LINPACK_Q
Linear Algebra Library
Quadruple Precision

LINPACK_Q is a FORTRAN90 library which implements some of the LINPACK library of linear solvers, using quadruple precision.

Quadruple precision real variables are declared by using a selected_real_kind() statement first:

  integer, parameter :: qp = selected_real_kind ( 33, 4931 )

after which, variables may be declared by statements like

  real ( kind = qp ) x(*)

Constants that need more than single precision should include the "Q" marker:

        pi = 3.1415925....(lots of digits)....762Q+00

or else the value will be truncated to single precision, one of Fortran's unnecessary, unnoticeable defects that has been zealously preserved through decades.

If your compiler doesn't support the requested quadruple precision arithmetic, then qp is returned as -1, and your code will not compile.

Licensing:

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

Languages:

LINPACK_Q is available in a FORTRAN90 version.

Related Data and Programs:

BLAS1_D, a FORTRAN90 library which contains basic linear algebra routines for vector-vector operations, using double precision real arithmetic.

CONDITION, a FORTRAN90 library which implements methods of computing or estimating the condition number of a matrix.

GEQP3, a FORTRAN90 library which contains the portion of the LAPACK library that carries out the QR factorization, with column pivoting, of an M by N rectangular matrix, with N <= M.

LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.

LINPACK_BENCH, a FORTRAN90 program which is a benchmark which measures the time taken by LINPACK to solve a particular linear system.

LINPACK_C, a FORTRAN90 library which is a version of LINPACK for single precision complex arithmetic.

LINPACK_D, a FORTRAN90 library which is a version of LINPACK for double precision real arithmetic.

LINPACK_S, a FORTRAN90 library which is a version of LINPACK for single precision real arithmetic.

LINPACK_Z, a FORTRAN90 library which is a version of LINPACK for double precision complex arithmetic.

NMS, a FORTRAN90 library which includes LINPACK.

QR_SOLVE, a FORTRAN90 library which computes the least squares solution of a linear system A*x=b.

SLATEC, a FORTRAN90 library which includes LINPACK.

SVD_DEMO, a FORTRAN90 program which demonstrates the singular value decomposition for a simple example.

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

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

Reference:

Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979,
ISBN13: 978-0-898711-72-1,
LC: QA214.L56.
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
Algorithm 539, Basic Linear Algebra Subprograms for Fortran Usage,
ACM Transactions on Mathematical Software,
Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

linpack_q.f90, the source code.

Examples and Tests:

linpack_q_test.f90, a sample calling program.
linpack_q_test.txt, the output file.

List of Routines:

IQAMAX finds the index of the vector element of maximum absolute value.
QAXPY adds a constant times one vector to another.
QGECO factors a matrix and estimates its condition number.
QGEDI: determinant and inverse of a matrix factored by QGECO or QGEFA.
QGEFA factors a real matrix.
QGESL solves a real general linear system A * X = B.
QSCAL scales a vector by a constant.
QSWAP interchanges two vectors.
TIMESTAMP prints the current YMDHMS date as a time stamp.

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

Last revised on 15 March 2016.

LINPACK_Q Linear Algebra Library Quadruple Precision