▼Linear solve, AX = B | Solve \(AX = B\) |
General matrix: LU | |
General matrix: LU: banded | |
General matrix: LU: tridiagonal | |
Positive definite: Cholesky | |
Positive definite: Cholesky: packed | |
Positive definite: Cholesky: banded | |
Positive definite: Cholesky: tridiagonal | |
Symmetric indefinite | |
Symmetric indefinite: packed | |
Hermitian indefinite | |
Hermitian indefinite: packed | |
▼Linear solve: computational routines | Factor \(LU\), \(LL^H\), \(LDL^H\); solve; inverse; condition number estimate |
General matrix: LU | |
General matrix: LU: banded | |
General matrix: LU: tridiagonal | |
Positive definite: Cholesky | |
Positive definite: Cholesky: packed | |
Positive definite: Cholesky: RFP | |
Positive definite: Cholesky: banded | |
Positive definite: Cholesky: tridiagonal | |
Symmetric indefinite: Bunch-Kaufman | |
Symmetric indefinite: Bunch-Kaufman: packed | |
Symmetric indefinite: Rook | |
Symmetric indefinite: Aasen's | |
Hermitian indefinite: Bunch-Kaufman | |
Hermitian indefinite: Bunch-Kaufman: packed | |
Hermitian indefinite: Rook | |
Hermitian indefinite: Aasen's | |
Triangular | |
Triangular: packed | |
Triangular: RFP | |
Triangular: banded | |
▼Least squares | |
Standard, AX = B | Solve \(AX \approx B\) |
Constrained | |
▼Orthogonal/unitary factorizations (QR, etc.) | |
A = QR factorization | |
A = QR factorization, triangle-pentagonal tiles | |
AP = QR factorization with pivoting | |
A = LQ factorization | |
A = LQ factorization, triangle-pentagonal tiles | |
A = QL factorization | |
A = RQ factorization | |
A = RZ factorization | |
Generalized QR factorization | |
Generalized RQ factorization | |
Cosine-Sine (CS) decomposition | |
Householder reflectors and plane rotations | |
▼Symmetric/Hermitian eigenvalues | |
Standard, AV = V Lambda | |
Standard, AV = V Lambda: packed | |
Standard, AV = V Lambda: banded | |
Standard, AV = V Lambda: tridiagonal | |
Generalized, AV = BV Lambda, etc. | |
Generalized, AV = BV Lambda, etc.: packed | |
Generalized, AV = BV Lambda, etc.: banded | |
Computational routines | |
▼Non-symmetric eigenvalues | |
Standard, AV = V Lambda | |
Generalized, AV = BV Lambda | |
Schur form, A = ZTZ^H | |
Generalized Schur form | |
Computational routines | |
▼Singular Value Decomposition (SVD) | |
Standard, A = U Sigma V^H | |
Standard, A = U Sigma V^H, bidiagonal | |
Generalized | |
Computational routines | |
▼Auxiliary routines | |
Initialize, copy, convert matrices | |
Matrix norms | |
Other auxiliary routines | |
▼BLAS extensions in LAPACK | |
symv: Symmetric matrix-vector multiply | \(y = \alpha Ax + \beta y\) |
syr: Symmetric rank 1 update | \(A = \alpha xx^T + A\) |
▼Test routines | |
Test matrix generation | |
Utilities | |