TOEPLITZ
Solution of Toeplitz linear systems

TOEPLITZ is a FORTRAN90 library which solves a variety of Toeplitz and circulant linear systems.

The package can also handle circulant Toeplitz systems, and some other more complicated but related forms.

The TOEPLITZ package was written in the early 1980's by a joint working group of American and Soviet mathematicians.

The original, true, correct version of TOEPLITZ is available in the TOEPLITZ subdirectory of the NETLIB web site.

Licensing:

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

Languages:

TOEPLITZ is available in a FORTRAN90 version.

Related Data and Programs:

BLAS1, a FORTRAN90 library which contains the level 1 Basic Linear Algebra Subprograms.

LINPACK, a FORTRAN90 library which carries out the factorization and solution of linear systems of a variety of types.

LINPLUS, a FORTRAN90 library which includes some routines for manipulating Toeplitz matrices.

TEST_MAT, a FORTRAN90 library which includes some routines which define sample Toeplitz matrices.

TOEPLITZ_CHOLESKY, a FORTRAN90 library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.

Reference:

1. Oleg Arushanian, MK Samarin, Valentin Voevodin, Evgeny Tyrtyshnikov, Burton Garbow, James Boyle, Wayne Cowell, Kenneth Dritz,
   The TOEPLITZ Package User's Guide,
   Argonne National Laboratory,
   ANL-83-16, 1983.
2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1.
3. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Basic Linear Algebra Subprograms for Fortran Usage,
   Algorithm 539,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• toeplitz.f90, the source code.

Examples and Tests:

• toeplitz_test.f90, a sample problem.
• toeplitz_test.txt, sample problem output.

List of Routines:

• C4_ABS1 computes the L1 absolute value of a C4.
• C4BTO_SL solves the C4 block Toeplitz linear system A * X = B.
• C4CCC_SL solves the C4 double column circulant system A * X = B.
• C4CCG_SL solves the C4 CCG linear system A * X = B.
• C4CC_SL solves the C4 column circulant system A * X = B.
• C4CCT_SL solves the C4 CCT linear system A * X = B..
• C4CG_SL solves the C4 CG linear system A * X = B.
• C4CI_MXV multiplies a C4 circulant matrix times a vector.
• C4CI_PRINT prints a C4 circulant matrix.
• C4CI_PRINT_SOME prints some of a C4 circulant matrix.
• C4CI_RANDOM randomizes a C4 circulant matrix.
• C4CI_SL solves the C4 circulant system A * X = B.
• C4CTG_SL solves the C4 CTG linear system A * X = B.
• C4CT_SL solves the C4 CT linear system A * X = B.
• C4GEFA factors a C4 matrix by gaussian elimination.
• C4GESL solves the C4 general system A * X = B.
• C4SALW Fourier transforms the rows of a C4 rectangular matrix.
• C4_SWAP swaps two C4's.
• C4TG_SL1 solves a C4 TG linear system.
• C4TG_SL solves a linear system involving a C4 TG matrix.
• C4TO_MXV multiplies a C4 Toeplitz matrix times a vector.
• C4TO_PRINT prints a C4 Toeplitz matrix.
• C4TO_PRINT_SOME prints some of a C4 Toeplitz matrix.
• C4TO_RANDOM randomizes a C4 Toeplitz matrix.
• C4TO_SL solves the C4 Toeplitz system A * X = B.
• C4TO_VXM multiplies a vector times a C4 Toeplitz matrix.
• C4TRDI computes the determinant and inverse of a C4 triangular matrix.
• C4VEC_AMAX_INDEX indexes the C4VEC element of maximum absolute value.
• C4VEC_AXPY adds a constant times one C4VEC to another.
• C4VEC_DOTC forms the dot product of two C4 vectors, conjugating the first.
• C4VEC_INDICATOR sets a C4VEC to the indicator vector.
• C4VEC_NRM2 computes the unitary norm of a C4 vector.
• C4VEC_PRINT prints a C4VEC, with an optional title.
• C4VEC_PRINT_SOME prints some of a C4VEC.
• C4VEC_SCAL scales a C4 vector by a constant.
• C4VEC_SCAL_R4 scales a C4 vector by an R4 constant.
• C4VEC_UNIFORM_01 returns a unit pseudorandom C4VEC.
• C8_ABS1 computes the L1 absolute value of a C8.
• C8BTO_SL solves the C8 block Toeplitz linear system A * X = B.
• C8CCC_SL solves the C8 double column circulant system A * X = B.
• C8CCG_SL solves the C8 CCG linear system A * X = B.
• C8CC_SL solves the C8 column circulant system A * X = B.
• C8CCT_SL solves the C8 CCT linear system A * X = B.
• C8CG_SL solves the C8 CG linear system A * X = B.
• C8CI_MXV multiplies a C8 circulant matrix times a vector.
• C8CI_PRINT prints a C8 circulant matrix.
• C8CI_PRINT_SOME prints some of a C8 circulant matrix.
• C8CI_RANDOM randomizes a C8 circulant matrix.
• C8CI_SL solves the C8 circulant system A * X = B.
• C8CTG_SL solves the C8 CTG linear system A * X = B.
• C8CT_SL solves the C8 CT linear system A * X = B.
• C8GEFA factors a C8 matrix by gaussian elimination.
• C8GESL solves the C8 general system A * X = B.
• C8SALW Fourier transforms the rows of a C8 rectangular matrix.
• C8_SWAP swaps two C8's.
• C8TG_SL1 solves a C8 TG linear system.
• C8TG_SL solves a linear system involving a C8 TG matrix.
• C8TO_MXV multiplies a C8 Toeplitz matrix times a vector.
• C8TO_PRINT prints a C8 Toeplitz matrix.
• C8TO_PRINT_SOME prints some of a C8 Toeplitz matrix.
• C8TO_RANDOM randomizes a C8 Toeplitz matrix.
• C8TO_SL solves the C8 Toeplitz system A * X = B.
• C8TO_VXM multiplies a vector times a C8 Toeplitz matrix.
• C8TRDI computes the determinant and inverse of a C8 triangular matrix.
• C8VEC_AMAX_INDEX indexes the C8VEC element of maximum absolute value.
• C8VEC_AXPY adds a constant times one C8VEC to another.
• C8VEC_DOTC forms the dot product of two C8 vectors, conjugating the first.
• C8VEC_INDICATOR sets a C8VEC to the indicator vector.
• C8VEC_NRM2 computes the unitary norm of a C8 vector.
• C8VEC_PRINT prints a C8VEC, with an optional title.
• C8VEC_PRINT_SOME prints some of a C8VEC.
• C8VEC_SCAL scales a C8 vector by a constant.
• C8VEC_SCAL_R8 scales a C8 vector by an R8 constant.
• C8VEC_UNIFORM_01 returns a unit pseudorandom C8VEC.
• R4BTO_MXV computes the real block Toeplitz matrix product A * X = B.
• R4BTO_PRINT prints a block Toeplitz matrix.
• R4BTO_PRINT_SOME prints some of a block Toeplitz matrix.
• R4BTO_SL solves the real block Toeplitz linear system A * X = B.
• R4BTO_TO_R4GE converts a block Toeplitz matrix to a Linpack General matrix.
• R4BTO_VXM computes the real block Toeplitz matrix product X * A = B.
• R4CC_QR computes QR factorization of a real M by L column circulant matrix.
• R4GEFA factors a real matrix.
• R4GESL solves a real general linear system A * X = B.
• R4_RANDOM returns a random real in a given range.
• R4TO_MXV multiplies a Toeplitz matrix times a vector.
• R4TO_PRINT prints a Toeplitz matrix.
• R4TO_PRINT_SOME prints some of a Toeplitz matrix.
• R4TO_RANDOM randomizes a Toeplitz matrix.
• R4TO_SL solves the real Toeplitz system A * X = B.
• R4TO_VXM multiplies a vector times a Toeplitz matrix.
• R4TRDI computes the determinant and inverse of a real triangular matrix.
• R4VEC_AMAX returns the maximum absolute value of the entries in a vector.
• R4VEC_AMAX_INDEX indexes the R4 vector element of maximum absolute value.
• R4VEC_AXPY adds a constant times one vector to another.
• R4VEC_DOT forms the dot product of two vectors.
• R4VEC_INDICATOR sets a real vector to the indicator vector.
• R4VEC_NRM2 computes the Euclidean norm of a vector.
• R4VEC_PRINT prints a real vector.
• R4VEC_PRINT_SOME prints "some" of a real vector.
• R4VEC_RANDOM returns a random real vector in a given range.
• R4VEC_SCAL scales a vector by a constant.
• R4VEC_UNIFORM_01 returns a unit pseudorandom R4VEC.
• R8BTO_MXV computes the R8 block Toeplitz matrix product A * X = B.
• R8BTO_PRINT prints a block Toeplitz matrix.
• R8BTO_PRINT_SOME prints some of a block Toeplitz matrix.
• R8BTO_SL solves the real block Toeplitz linear system A * X = B.
• R8BTO_TO_R8GE converts a block Toeplitz matrix to a Linpack General matrix.
• R8BTO_VXM computes the real block Toeplitz matrix product X * A = B.
• R8CC_QR computes QR factorization of a real M by L column circulant matrix.
• R8GEFA factors a real matrix.
• R8GESL solves a real general linear system A * X = B.
• R8_RANDOM returns a random real in a given range.
• R8TO_MXV multiplies a Toeplitz matrix times a vector.
• R8TO_PRINT prints a Toeplitz matrix.
• R8TO_PRINT_SOME prints some of a Toeplitz matrix.
• R8TO_RANDOM randomizes a Toeplitz matrix.
• R8TO_SL solves the real Toeplitz system A * X = B.
• R8TO_VXM multiplies a vector times a Toeplitz matrix.
• R8TRDI computes the determinant and inverse of a real triangular matrix.
• R8VEC_AMAX returns the maximum absolute value of the entries in a vector.
• R8VEC_AMAX_INDEX indexes the R8 vector element of maximum absolute value.
• R8VEC_AXPY adds a constant times one vector to another.
• R8VEC_DOT forms the dot product of two vectors.
• R8VEC_INDICATOR sets a real vector to the indicator vector.
• R8VEC_NRM2 computes the Euclidean norm of a vector.
• R8VEC_PRINT prints a real vector.
• R8VEC_PRINT_SOME prints "some" of a real vector.
• R8VEC_RANDOM returns a random real vector in a given range.
• R8VEC_SCAL scales a vector by a constant.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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