Linear Systems

LINEAR SOLVERS

ROUTINE DESCRIPTION
LIN_SOL_GEN Solves a real general system of linear equations Ax = b.
LIN_SOL_SELF Solves a system of linear equations Ax = b, where A is a self-adjoint matrix.
LIN_SOL_LSQ Solves a rectangular system of linear equations Ax ≅ b, in a least-squares sense.
LIN_SOL_SVD Solves a rectangular least-squares system of linear equations Ax ≅ b using singular value decomposition.
LIN_SOL_TRI Solves multiple systems of linear equations.
LIN_SVD Computes the singular value decomposition (SVD) of a rectangular matrix, A.
 

LARGE-SCALE PARALLEL SOLVERS

ROUTINE DESCRIPTION
PARALLEL_NONNEGATIVE_LSQ Solves a linear, non-negative constrained least-squares system.
PARALLEL_BOUNDED_LSQ Solves a linear least-squares system with bounds on the unknowns.
 

SOLUTION OF LINEAR SYSTEMS, MATRIX INVERSION, AND DETERMINANT EVALUATION

REAL GENERAL MATRICES

ROUTINE DESCRIPTION
LSARG Solves a real general system of linear equations with iterative refinement.
LSLRG Solves a real general system of linear equations without iterative refinement.
LFCRG Computes the LU factorization of a real general matrix and estimates its L1 condition number.
LFTRG Computes the LU factorization of a real general matrix.
LFSRG Solves a real general system of linear equations given the LU factorization of the coefficient matrix.
LFIRG Uses iterative refinement to improve the solution of a real general system of linear equations.
LFDRG Computes the determinant of a real general matrix given the LU factorization of the matrix.
LINRG Computes the inverse of a real general matrix.
 

COMPLEX GENERAL MATRICESS

ROUTINE DESCRIPTION
LSACG Solves a complex general system of linear equations with iterative refinement.
LSLCG Solves a complex general system of linear equations without iterative refinement.
LFCCG Computes the LU factorization of a complex general matrix and estimates its L1 condition number.
LFTCG Computes the LU factorization of a complex general matrix.
LFSCG Solves a complex general system of linear equations given the LU factorization of the coefficient matrix.
LFICG Uses iterative refinement to improve the solution of a complex general system of linear equations.
LFDCG Computes the determinant of a complex general matrix given the LU factorization of the matrix.
LINCG Computes the inverse of a complex general matrix.
 

REAL TRIANGULAR MATRICES

ROUTINE DESCRIPTION
LSLRT Solves a real triangular system of linear equations.
LFCRT Estimates the condition number of a real triangular matrix.
LFDRT Computes the determinant of a real triangular matrix.
LINRT Computes the inverse of a real triangular matrix.
 

COMPLEX TRIANGULAR MATRICES

ROUTINE DESCRIPTION
LSLCT Solves a complex triangular system of linear equations.
LFCCT Estimates the condition number of a complex triangular matrix.
LFDCT Computes the determinant of a complex triangular matrix.
LINCT Computes the inverse of a complex triangular matrix.
 

REAL POSITIVE DEFINITE MATRICES

ROUTINE DESCRIPTION
LSADS Solves a real symmetric positive definite system of linear equations with iterative refinement.
LSLDS Solves a real symmetric positive definite system of linear equations without iterative refinement.
LFCDS Computes the RTR Cholesky factorization of a real symmetric positive definite matrix and estimates its L1 condition number.
LFTDS Computes the RTR Cholesky factorization of a real symmetric positive definite matrix.
LFSDS Solves a real symmetric positive definite system of linear equations given the RTR Cholesky factorization of the coefficient matrix.
LFIDS Uses the iterative refinement to improve the solution of a real symmetric positive definite system of linear equations.
LFDDS Computes the determinant of a real symmetric positive matrix given the RTR Cholesky factorization of the matrix.
LINDS Computes the inverse of a real symmetric positive definite matrix.
 

REAL SYMMETRIC MATRICES

ROUTINE DESCRIPTION
LSASF Solves a real symmetric system of linear equations with iterative refinement.
LSLSF Solves a real symmetric system of linear equations without iterative refinement.
LFCSF Computes the U DUT factorization of a real symmetric matrix and estimates its L1 condition number.
LFTSF Computes the U DUT factorization of a real symmetric matrix.
LFSSF Solves a real symmetric system of linear equations given the U DUT factorization of the coefficient matrix.
LFISF Uses iterative refinement to improve the solution of a real symmetric system of linear equations.
LFDSF Computes the determinant of a real symmetric matrix given the U DUT factorization of the matrix.
 

COMPLEX HERMITIAN POSITIVE DEFINITE MATRICES

ROUTINE DESCRIPTION
LSADH Solves a complex Hermitian positive definite system of linear equations with iterative refinement.
LSLDH Solves a complex Hermitian positive definite system of linear equations without iterative refinement.
LFCDH Computes the RHR factorization of a complex Hermitian positive definite matrix and estimates its L1 condition number.
LFTDH Computes the RHR factorization of a complex Hermitian positive definite matrix.
LFSDH Solves a complex Hermitian positive definite system of linear equations given the RHR factorization of the coefficient matrix.
LFIDH Uses the iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations.
LFDDH Computes the determinant of a complex Hermitian positive definite matrix given the RHR Cholesky factorization of the matrix.
 

COMPLEX HERMITIAN MATRICES

ROUTINE DESCRIPTION
LSAHF Solves a complex Hermitian system of linear equations with iterative refinement.
LSLHF Solves a complex Hermitian system of linear equations without iterative refinement.
LFCHF Computes the U DUH factorization of a complex Hermitian matrix and estimates its L1 condition number.
LFTHF Computes the U DUH factorization of a complex Hermitian matrix.
LFSHF Solves a complex Hermitian system of linear equations given the U DUH factorization of the coefficient matrix.
LFIHF Uses iterative refinement to improve the solution of a complex Hermitian system of linear equations.
LFDHF Computes the determinant of a complex Hermitian matrix given the U DUH factorization of the matrix.
 

REAL BAND MATRICES IN BAND STORAGE MODE

ROUTINE DESCRIPTION
LSLTR Solves a real tridiagonal system of linear equations.
LSLCR Computes the L DU factorization of a a real tridiagonal matrix A using a cyclic reduction algorithm.
LSARB Solves a real system of linear equations in band storage mode with iterative refinement.
LSLRB Solves a real system of linear equations in band storage mode without iterative refinement.
LFCRB Computes the LU factorization of a real matrix in band storage mode and estimates its L1 condition number.
LFTRB Computes the LU factorization of a real matrix in band storage mode.
LFSRB Solves a real system of linear equations given the LU factorization of the coefficient matrix in band storage mode.
LFIRB Uses iterative refinement to improve the solution of a real system of linear equations in band storage mode.
LFDRB Computes the determinant of a real matrix in band storage mode given the LU factorization of the matrix.
 

REAL BAND SYMMETRIC POSITIVE DEFINITE MATRICES IN BAND STORAGE MODE

ROUTINE DESCRIPTION
LSAQS Solves a real symmetric positive definite system of linear equations in band symmetric storage mode with iterative refinement.
LSLQS Solves a real symmetric positive definite system of linear equations in band symmetric storage mode without iterative refinement.
LSLPB Computes the RTDR Cholesky factorization of a real symmetric positive definite matrix A in codiagonal band symmetric storage mode. Solves a system Ax = b.
LFCQS Computes the RTR Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode and estimates its L1 condition number.
LFTQS Computes the RTR Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode.
LFSQS Solves a real symmetric positive definite system of linear equations given the factorization of the coefficient matrix in band symmetric storage mode.
LFIQS Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations in band symmetric storage mode.
LFDQS Computes the determinant of a real symmetric positive definite matrix given the RTR Cholesky factorization of the matrix in band symmetric storage mode.
 

COMPLEX BAND MATRICES IN BAND STORAGE MODE

ROUTINE DESCRIPTION
LSLTQ Solves a complex tridiagonal system of linear equations.
LSLCQ Computes the LDU factorization of a complex tridiagonal matrix A using a cyclic reduction algorithm.
LSACB Solves a complex system of linear equations in band storage mode with iterative refinement.
LSLCB Solves a complex system of linear equations in band storage mode without iterative refinement.
LFCCB Computes the LU factorization of a complex matrix in band storage mode and estimates its L1 condition number.the U DUH factorization of the coefficient matrix.
LFTCB Computes the LU factorization of a complex matrix in band storage mode given the coefficient matrix in band storage mode.
LFSCB Solves a complex system of linear equations given the LU factorization of the coefficient matrix in band storage mode.
LFICB Uses iterative refinement to improve the solution of a complex system of linear equations in band storage mode.
LFDCB Computes the determinant of a complex matrix given the LU factorization of the matrix in band storage mode.
 

COMPLEX BAND POSITIVE DEFINITE MATRICES IN BAND STORAGE MODE

ROUTINE DESCRIPTION
LSAQH Solves a complex Hermitian positive definite system of linear equations in band Hermitian storage mode with iterative refinement.
LSLQH Solves a complex Hermitian positive definite system of linear equations in band Hermitian storage mode without iterative refinement.
LSLQB Computes the RHDR Cholesky factorization of a complex Hermitian positive-definite matrix A in codiagonal band Hermitian storage mode. Solves a system Ax = b.
LFCQH Computes the RHR factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode and estimates its L1 condition number.
LFTQH Computes the RHR factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode.
LFSQH Solves a complex Hermitian positive definite system of linear equations given the factorization of the coefficient matrix in band Hermitian storage mode.
LFIQH Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations in band Hermitian storage mode.
LFDQH Computes the determinant of a complex Hermitian positive definite matrix given the RHR Cholesky factorization in band Hermitian storage mode.
 

REAL SPARSE LINEAR EQUATION SOLVERS

ROUTINE DESCRIPTION
LSLXG Solves a sparse system of linear algebraic equations by Gaussian elimination.
LFTXG Computes the LU factorization of a real general sparse matrix.
LFSXG Solves a sparse system of linear equations given the LU factorization of the coefficient matrix.
 

COMPLEX SPARSE LINEAR EQUATION SOLVERS

ROUTINE DESCRIPTION
LSLZG Solves a complex sparse system of linear equations by Gaussian elimination.
LSTZG Computes the LU factorization of a complex general sparse matrix.
LFSZG Solves a complex sparse system of linear equations given the LU factorization of the coefficient matrix.
 

REAL SPARSE SYMMETRIC POSITIVE DEFINITE LINEAR EQUATIONS SOLVERS

ROUTINE DESCRIPTION
LSLXD Solves a sparse system of symmetric positive definite linear algebraic equations by Gaussian elimination.
LSCXD Performs the symbolic Cholesky factorization for a sparse symmetric matrix using a minimum degree ordering or a user-specified ordering, and sets up the data structure for the numerical Cholesky factorization.
LNFXD Computes the numerical Cholesky factorization of a sparse symmetrical matrix A.
LFSXD Solves a real sparse symmetric positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.
 

COMPLEX SPARSE HERMITIAN POSITIVE DEFINITE LINEAR EQUATIONS SOLVERS

ROUTINE DESCRIPTION
LSLZD Solves a complex sparse Hermitian positive definite system of linear equations by Gaussian elimination.
LNFZD Computes the numerical Cholesky factorization of a sparse Hermitian matrix A.
LFSZD Solves a complex sparse Hermitian positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.
 

REAL TOEPLITZ MATRICES IN TOEPLITZ STORAGE MODE

ROUTINE DESCRIPTION
LSLTO Solves a real Toeplitz linear system.
 

COMPLEX TOEPLITZ MATRICES IN TOEPLITZ STORAGE MODE

ROUTINE DESCRIPTION
LSLTC Solves a complex Toeplitz linear system.
 

COMPLEX CIRCULAR MATRICES IN CIRCULANT STORAGE MODE

ROUTINE DESCRIPTION
LSLCC Solves a complex circulant linear system.
 

ITERATIVE METHODS

ROUTINE DESCRIPTION
PCGRC Solves a real symmetric definite linear system using a preconditioned conjugate gradient method with reverse communication.
JCGRC Solves a real symmetric definite linear system using the Jacobi-preconditioned conjugate gradient method with reverse communication.
GMRES Uses GMRES with reverse communication to generate an approximate solution of Ax = b.
 

LINEAR LEAST SQUARES AND MATRIX FACTORIZATION

LEAST SQUARES, QR DECOMPOSITION AND GENERALIZED INVERSE LEAST SQUARES

ROUTINE DESCRIPTION
LSQRR Solves a linear least-squares problem without iterative refinement.
LQRRV Computes the least-squares solution using Householder transformations applied in blocked form.
LSBRR Solves a linear least-squares problem with iterative refinement.
LCLSQ Solves a linear least-squares problem with linear constraints.
LQRRR Computes the QR decomposition, AP = QR, using Householder transformations.
LQERR Accumulate the orthogonal matrix Q from its factored form given the QR factorization of a rectangular matrix A.
LQRSL Computes the coordinate transformation, projection, and complete the solution of the least-squares problem Ax = b.
LUPQR Computes an updated QR factorization after the rank-one matrix αxyT is added.
 

CHOLESKY FACTORIZATION

ROUTINE DESCRIPTION
LCHRG Computes the Cholesky decomposition of a symmetric positive semidefinite matrix with optional column pivoting.
LUPCH Updates the RTR Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is added.
LDNCH Downdates the RTR Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is removed.
 

SINGULAR VALUE DECOMPOSITIONS

ROUTINE DESCRIPTION
LSVRR Computes the singular value decomposition of a real matrix.
LSVCR Computes the singular value decomposition of a complex matrix.
LSGRR Computes the generalized inverse of a real matrix.