Routines

Linear Solvers

Solves a general system of linear equations Ax = b.......................................... LIN_SOL_GEN

Solves a system of linear equations Ax = b, where A is a
self-adjoint matrix............................................................................. LIN_SOL_SELF

Solves a rectangular system of linear equations Ax b, in
a least-squares sense........................................................................ LIN_SOL_LSQ

Solves a rectangular least-squares system of linear equations
Ax b using singular value decomposition........................................... LIN_SOL_SVD

Solves multiple systems of linear equations........................................................ LIN_SOL_TRI

Computes the singular value decomposition (SVD)
of a rectangular matrix, A............................................................................ LIN_SVD

Large-Scale Parallel Solvers

Parallel Constrained Least-Squares Solvers

Solves a linear, non-negative constrained least-squares
system................................................................. PARALLEL_NONNEGATIVE_LSQ

Solves a linear least-squares system with bounds on
the unknowns............................................................... PARALLEL_BOUNDED_LSQ

Solution of Linear Systems, Matrix Inversion, and Q Determinant Evaluation

Real General Matrices

High accuracy linear system solution ........................................................................ LSARG

Solves a linear system.............................................................................................. LSLRG

Factors and computes condition number.................................................................... LFCRG

Factors.................................................................................................................... LFTRG

Solves after factoring................................................................................................. LFSRG

High accuracy linear system solution after factoring...................................................... LFIRG

Computes determinant after factoring......................................................................... LFDRG

Inverts....................................................................................................................... LINRG

Complex General Matrices

High accuracy linear system solution......................................................................... LSACG

Solves a linear system.............................................................................................. LSLCG

Factors and computes condition number.................................................................... LFCCG

Factors.................................................................................................................... LFTCG

Solves a linear system after factoring......................................................................... LFSCG

High accuracy linear system solution after factoring...................................................... LFICG

Computes determinant after factoring......................................................................... LFDCG

Inverts....................................................................................................................... LINCG

Real Triangular Matrices

Solves a linear system............................................................................................... LSLRT

Computes condition number....................................................................................... LFCRT

Computes determinant after factoring.......................................................................... LFDRT

Inverts....................................................................................................................... LINRT

Complex Triangular Matrices

Solves a linear system............................................................................................... LSLCT

Computes condition number....................................................................................... LFCCT

Computes determinant after factoring.......................................................................... LFDCT

Inverts....................................................................................................................... LINCT

Real Positive Definite Matrices

High accuracy linear system solution......................................................................... LSADS

Solves a linear system.............................................................................................. LSLDS

Factors and computes condition number..................................................................... LFCDS

Factors.................................................................................................................... LFTDS

Solve a linear system after factoring........................................................................... LFSDS

High accuracy linear system solution after factoring...................................................... LFIDS

Computes determinant after factoring.......................................................................... LFDDS

Inverts....................................................................................................................... LINDS

Real Symmetric Matrices

High accuracy linear system solution......................................................................... LSASF

Solves a linear system............................................................................................... LSLSF

Factors and computes condition number..................................................................... LFCSF

Factors..................................................................................................................... LFTSF

Solves a linear system after factoring.......................................................................... LFSSF

High accuracy linear system solution after factoring....................................................... LFISF

Computes determinant after factoring.......................................................................... LFDSF

Complex Hermitian Positive Definite Matrices

High accuracy linear system solution......................................................................... LSADH

Solves a linear system.............................................................................................. LSLDH

Factors and computes condition number..................................................................... LFCDH

Factors.................................................................................................................... LFTDH

Solves a linear system after factoring.......................................................................... LFSDH

High accuracy linear system solution after factoring...................................................... LFIDH

Computes determinant after factoring.......................................................................... LFDDH

Complex Hermitian Matrices

High accuracy linear system solution......................................................................... LSAHF

Solves a linear system............................................................................................... LSLHF

Factors and computes condition number..................................................................... LFCHF

Factors..................................................................................................................... LFTHF

Solves a linear system after factoring.......................................................................... LFSHF

High accuracy linear system solution after factoring....................................................... LFIHF

Computes determinant after factoring.......................................................................... LFDHF

Real Band Matrices in Band Storage

Solves a tridiagonal system........................................................................................ LSLTR

Solves a tridiagonal system: Cyclic Reduction............................................................. LSLCR

High accuracy linear system solution......................................................................... LSARB

Solves a linear system.............................................................................................. LSLRB

Factors and compute condition number...................................................................... LFCRB

Factors.................................................................................................................... LFTRB

Solves a linear system after factoring.......................................................................... LFSRB

High accuracy linear system solution after factoring...................................................... LFIRB

Computes determinant after factoring.......................................................................... LFDRB

Real Band Symmetric Positive Definite Matrices in Band Storage

High accuracy linear system solution......................................................................... LSAQS

Solves a linear system.............................................................................................. LSLQS

Solves a linear system.............................................................................................. LSLPB

Factors and computes condition number.................................................................... LFCQS

Factors.................................................................................................................... LFTQS

Solves a linear system after factoring......................................................................... LFSQS

High accuracy linear system solution after factoring...................................................... LFIQS

Computes determinant after factoring......................................................................... LFDQS

Complex Band Matrices in Band Storage

Solves a tridiagonal system........................................................................................ LSLTQ

Solves a tridiagonal system: Cyclic Reduction............................................................. LSLCQ

High accuracy linear system solution......................................................................... LSACB

Solves a linear system.............................................................................................. LSLCB

Factors and computes condition number..................................................................... LFCCB

Factors.................................................................................................................... LFTCB

Solves a linear system after factoring.......................................................................... LFSCB

High accuracy linear system solution after factoring...................................................... LFICB

Computes determinant after factoring.......................................................................... LFDCB

Complex Band Positive Definite Matrices in Band Storage

High accuracy linear system solution......................................................................... LSAQH

Solves a linear system.............................................................................................. LSLQH

Solves a linear system.............................................................................................. LSLQB

Factors and compute condition number...................................................................... LFCQH

Factors.................................................................................................................... LFTQH

Solves a linear system after factoring......................................................................... LFSQH

High accuracy linear system solution after factoring...................................................... LFIQH

Computes determinant after factoring......................................................................... LFDQH

Real Sparse Linear Equation Solvers

Solves a sparse linear system.................................................................................... LSLXG

Factors..................................................................................................................... LFTXG

Solves a linear system after factoring.......................................................................... LFSXG

Complex Sparse Linear Equation Solvers

Solves a sparse linear system.................................................................................... LSLZG

Factors..................................................................................................................... LFTZG

Solves a linear system after factoring.......................................................................... LFSZG

Real Sparse Symmetric Positive Definite Linear Equation Solvers

Solves a sparse linear system.................................................................................... LSLXD

Symbolic Factor....................................................................................................... LSCXD

Computes Factor...................................................................................................... LNFXD

Solves a linear system after factoring.......................................................................... LFSXD

Complex Sparse Hermitian Positive Definite Linear Equation Solvers

Solves a sparse linear system.................................................................................... LSLZD

Computes Factor...................................................................................................... LNFZD

Solves a linear system after factoring.......................................................................... LFSZD

Real Toeplitz Matrices in Toeplitz Storage

Solves a linear system............................................................................................... LSLTO

Complex Toeplitz Matrices in Toeplitz Storage

Solves a linear system............................................................................................... LSLTC

Complex Circulant Matrices in Circulant Storage

Solves a linear system.............................................................................................. LSLCC

Iterative Methods

Preconditioned conjugate gradient............................................................................. PCGRC

Jacobi conjugate gradient.......................................................................................... JCGRC

Generalized minimum residual.................................................................................. GMRES

Linear Least Squares and Matrix Factorization

Least Squares, QR Decomposition and Generalized Inverse

Solves a Least-squares system................................................................................. LSQRR

Solves a Least-squares system................................................................................. LQRRV

High accuracy Least squares.................................................................................... LSBRR

Linearly constrained Least squares............................................................................ LCLSQ

QR decomposition.................................................................................................... LQRRR

Accumulation of QR decomposition........................................................................... LQERR

QR decomposition Utilities........................................................................................ LQRSL

QR factor update...................................................................................................... LUPQR

Cholesky Factorization

Cholesky factoring for rank deficient matrices............................................................. LCHRG

Cholesky factor update............................................................................................. LUPCH

Cholesky factor down-date........................................................................................ LDNCH

Singular Value Decomposition (SVD)

Real singular value decomposition.............................................................................. LSVRR

Complex singular value decomposition....................................................................... LSVCR

Generalized inverse.................................................................................................. LSGRR


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Visual Numerics - Developers of IMSL and PV-WAVE
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