GDD8000
Hand coded optimised EISPACK library for
solving eigenvalue/eigenvector problems, incl. 20 run-time licensees
GDD-8000 Extended C Callable EISPACK LINEAR EIGENVALUE/EIGENVECTOR
SYSTEMS PACKAGE for TMS320C6000.
The library is a set of about 100 functions and macros
that find a solution to a linear algebraic eigensystems with various matrices,
real or complex, general, band, symmetric or Hermitian. All or selected
eigenvalues and eigenvectors can be computed. Several types of matrix
decompositions like SVD or QR are performed by the library functions.
A set of memory allocation functions provides with economical storage for
general/structured matrix classes. By using these memory allocation routines the
amount of RAM storage is minimized for structured types of matrices, like
symmetric, band and triangular classes of matrices.
The library implements and make use of complete Level 1 BLAS (Basic Linear
Algebra Subroutines) standard.
Library's functions have been optimised algorithmically at the assembly level to
fully utilize advantages of TMS320C6000 parallel architecture, floating point
arithmetic and pipeline. BLAS Level 1 functions are hand-coded in assembly to
obtain maximum possible performance of the TMS320C6000 DSPs.
The user's manual gives the details on using library functions.
Functions
REAL GENERALIZED EIGENSYSTEMS
QZAB Find Generalized Eigenvalues and Eigenvectors
RGG Find
Generalized Eigenvalues and Eigenvectors
REAL SYMMETRIC GENERALIZED EIGENSYSTEMS
RSG Find Generalized Eigenvalues and Eigenvectors
RSGAB Find
Generalized Eigenvalues and Eigenvectors
RSGBA Find
Generalized Eigenvalues and Eigenvectors
REAL GENERAL EIGENSYSTEMS
RG Find Eigenvalues and Eigenvectors
REAL SYMMETRIC EIGENSYSTEMS
RS Find Eigenvalues and Eigenvectors
RSM Find All
Eigenvalues and Some Eigenvectors
REAL SYMMETRIC BAND EIGENSYSTEMS
RSB Find Eigenvalues and Eigenvectors
REAL SYMMETRIC TRIDIAGONAL EIGENSYSTEMS
RST Find Eigenvalues and Eigenvectors
REAL SPECIAL TRIDIAGONAL EIGENSYSTEMS
RT Find Eigenvalues and Eigenvectors
COMPLEX GENERALIZED EIGENSYSTEMS
CGG Find Generalized Eigenvalues and Eigenvectors
HERMITIAN GENERALIZED EIGENSYSTEM
CHG Find Generalized Eigenvalues and Eigenvectors
CHGAB Find
Generalized Eigenvalues and Eigenvectors
CHGBA Find
Generalized Eigenvalues and Eigenvectors
COMPLEX GENERAL EIGENSYSTEMS
CG Find Eigenvalues and Eigenvectors, QZ Algorithm
CGLZ Find
Eigenvalues and Eigenvectors, LZ Algorithm
HERMITIAN EIGENSYSTEMS
CH Find Eigenvalues and Eigenvectors
REAL GENERALIZED EIGENSYSTEMS
QZ Algorithm
QZHES
Reduction to Hessenberg Find
QZIT QZ
Algorithm Iteration Step
QZVAL Find
Generalized Eigenvalues
QZVEC Find
Generalized Eigenvectors
REAL SYMMETRIC GENERALIZED EIGENSYSTEMS
Reduction to
Standard Symmetric Eigenproblem
REDUC
Reduction Using Cholesky Factorization for AB
REDUC2
Reduction Using Cholesky Factorization for BA
Eigenvectors
REBAK Find
Eigenvectors for AB
REBAKB Find
Eigenvectors for BA
REAL GENERAL EIGENSYSTEMS
Balancing
BALANC Matrix
Balancing
Reduction to Hessenberg form
ORTHES
Reduction by Orthogonal Transformations
ORTRAN
Reduction and Accumulation the Transformations
ELMHES
Reduction by Elementary Transformations
ELTRAN
Reduction and Accumulation the Transformations
Eigenvalues and Eigenvectors
HQR Find
Eigenvalues, QR Algorithm
HQR2 Find
Eigenvalues and Eigenvectors, QR Algorithm
INVIT Find
Eigenvectors Corresponding to Specified Eigenvalues, Inverse
Iteration
ORTBAK Find
Eigenvectors, Orthogonal Transformations
ELMBAK Find
Eigenvectors, Elementary Transformations
BALBAK Find
Eigenvectors of Balanced Matrix
REAL SYMMETRIC EIGENSYSTEMS
Reduction to Symmetric
Tridiagonal Find
TRED1
Reduction by Orthogonal Transformations
TRED2
Reduction and Accumulation the Transformations
Eigenvectors
TRBAK1 Find
Eigenvectors
REAL SYMMETRIC BAND EIGENSYSTEMS
Reduction to
Symmetric Tridiagonal Find
BANDR
Reduction and Accumulation Orthogonal Transformations
Eigenvalues
BQR Find
Eigenvalue of Smallest Magnitude, QR Algorithm
Eigenvectors
BANDV Find
Eigenvectors Corresponding to Specified Eigenvalues
REAL TRIDIAGONAL EIGENSYSTEMS
Reduction to Symmetric
Tridiagonal Find
FIGI
Reduction by Diagonal Transformations
FIGI2
Reduction and Accumulation the Transformations
Eigenvectors
BAKVEC Find
Eigenvectors
REAL SYMMETRIC TRIDIAGONAL EIGENSYSTEMS
Eigenvalues
and Eigenvectors
TQL1 Find
Eigenvalues, QL Algorithm
IMTQL1 Find
Eigenvalues, Implicit QL Algorithm
IMTQLV Find
Eigenvalues, Implicit QL Algorithm
TQLRAT Find
Eigenvalues, Rational QL Algorithm
TQL2 Find
Eigenvalues and Eigenvectors, QL Algorithm
IMTQL2 Find
Eigenvalues and Eigenvectors, Implicit QL Algorithm
RATQR Find
Smallest or Largest Eigenvalue, Rational QR Algorithm
BISECT Find
Eigenvalues Within Specified Interval
TRIDIB Find
Eigenvalues Between Specified Boundary Indices
TSTURM Find
Eigenvalues Within Specified Interval and Corresponding Eigenvectors
TINVIT Find
Eigenvectors Corresponding to Specified Eigenvalues
COMPLEX GENERALIZED EIGENSYSTEMS
LZ Algorithm
CLZHES
Reduction to Hessenberg Find
CLZIT LZ
Algorithm Iteration Step
CLZVEC Find
Generalized Eigenvectors
QZ Algorithm
CQZHES
Reduction to Hessenberg Find
CQZIT QZ
Algorithm Iteration Step
CQZVEC Find
Generalized Eigenvectors
HERMITIAN GENERALIZED EIGENSYSTEMS
Reduction to
Hermitian Eigenproblem
HRDUC
Reduction Using Cholesky Factorization for AB
HRDUC2
Reduction Using Cholesky Factorization for BA
Eigenvectors
HRBAK Find
Eigenvectors for AB
HRBAKB Find
Eigenvectors for BA
COMPLEX GENERAL EIGENSYSTEMS
Balancing
CBAL Matrix
Balancing
Reduction to Hessenberg form
CORTH
Reduction by Unitary Transformations
COMHES
Reduction by Elementary Transformations
Eigenvalues and Eigenvectors
COMLR Find
Eigenvalues, LR Algorithm
COMLR2 Find
Eigenvalues and Eigenvectors, LR Algorithm
COMQR Find
Eigenvalues, QR Algorithm
COMQR2 Find
Eigenvalues and Eigenvectors, QR Algorithm
COMBAK Find
Eigenvectors
CORTB Find
Eigenvectors
CINVIT Find
Eigenvectors Coresponding to Specified Eigenvalues, Inverse Iteration
CBABK2 Find
Eigenvectors of Balanced Matrix
HERMITIAN EIGENSYSTEMS
Reduction to Real Symmetric
Tridiagonal Find
HTRID3
Reduction by Unitary Transformations
HTRIDI
Reduction by Unitary Transformations
Eigenvectors
HTRIB3 Find
Eigenvectors
HTRIBK Find
Eigenvectors
SINGULAR VALUE DECOMPOSITION
SSVDC Decomposition of a Real Matrix
MINFIT
Minimum Norm Least Squares Solutions
CSVDC
Decomposition of a Complex Matrix
QUASI-TRIANGULAR DECOMPOSITION
HQRDC Orthogonal Quasi-Triangular Decomposition
MEMORY STORAGE ALLOCATION
Real Matrices, Vectors
Allocate
storage for a real vector (macro)
Allocate
storage for a real general matrix
Allocate
storage for a real general band matrix
Allocate
storage for a real symmetric/triangular matrix
Allocate
storage for a real symmetric/triangular band matrix
Complex Matrices, Vectors
Allocate
storage for a complex vector (macro)
Allocate
storage for a complex general matrix
Allocate
storage for a complex general band matrix
Allocate
storage for a complex symmetric/hermitian/triangular matrix
Allocate
storage for a complex symmetric/hermitian/triangular band matrix