Initialization |
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Utilities |
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▼Linear Systems | Solve \( Ax = b \) |
►LU solve | Solve \( Ax = b \), using LU factorization for general \( A \) |
►LU solve: driver | Whole \( Ax=b \) problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►LU solve: computational | Major computational phases of solving \( Ax=b \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►LU solve: auxiliary | Low-level functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Tiled LU | Functions for tiled algorithms (incremental pivoting) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Cholesky solve | Solve \( Ax = b \), using Cholesky factorization for symmetric positive definite (SPD) \( A \) |
►Cholesky solve: driver | Whole \( Ax=b \) (SPD) problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Cholesky solve: computational | Major computational phases of solving \( Ax=b \) (SPD) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Cholesky solve: auxiliary | Low-level functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Least Squares | Solve over- or under-determined \( Ax = b \) |
►Least Squares solve: driver | Whole \( Ax=b \) (least squares) problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Least Squares solve: computational | Major computational phases of solving \( Ax=b \) (least squares); |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
▼Orthogonal factorizations |
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►QR factorization | Factor \( A = QR \) |
►QR factorization: computational | Major computational phase of least squares and SVD problems |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►QR with pivoting | Slower but more stable QR, especially for rank-deficient matrices |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Tiled QR factorization | Functions for tiled algorithms |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►RQ factorization | Factor \( A = RQ \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►QL factorization | Factor \( A = QL \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►LQ factorization | Factor \( A = LQ \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
▼Eigenvalue |
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►Non-symmetric eigenvalue | Solve \( Ax = \lambda x \) for non-symmetric \( A \) |
►Non-symmetric eigenvalue: driver | Whole \( Ax = \lambda x \) non-symmetric eigenvalue problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Non-symmetric eigenvalue: computational | Major computational phases of non-symmetric eigenvalue problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Non-symmetric eigenvalue: auxiliary | Low-level functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Symmetric eigenvalue | Solve \( Ax = \lambda x \) for symmetric \( A \) |
►Symmetric eigenvalue: driver | Whole \( Ax = \lambda x \) eigenvalue problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Generalized symmetric eigenvalue: driver | Whole \( Ax = \lambda Bx \), or \( ABx = \lambda x \), or \( BAx = \lambda x \) generalized symmetric eigenvalue problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Symmetric eigenvalue: computational | Major computational phases of eigenvalue problem, 1-stage algorithm |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Symmetric eigenvalue: computational, 2-stage | Major computational phases of eigenvalue problem, 2-stage algorithm |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Symmetric eigenvalue: auxiliary | Low-level functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
▼Singular Value Decomposition (SVD) |
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►SVD: driver | Whole SVD problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►SVD: computational | Major computational phases of SVD problem |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►SVD: auxiliary | Low-level functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
▼BLAS and auxiliary |
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►Level-1 BLAS | Level-1, vector operations: \( O(n) \) operations on \( O(n) \) data; memory bound |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Level-2 BLAS | Level-2, matrix–vector operations: \( O(n^2) \) operations on \( O(n^2) \) data; memory bound |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Level-3 BLAS | Level-3, matrix–matrix operations: \( O(n^3) \) operations on \( O(n^2) \) data; compute bound |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Math auxiliary | Element operations, \( O(1) \) operations on \( O(1) \) data |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Level-1 auxiliary | Additional auxiliary Level-1 functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Level-2 auxiliary | Additional auxiliary Level-2 functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Level-3 auxiliary | Additional auxiliary Level-3 functions |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Communication | CPU to GPU communication |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
▼Sparse |
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►Sparse Linear Systems | Solve \( Ax = b \) |
►General solver | Solve \( Ax = b \), for general \( A \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Hermitian (SPD for real) solver | Solve \( Ax = b \), for symmetric positive definite (SPD) \( A \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Sparse eigenvalue | Solve \( Ax = \lambda x \) |
►general eigenvalue | Solve \( Ax = \lambda x \) for non-symmetric \( A \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►hermitian eigenvalue | Solve \( Ax = \lambda x \) for symmetric \( A \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Sparse preconditioner | Preconditioner for solving \( Ax = \lambda x \) |
►general preconditioner | Preconditioner for \( Ax = \lambda x \) for non-symmetric \( A \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►hermitian preconditioner | Preconditioner for \( Ax = \lambda x \) for symmetric \( A \) |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►GPU kernels for sparse LA | Preconditioner for solving \( Ax = \lambda x \) |
►GPU kernels for non-symmetric sparse LA | GPU kernels for Non-symmetric sparse LA |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►GPU kernels for symmetric sparse LA | GPU kernels for symmetric sparse LA |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Sparse BLAS | |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Sparse auxiliary | |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |
►Sparse unfiled | |
single precision | |
double precision | |
single-complex precision | |
double-complex precision | |