Sun Performance Library Reference

Preface

1. LAPACK Subroutines

Naming Conventions

Error Handling

Extensions to LAPACK

Reciprocal Condition Number of an LU-Factored General Matrix in Banded Storage

Equilibration Scale Factors for a General Matrix in Banded Storage

Refined Solution to a Linear System in an LU-Factored General Matrix in Banded Storage

Solution to a Linear System in a General Matrix in Banded Storage (Simple Driver)

Solution to a Linear System in a General Matrix in Banded Storage (Expert Driver)

LU Factorization of a General Matrix in Banded Storage

Solution to a Linear System in an LU-Factored General Matrix in Banded Storage

Reciprocal Condition Number of an LU-Factored General Matrix

Equilibration Scale Factors for a General Matrix

Eigenvalues, Schur Form, and Schur Factorization of a General Matrix (Simple Driver)

Eigenvalues, Schur Form, and Schur Factorization of a General Matrix (Expert Driver)

Eigenvalues and Eigenvectors of a General Matrix (Simple Driver)

Eigenvalues, Eigenvectors, and Reciprocal Condition Numbers of a General Matrix (Expert Driver)

Generalized Eigenvalues, Schur Form, and Schur Vectors of General Matrices

Generalized Eigenvalues and Eigenvectors for General Matrices

LQ Factorization of a General Matrix

Solution to a Least Squares Problem for a Full-Rank General Matrix (Simple Driver)

Solution to a Least Squares Problem for a Rank-Deficient General Matrix (Simple Driver)

Solution to a Least Squares Problem for a Rank-Deficient General Matrix (Expert Driver)

QL Factorization of a General Matrix

QR Factorization with Column Pivoting of a General Matrix

QR Factorization of a General Matrix

Refined Solution to a Linear System in an LU-Factored General Matrix

RQ Factorization of a General Matrix

Solution to a Linear System in a General Matrix (Simple Driver)

Singular Value Decomposition of a General Matrix

Solution to a Linear System in a General Matrix (Expert Driver)

LU Factorization of a General Matrix

Inverse of an LU-Factored General Matrix

Solution to a Linear System in an LU-Factored General Matrix

Solution to a Generalized Linear Regression Model Problem

Solution to a Linear Equality Constrained Least Squares Problem

Generalized Singular Value Decomposition of General Matrices

Reciprocal Condition Number of an LU-Factored Tridiagonal Matrix

Refined Solution to a Linear System in an LU-Factored General Tridiagonal Matrix

Solution to a Linear System in a General Tridiagonal Matrix (Simple Driver)

Solution to a Linear System in a General Tridiagonal Matrix (Expert Driver)

LU Factorization of a Tridiagonal Matrix

Solution to a Linear System in an LU-Factored General Tridiagonal Matrix

Eigenvalues and Eigenvectors of a Hermitian Matrix in Banded Storage (Simple Driver)

Eigenvalues and Eigenvectors of a Hermitian Matrix in Banded Storage (Expert Driver)

Reciprocal Condition Number of a UDU- or LDL-Factored Hermitian Matrix

Eigenvalues and Eigenvectors of a Hermitian Matrix (Simple Driver)

Eigenvalues and Eigenvectors of a Hermitian Matrix (Expert Driver)

Generalized Eigenvalues and Eigenvectors for Hermitian Matrices

Refined Solution to a Linear System in a UDU- or LDL-Factored Hermitian Matrix

Solution to a Linear System in a Hermitian Matrix (Simple Driver)

Solution to a Linear System in a Hermitian Matrix (Expert Driver)

UDU or LDL Factorization of a Hermitian Matrix

Inverse of a UDU- or LDL-Factored Hermitian Matrix

Solution to a Linear System in a UDU- or LDL-Factored Hermitian Matrix

Reciprocal Condition Number of a UDU- or LDL-Factored Hermitian Matrix in Packed Storage

Eigenvalues and Eigenvectors of a Hermitian Matrix in Packed Storage (Simple Driver)

Eigenvalues and Eigenvectors of a Hermitian Matrix in Packed Storage (Expert Driver)

Generalized Eigenvalues and Eigenvectors for Hermitian Matrices in Packed Storage

Refined Solution to a Linear System in a UDU- or LDL-Factored Hermitian Matrix in Packed Storage

Solution to a Linear System in a Hermitian Matrix in Packed Storage (Simple Driver)

Solution to a Linear System in a Hermitian Matrix in Packed Storage (Expert Driver)

UDU or LDL Factorization of a Hermitian Matrix in Packed Storage

Inverse of a UDU- or LDL-Factored Hermitian Matrix in Packed Storage

Solution to a Linear System in a UDU- or LDL-Factored Hermitian Matrix in Packed Storage

Generation of Q Defined in LQ Factorization

Generation of Q Defined in QL Factorization

Generation of Q Defined in QR Factorization

Generation of Q Defined in RQ Factorization

Reciprocal Condition Number of a Cholesky-Factored Symmetric Positive Definite Matrix in Banded Storage

Equilibration Scale Factors for a Symmetric Positive Definite Matrix in Banded Storage

Refined Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix in Banded Storage

Solution to a Linear System in a Symmetric Positive Definite Matrix in Banded Storage (Simple Driver)

Solution to a Linear System in a Symmetric Positive Definite Matrix in Banded Storage (Expert Driver)

Cholesky Factorization of a Symmetric Positive Definite Matrix in Banded Storage

Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix in Banded Storage

Reciprocal Condition Number of a Cholesky-Factored Symmetric Positive Definite Matrix

Equilibration Scale Factors for a Symmetric Positive Definite Matrix

Refined Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix

Solution to a Linear System in a Symmetric Positive Definite Matrix (Simple Driver)

Solution to a Linear System in a Symmetric Positive Definite Matrix (Expert Driver)

Cholesky Factorization of a Symmetric Positive Definite Matrix

Inverse of a Cholesky-Factored Symmetric Positive Definite Matrix

Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix

Reciprocal Condition Number of a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Equilibration Scale Factors for a Symmetric Positive Definite Matrix in Packed Storage

Refined Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Solution to a Linear System in a Symmetric Positive Definite Matrix in Packed Storage (Simple Driver)

Solution to a Linear System in a Symmetric Positive Definite Matrix in Packed Storage (Expert Driver)

Cholesky Factorization of a Symmetric Positive Definite Matrix in Packed Storage

Inverse of a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Reciprocal Condition Number of a UDU- or LDL-Factored Symmetric Positive Definite Tridiagonal Matrix

Refined Solution to a Linear System in a UDU- or LDL-Factored Symmetric Positive Definite Tridiagonal Matrix

Solution to a Linear System in a Symmetric Positive Definite Tridiagonal Matrix (Simple Driver)

Solution to a Linear System in a Symmetric Positive Definite Tridiagonal Matrix (Expert Driver)

UDU or LDL Factorization of a Symmetric Positive Definite Tridiagonal Matrix

Solution to a Linear System in a UDU- or LDL-Factored Symmetric Positive Definite Tridiagonal Matrix

Eigenvalues and Eigenvectors of a Symmetric Matrix in Banded Storage (Simple Driver)

Eigenvalues and Eigenvectors of a Symmetric Matrix in Banded Storage (Expert Driver)

Reciprocal Condition Number of a UDU- or LDL-Factored Symmetric Matrix in Packed Storage

Eigenvalues and Eigenvectors of a Symmetric Matrix in Packed Storage (Simple Driver)

Eigenvalues and Eigenvectors of a Symmetric Matrix in Packed Storage (Expert Driver)

Generalized Eigenvalues and Eigenvectors for Symmetric Matrices in Packed Storage

Refined Solution to a Linear System in a UDU- or LDL-Factored Symmetric Matrix in Packed Storage

Solution to a Linear System in a Symmetric Matrix in Packed Storage (Simple Driver)

Solution to a Linear System in a Symmetric Matrix in Packed Storage (Expert Driver)

UDU or LDL Factorization of a Symmetric Matrix in Packed Storage

Inverse of a UDU- or LDL-Factored Symmetric Matrix in Packed Storage

Solution to a Linear System in a UDU- or LDL-Factored Symmetric Matrix in Packed Storage

Eigenvalues and Eigenvectors of a Symmetric Tridiagonal Matrix (Simple Driver)

Eigenvalues and Eigenvectors of a Symmetric Tridiagonal Matrix (Expert Driver)

Reciprocal Condition Number of a UDU- or LDL-Factored Symmetric Matrix

Eigenvalues and Eigenvectors of a Symmetric Matrix (Simple Driver)

Eigenvalues and Eigenvectors of a Symmetric Matrix (Expert Driver)

Generalized Eigenvalues and Eigenvectors for Symmetric Matrices

Refined Solution to a Linear System in a UDU- or LDL-Factored Symmetric Matrix

Solution to a Linear System in a Symmetric Matrix (Simple Driver)

Solution to a Linear System in a Symmetric Matrix (Expert Driver)

UDU or LDL Factorization of a Symmetric Matrix

Inverse of a UDU- or LDL-Factored Symmetric Matrix

Solution to a Linear System in a UDU- or LDL-Factored Symmetric Matrix

Reciprocal Condition Number of a Triangular Matrix in Banded Storage

Error Bounds and Estimates for the Solution to a Linear System in a Triangular Matrix in Banded Storage

Solution to a Linear System in a Triangular Matrix in Banded Storage

Reciprocal Condition Number of a Triangular Matrix in Packed Storage

Error Bounds and Estimates for the Solution of a Linear System in a Triangular Matrix in Packed Storage

Inverse of a Triangular Matrix in Packed Storage

Solution to a Linear System in a Triangular Matrix in Packed Storage

Reciprocal Condition Number of a Triangular Matrix

Error Bounds and Estimates for the Solution of a Linear System in a Triangular Matrix

Inverse of a Triangular Matrix

Solution to a Linear System in a Triangular Matrix

2. LINPACK Subroutines

Naming Conventions

Argument Conventions

Error Handling

Extensions to LINPACK

Cholesky Decomposition of a Symmetric Positive Definite Matrix

Downdate an Augmented Cholesky Decomposition

Update an Augmented Cholesky Decomposition with Permutations

Update an Augmented Cholesky Decomposition

LU Factorization and Condition Number of a General Matrix in Banded Storage

Determinant of an LU-Factored General Matrix in Banded Storage

LU Factorization of a General Matrix in Banded Storage

Solution to a Linear System in an LU-Factored Matrix in Banded Storage

LU Factorization and Condition Number of a General Matrix

Determinant and Inverse of an LU-Factored General Matrix

LU Factorization of a General Matrix

Solution to a Linear System in an LU-Factored General Matrix

Solution to a Linear System in a Tridiagonal Matrix

UDU Factorization and Condition Number of a Hermitian Matrix

Determinant, Inertia, and Inverse of a UDU-Factored Hermitian Matrix

UDU Factorization of a Hermitian Matrix

Solution to a Linear System in a UDU-Factored Hermitian Matrix

UDU Factorization and Condition Number of a Hermitian Matrix in Packed Storage

Determinant, Inertia, and Inverse of a UDU-Factored Hermitian Matrix in Packed Storage

UDU Factorization of a Hermitian Matrix in Packed Storage

Solution to a Linear System in a UDU-Factored Hermitian Matrix in Packed Storage

Cholesky Factorization and Condition Number of a Symmetric Positive Definite Matrix in Banded Storage

Determinant of a Cholesky-Factored Symmetric Positive Definite Matrix in Banded Storage

Cholesky Factorization of a Symmetric Positive Definite Matrix in Banded Storage

Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix in Banded Storage

Cholesky Factorization and Condition Number of a Symmetric Positive Definite Matrix

Determinant and Inverse of a Cholesky-Factored Symmetric Positive Definite Matrix

Cholesky Factorization of a Symmetric Positive Definite Matrix

Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix

Cholesky Factorization and Condition Number of a Symmetric Positive Definite Matrix in Packed Storage

Determinant and Inverse of a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Cholesky Factorization of a Symmetric Positive Definite Matrix in Packed Storage

Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Solution to a Linear System in a Symmetric Positive Definite Tridiagonal Matrix

QR Factorization of a General Matrix

Solution to a Linear System in a QR-Factored General Matrix

UDU Factorization and Condition Number of a Symmetric Matrix

Determinant, Inertia, and Inverse of a UDU-Factored Symmetric Matrix

UDU Factorization of a Symmetric Matrix

Solution to a Linear System in a UDU-Factored Symmetric Matrix

UDU Factorization and Condition Number of a Symmetric Matrix in Packed Storage

Determinant, Inertia, and Inverse of a UDU-Factored Symmetric Matrix in Packed Storage

UDU Factorization of a Symmetric Matrix in Packed Storage

Solution to a Linear System in a UDU-Factored Symmetric Matrix in Packed Storage

Singular Value Decomposition of a General Matrix

Condition Number of a Triangular Matrix

Determinant and Inverse of a Triangular Matrix

Solution to a Linear System in a Triangular Matrix

3. Basic Linear Algebra Subprograms, Level 1 (BLAS1)

Conventions

Extensions to the Basic Linear Algebra Subprograms

Sum of the Absolute Values of a Vector

Product of a Scalar and Vector Plus a Vector

Copy a Vector

Dot Product (Inner Product)

Givens Plane Rotation

Applied Given's Plane Rotation

Modified Given's Plane Rotation

Applied Modified Given's Transformation

Index of Element with Maximum Absolute Value

Euclidean Norm of a Vector

Scale a Vector

Swap Two Vectors

4. Basic Linear Algebra Subprograms, Level 2 (BLAS2)

Naming Conventions

Argument Conventions

Error Handling

Extensions to the Basic Linear Algebra Subprograms

Product of a Matrix in Banded Storage and a Vector

Product of a General Matrix and a Vector

Rank-1 Update to a General Matrix

Product of a Hermitian Matrix in Banded Storage and a Vector

Product of a Hermitian Matrix and a Vector

Rank-1 Update to a Hermitian Matrix

Rank-2 Update to a Hermitian Matrix

Product of a Hermitian Matrix in Packed Storage and a Vector

Rank-1 Update to a Hermitian Matrix in Packed Storage

Rank-2 Update to a Hermitian Matrix in Packed Storage

Product of a Symmetric Matrix in Banded Storage and a Vector

Product of a Symmetric Matrix in Packed Storage and a Vector

Rank-1 Update to a Real Symmetric Matrix in Packed Storage

Rank-2 Update to a Real Symmetric Matrix in Packed Storage

Product of a Symmetric Matrix and a Vector

Rank-1 Update to a Real Symmetric Matrix

Rank-2 Update to a Real Symmetric Matrix

Product of a Triangular Matrix in Banded Storage and a Vector

Solution to a Triangular System in Banded Storage of Linear Equations

Product of a Triangular Matrix in Packed Storage and a Vector

Solution to a Triangular System of Linear Equations in Packed Storage

Product of a Triangular Matrix and a Vector

Solution to a Triangular System of Linear Equations

5. Basic Linear Algebra Subprograms, Level 3 (BLAS3)

Naming Conventions

Argument Conventions

Error Handling

Extensions to the Basic Linear Algebra Subprograms

Product of Two General Matrices

Product of a Hermitian Matrix and a General Matrix

Rank-k Update of a Hermitian Matrix

Rank-2k Update of a Hermitian Matrix

Product of a Symmetric Matrix and a General Matrix

Rank-k Update of a Symmetric Matrix

Rank-2k Update of a Symmetric Matrix

Product of a Triangular Matrix and a General Matrix

Solution for a Triangular System of Equations

6. Fast Fourier Transform Subroutines (FFTPACK and VFFTPACK)

Naming Conventions

Extensions to FFTPACK and VFFTPACK

Transpose Array

Cosine Quarter-Wave Synthesis

Cosine Quarter-Wave Transform

Initialize Cosine Quarter-Wave Transform and Synthesis

Cosine Even-Wave Transform

Initialize Cosine Even-Wave Transform

EZ Fourier Synthesis

EZ Fourier Transform

Initialize EZ Fourier Transform and Synthesis

Fourier Synthesis

Fourier Transform

Initialize Fourier Transform and Synthesis

Sine Quarter-Wave Synthesis

Sine Quarter-Wave Transform

Initialize Sine Quarter-Wave Transform and Synthesis

Sine Odd-Wave Transform

Initialize Sine Odd-Wave Transform