Chapter 1: Linear Systems

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

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

Partial Singular Value Decomposition......................................................... ARPACK_SVD

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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