDICATOR sets up an R8GE indicator matrix.
• R8GE_INDICATOR_TEST tests R8GE_INDICATOR.
• R8GE_MTV multiplies an R8VEC by an R8GE matrix.
• R8GE_MTV_TEST tests R8GE_MTV
• R8GE_MV multiplies an R8GE matrix by an R8VEC.
• R8GE_MV_TEST tests R8GE_MV
• R8GE_PRINT prints an R8GE matrix.
• R8GE_PRINT_TEST tests R8GE_PRINT.
• R8GE_PRINT_SOME prints some of an R8GE matrix.
• R8GE_PRINT_SOME_TEST tests R8GE_PRINT_SOME.
• R8GE_TO_R83V copies (some of) an R8GE matrix to an R83V matrix.
• R8GE_TO_R83V_TEST tests R8GE_TO_R83V.
• R8VEC_INDICATOR1 sets an R8VEC to the indicator vector (1,2,3,...).
• R8VEC_INDICATOR1_TEST tests R8VEC_INDICATOR1.
• R8VEC_NORM returns the L2 norm of an R8VEC.
• R8VEC_NORM_TEST tests R8VEC_NORM.
• R8VEC_NORM_AFFINE returns the affine norm of an R8VEC.
• R8VEC_NORM_AFFINE_TEST tests R8VEC_NORM_AFFINE.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_PRINT_TEST tests R8VEC_PRINT.
• R8VEC_TO_R83V copies an R8VEC to an R83V matrix.
• R8VEC_TO_R83V_TEST tests R8VEC_TO_R83V.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• R8VEC_UNIFORM_01_TEST tests R8VEC_UNIFORM_01.
• R8VEC2_PRINT prints an R8VEC2.
• R8VEC2_PRINT_TEST tests R8VEC2_PRINT.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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