Computes the Cholesky decomposition of a symmetric positive semidefinite matrix with optional column pivoting.

Solves a linear least-squares problem with linear constraints.

Minimizes a general objective function subject to linear equality/inequality constraints.

Minimizes a general objective function subject to linear equality/inequality constraints.

Downdates the RT R Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is removed

Computes the LU factorization of a complex matrix in band storage mode and estimate its L1⋅ condition number.

Computes the LU factorization of a complex general matrix and estimate its L1 condition number.

Estimates the condition number of a complex triangular matrix.

Computes the RH R factorization of a complex Hermitian positive definite matrix and estimate its L1 condition number.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix and estimate its L1condition number.

Computes the U DUH factorization of a complex Hermitian matrix and estimate its L1 condition number.

Computes the RH R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode and estimate its L1 condition number.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode and estimate its L1 condition number.

Computes the LU factorization of a real matrix in band storage mode and estimate its L1 condition number.

Computes the LU factorization of a real general matrix and estimate its L1 condition number.

Estimates the condition number of a real triangular matrix.

Computes the U DUT factorization of a real symmetric matrix and estimate its L1 condition number.

Computes the determinant of a complex matrix given the LU factorization of the matrix in band storage mode.

Computes the determinant of a complex general matrix given the LU factorization of the matrix.

Computes the determinant of a complex triangular matrix.

Computes the determinant of a complex Hermitian positive definite matrix given the RH R Cholesky factorization of the matrix.

Computes the determinant of a real symmetric positive definite matrix given the RH R Cholesky factorization of the matrix.

Computes the determinant of a complex Hermitian matrix given the U DUH factorization of the matrix.

Computes the determinant of a complex Hermitian positive definite matrix given the RH R Cholesky factorization in band Hermitian storage mode.

Computes the determinant of a real symmetric positive definite matrix given the RT R Cholesky factorization of the band symmetric storage mode.

Computes the determinant of a real matrix in band storage mode given the LU factorization of the matrix.

Computes the determinant of a real general matrix given the LU factorization of the matrix.

Computes the determinant of a real triangular matrix.

Computes the determinant of a real symmetric matrix given the U DUT factorization of the matrix.

Uses iterative refinement to improve the solution of a complex system of linear equations in band storage mode.

Uses iterative refinement to improve the solution of a complex general system of linear equations.

Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations.

Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations.

Uses iterative refinement to improve the solution of a complex Hermitian system of linear equations.

Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations in band Hermitian storage mode.

Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations in band symmetric storage mode.

Uses iterative refinement to improve the solution of a real system of linear equations in band storage mode.

Uses iterative refinement to improve the solution of a real general system of linear equations.

Uses iterative refinement to improve the solution of a real symmetric system of linear equations.

Solves a complex system of linear equations given the LU factorization of the coefficient matrix in band storage mode.

Solves a complex general system of linear equations given the LU factorization of the coefficient matrix.

Solves a complex Hermitian positive definite system of linear equations given the RH R factorization of the coefficient matrix.

Solves a real symmetric positive definite system of linear equations given the RT R Choleksy factorization of the coefficient matrix.

Solves a complex Hermitian system of linear equations given the U DUH factorization of the coefficient matrix.

Solves a complex Hermitian positive definite system of linear equations given the factorization of the coefficient matrix in band Hermitian storage mode.

Solves a real symmetric positive definite system of linear equations given the factorization of the coefficient matrix in band symmetric storage mode.

Solves a real system of linear equations given the LU factorization of the coefficient matrix in band storage mode.

Solves a real general system of linear equations given the LU factorization of the coefficient matrix.

Solves a real symmetric system of linear equations given the U DUT factorization of the coefficient matrix.

Solves a real sparse symmetric positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.

Solves a sparse system of linear equations given the LU factorization of the coefficient matrix.

Solves a complex sparse Hermitian positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.

Solves a complex sparse system of linear equations given the LU factorization of the coefficient matrix.

Computes the LU factorization of a complex matrix in band storage mode.

Computes the LU factorization of a complex general matrix.

Computes the RH R factorization of a complex Hermitian positive definite matrix.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix.

Computes the U DUH factorization of a complex Hermitian matrix.

Computes the RH R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode.

Computes the LU factorization of a real matrix in band storage mode.

Computes the LU factorization of a real general matrix.

Computes the U DUT factorization of a real symmetric matrix.

Computes the LU factorization of a real general sparse matrix.

Computes the LU factorization of a complex general sparse matrix.

Computes the inverse of a complex general matrix.

Computes the inverse of a complex triangular matrix.

Computes the inverse of a real symmetric positive definite matrix.

Computes the inverse of a real general matrix.

Computes the inverse of a real triangular matrix.

Computes the eigenvalues of a self-adjoint matrix, A.

Computes the eigenvalues of a self-adjoint matrix, A.

Computes the generalized eigenvalues of an n ×  n matrix pencil, Av = λBv.

Solves a general system of linear equations Ax = b.

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

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

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

Solves multiple systems of linear equations.

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

Computes the numerical Cholesky factorization of a sparse symmetrical matrix A.

Computes the numerical Cholesky factorization of a sparse Hermitian matrix A.

Accumulates the orthogonal matrix Q from its factored form given the QR factorization of a rectangular matrix A.

Computes the QR decomposition, AP = QR, using Householder transformations.

Computes the least-squares solution using Householder transformations applied in blocked form.

Computes the coordinate transformation, projection, and complete the solution of the least-squares problem Ax = b.

Solves a complex system of linear equations in band storage mode with iterative refinement.

Solves a complex general system of linear equations with iterative refinement.

Solves a Hermitian positive definite system of linear equations with iterative refinement.

Solves a real symmetric positive definite system of linear equations with iterative refinement.

Solves a complex Hermitian system of linear equations with iterative refinement.

Solves a complex Hermitian positive definite system of linear equations in band Hermitian storage mode with iterative refinement.

Solves a real symmetric positive definite system of linear equations in band symmetric storage mode with iterative refinement.

Solves a real system of linear equations in band storage mode with iterative refinement.

Solves a real general system of linear equations with iterative refinement.

Solves a real symmetric system of linear equations with iterative refinement.

Solves a linear least-squares problem with iterative refinement.

Performs the symbolic Cholesky factorization for a sparse symmetric matrix using a minimum degree ordering or a userspecified ordering, and set up the data structure for the numerical Cholesky factorization.

Computes the generalized inverse of a real matrix.

Solves a complex system of linear equations in band storage mode without iterative refinement.

Solves a complex circulant linear system.

Solves a complex general system of linear equations without iterative refinement.

Computes the LDU factorization of a complex tridiagonal matrix A using a cyclic reduction algorithm.

Computes the LDU factorization of a real tridiagonal matrix A using a cyclic reduction algorithm.

Solves a complex triangular system of linear equations.

Solves a complex Hermitian positive definite system of linear equations without iterative refinement.

Solves a real symmetric positive definite system of linear equations without iterative refinement.

Solves a complex Hermitian system of linear equations without iterative refinement.

Computes the RT DR Cholesky factorization of a real symmetric positive definite matrix A in codiagonal band symmetric storage mode. Solve a system Ax = b.

Computes the RH DR Cholesky factorization of a complex hermitian positive-definite matrix A in codiagonal band hermitian storage mode. Solve a system Ax = b.

Solves a complex Hermitian positive definite system of linearequations in band Hermitian storage mode without iterative refinement.

Solves a real symmetric positive definite system of linear equations in band symmetric storage mode without iterative refinement.

Solves a real system of linear equations in band storage mode without iterative refinement.

Solves a real general system of linear equations without iterative refinement.

Solves a real triangular system of linear equations.

Solves a real symmetric system of linear equations without iterative refinement.

Solves a complex Toeplitz linear system.

Solves a real Toeplitz linear system.

Solves a complex tridiagonal system of linear equations.

Solves a real tridiagonal system of linear equations.

Solves a sparse system of symmetric positive definite linear algebraic equations by Gaussian elimination.

Solves a sparse system of linear algebraic equations by Gaussian elimination.

Solves a complex sparse Hermitian positive definite system of linear equations by Gaussian elimination.

Solves a complex sparse system of linear equations by Gaussian elimination.

Solves a linear least-squares problem without iterative refinement.

Computes the singular value decomposition of a complex matrix.

Computes the singular value decomposition of a real matrix.

Updates the RT R Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is added.

Computes an updated QR factorization after the rank-one matrix αxyT is added.