 Name  Description 

 BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Array2DTComplex, Int32) 
Computes the Cholesky factorization of a complex Hermitian
positive definite band matrix A. 
 BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Array2DTReal, Int32) 
Computes the Cholesky factorization of a real symmetric
positive definite band matrix A. 
 BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2DTComplex, TReal, TReal, Int32) 
Estimates the reciprocal of the condition number (in the
1norm) of a complex Hermitian positive definite band matrix using
the Cholesky factorization A = U^{H}*U or A = L*L^{H} computed by
ZPBTRF. 
 BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2DTReal, TReal, TReal, Int32) 
Estimates the reciprocal of the condition number (in the
1norm) of a real symmetric positive definite band matrix using the
Cholesky factorization A = U^{T}*U or A = L*L^{T} computed by DPBTRF. 
 BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2DTComplex, Array2DTComplex, Int32) 
Solves a system of linear equations A*X = B with a Hermitian
positive definite band matrix A using the Cholesky factorization
A = U^{H} *U or A = L*L^{H} computed by ZPBTRF. 
 BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2DTReal, Array2DTReal, Int32) 
Solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization
A = U^{T}*U or A = L*L^{T} computed by DPBTRF. 
 BandLUDecompose(Int32, Int32, Int32, Int32, Array2DTComplex, Array1DInt32, Int32) 
Computes an LU factorization of a complex mbyn band matrix A
using partial pivoting with row interchanges. 
 BandLUDecompose(Int32, Int32, Int32, Int32, Array2DTReal, Array1DInt32, Int32) 
Computes an LU factorization of a real mbyn band matrix A
using partial pivoting with row interchanges. 
 BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2DTComplex, Array1DInt32, TReal, TReal, Int32) 
Estimates the reciprocal of the condition number of a complex
general band matrix A, in either the 1norm or the infinitynorm,
using the LU factorization computed by ZGBTRF. 
 BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2DTReal, Array1DInt32, TReal, TReal, Int32) 
Estimates the reciprocal of the condition number of a real
general band matrix A, in either the 1norm or the infinitynorm,
using the LU factorization computed by DGBTRF. 
 BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Array2DTComplex, Array1DInt32, Array2DTComplex, Int32) 
Solves a system of linear equations
A * X = B, A^{T} * X = B, or A^{H} * X = B
with a general band matrix A using the LU factorization computed
by ZGBTRF. 
 BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Array2DTReal, Array1DInt32, Array2DTReal, Int32) 
Solves a system of linear equations
A * X = B or A^{T} * X = B
with a general band matrix A using the LU factorization computed
by DGBTRF. 
 BandTriangularSolve 
Solves a triangular system of the form
A * X = B or A^{T} * X = B,
where A is a triangular band matrix of order N, and B is an
Nby NRHS matrix. 
 CholeskyDecompose(MatrixTriangle, Int32, Array2DTComplex, Int32) 
Factors a symmetric positive definite matrix.

 CholeskyDecompose(MatrixTriangle, Int32, Array2DTReal, Int32) 
Computes the Cholesky factorization of a real symmetric
positive definite matrix A. 
 CholeskyEstimateCondition(MatrixTriangle, Int32, Array2DTComplex, TReal, TReal, Int32) 
Estimates the reciprocal of the condition number of a factored hermitian matrix.

 CholeskyEstimateCondition(MatrixTriangle, Int32, Array2DTReal, TReal, TReal, Int32) 
Estimates the reciprocal of the condition number (in the
1norm) of a real symmetric positive definite matrix using the
Cholesky factorization A = U^{T}*U or A = L*L^{T} computed by DPOTRF. 
 CholeskyInvert(MatrixTriangle, Int32, Array2DTComplex, Int32) 
Computes the inverse of a factored hermitian matrix.

 CholeskyInvert(MatrixTriangle, Int32, Array2DTReal, Int32) 
Computes the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization A = U^{T}*U or A = L*L^{T}
computed by DPOTRF. 
 CholeskySolve(MatrixTriangle, Int32, Int32, Array2DTComplex, Array2DTComplex, Int32) 
Solves a hermitian system of equations.

 CholeskySolve(MatrixTriangle, Int32, Int32, Array2DTReal, Array2DTReal, Int32) 
Solves a system of linear equations A*X = B with a symmetric
positive definite matrix A using the Cholesky factorization
A = U^{T}*U or A = L*L^{T} computed by DPOTRF. 
 EigenvalueDecompose(Char, Char, Int32, Array2DTComplex, Array1DTComplex, Array2DTComplex, Array2DTComplex, Int32) 
Computes for an NbyN complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors. 
 EigenvalueDecompose(Char, Char, Int32, Array2DTReal, Array1DTReal, Array1DTReal, Array2DTReal, Array2DTReal, Int32) 
Computes for an NbyN real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors. 
 Equals  Determines whether the specified Object is equal to the current Object. (Inherited from Object.) 
 Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) 
 GeneralizedEigenvalueDecompose(Char, Char, Int32, Array2DTComplex, Array2DTComplex, Array1DTComplex, Array1DTComplex, Array2DTComplex, Array2DTComplex, Int32) 
Computes for a pair of NbyN complex nonsymmetric matrices
(A,B), the generalized eigenvalues, and optionally, the left and/or
right generalized eigenvectors. 
 GeneralizedEigenvalueDecompose(Char, Char, Int32, Array2DTReal, Array2DTReal, Array1DTReal, Array1DTReal, Array1DTReal, Array2DTReal, Array2DTReal, Int32) 
Computes for a pair of NbyN real nonsymmetric matrices (A,B)
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors. 
 GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Array2DTComplex, Array2DTComplex, Array1DTReal, Array1DTReal, Array2DTComplex, Array2DTComplex, Array2DTComplex, Array1DInt32, Int32)  
 GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Array2DTReal, Array2DTReal, Array1DTReal, Array1DTReal, Array2DTReal, Array2DTReal, Array2DTReal, Array1DInt32, Int32)  
 GetHashCode  Serves as a hash function for a particular type. (Inherited from Object.) 
 GetType  Gets the Type of the current instance. (Inherited from Object.) 
 HermitianDecompose 
Computes the factorization of a complex Hermitian matrix A
using the BunchKaufman diagonal pivoting method. 
 HermitianEigenvalueDecompose 
Computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. 
 HermitianEstimateCondition 
Estimates the reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U^{H} or
A = L*D*L^{H} computed by ZHETRF. 
 HermitianGeneralizedEigenvalueDecompose 
Computes selected eigenvalues, and optionally, eigenvectors
of a complex generalized Hermitiandefinite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. 
 HermitianInvert 
Computes the inverse of a complex Hermitian indefinite matrix
A using the factorization A = U*D*U^{H} or A = L*D*L^{H} computed by
ZHETRF. 
 HermitianSolve 
Solves a system of linear equations A*X = B with a complex
Hermitian matrix A using the factorization A = U*D*U^{H} or
A = L*D*L^{H} computed by ZHETRF. 
 LQDecompose(Int32, Int32, Array2DTComplex, Array1DTComplex, Int32) 
Computes an LQ factorization of a complex MbyN matrix A:
A = L * Q. 
 LQDecompose(Int32, Int32, Array2DTReal, Array1DTReal, Int32) 
Computes an LQ factorization of a real MbyN matrix A:
A = L * Q. 
 LQOrthogonalMultiply 
Overwrites the general real MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(k) . 
 LQUnitaryMultiply 
Overwrites the general complex MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k)**H . 
 LUDecompose(Int32, Int32, Array2DTComplex, Array1DInt32, Int32) 
ZGETRF computes an LU decomposition of a general MbyN matrix A
using partial pivoting with row interchanges.
The decomposition has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the rightlooking Level 3 BLAS version of the algorithm.

 LUDecompose(Int32, Int32, Array2DTReal, Array1DInt32, Int32) 
Computes an LU decomposition of a general MbyN matrix A
using partial pivoting with row interchanges.
The decomposition has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the rightlooking Level 3 BLAS version of the algorithm.

 LUEstimateCondition(MatrixNorm, Int32, Array2DTComplex, TReal, TReal, Int32) 
ZGECON estimates the reciprocal of the condition number of a general
real matrix A, inthis. either the 1norm or the infinitynorm, using
the LU decomposition computed by ZGETRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
Arguments
=========
NORM (input) CHARACTER*1
Specifies whether the 1norm condition number or the
infinitynorm condition number is required:
= '1' or 'O': 1norm;
= 'I': Infinitynorm.
N (input) INTEGER
The elementOrder of the matrix A. N >= 0.
A (input) ZOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the decomposition A = P*L*U
as computed by ZGETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= Max(1,N).
ANORM (input) ZOUBLE PRECISION
If NORM = '1' or 'O', the 1norm of the original matrix A.
If NORM = 'I', the infinitynorm of the original matrix A.
RCOND (output) ZOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK (workspace) ZOUBLE PRECISION array, dimension (4*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value

 LUEstimateCondition(MatrixNorm, Int32, Array2DTReal, TReal, TReal, Int32) 
Estimates the reciprocal of the condition number of a general
real matrix A, in either the 1norm or the infinitynorm, using
the LU factorization computed by DGETRF. 
 LUInvert(Int32, Array2DTComplex, Array1DInt32, Int32) 
ZGETRI computes the inverse of a matrix using the LU decomposition
computed by ZGETRF.
This method inverts U and then computes inv(A) by solving the system
inv(A)*L = inv(U) for inv(A).
Arguments
=========
N (input) INTEGER
The elementOrder of the matrix A. N >= 0.
A (input/output) ZOUBLE PRECISION array, dimension (LDA,N)
On entry, the factors L and U from the decomposition
A = P*L*U as computed by ZGETRF.
On exit, if INFO = 0, the inverse of the original matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= Max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indexes from ZGETRF; for 1< =i< =N, row i of the
matrix was interchanged with row IPIVi.
WORK (workspace/output) ZOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO =0, then WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= Max(1,N).
For optimal performance LWORK >= N*NB, where NB is
the optimal blocksize returned by ILAENV.
If LWORK = 1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero; the matrix is
singular and its inverse could not be computed.

 LUInvert(Int32, Array2DTReal, Array1DInt32, Int32)  
 LUSolve(TransposeOperation, Int32, Int32, Array2DTComplex, Array1DInt32, Array2DTComplex, Int32) 
ZGETRS solves a system of linear equations
A * X = B or A' * X = B
with a general NbyN matrix A using the LU decomposition computed
by ZGETRF.
Arguments
=========
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= TransposeOperation.Transpose: A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The elementOrder of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input) ZOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the decomposition A = P*L*U
as computed by ZGETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= Max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indexes from ZGETRF; for 1< =i< =N, row i of the
matrix was interchanged with row IPIVi.
B (input/output) ZOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= Max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
=====================================================================

 LUSolve(TransposeOperation, Int32, Int32, Array2DTReal, Array1DInt32, Array2DTReal, Int32)  
 MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.) 
 QLDecompose(Int32, Int32, Array2DTComplex, Array1DTComplex, Int32) 
Computes a QL factorization of a complex MbyN matrix A:
A = Q * L. 
 QLDecompose(Int32, Int32, Array2DTReal, Array1DTReal, Int32) 
Computes a QL factorization of a real MbyN matrix A:
A = Q * L. 
 QLOrthogonalMultiply 
Overwrites the general real MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(k) . 
 QLUnitaryMultiply 
Overwrites the general complex MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . 
 QRDecompose(Int32, Int32, Array2DTComplex, Array1DTComplex, Int32) 
ZGEQRF computes a QR decomposition of a real MbyN matrix A:
A = Q * R.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) ZOUBLE PRECISION array, dimension (LDA,N)
On entry, the MbyN matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)byN upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Zetails).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) ZOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Zetails).
WORK (workspace/output) ZOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
If LWORK = 1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
Further Zetails
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i1) = 0 and v(i) = 1; v(i+1:m) is stored on exit inthis. A(i+1:m,i),
and tau inthis. TAU(i).

 QRDecompose(Int32, Int32, Array2DTReal, Array1DTReal, Int32) 
Computes a QR factorization of a real MbyN matrix A:
A = Q * R. 
 QRDecompose(Int32, Int32, Array2DTReal, Array1DInt32, Array1DTReal, Int32) 
Computes a QR factorization with column pivoting of a
matrix A: A*P = Q*R using Level 3 BLAS. 
 QROrthogonalMultiply 
Overwrites the general real MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q^{T} * C C * Q^{T}
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . 
 QRUnitaryMultiply 
Overwrites the general complex MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q^{H} * C C * Q^{H}
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . 
 RQDecompose(Int32, Int32, Array2DTComplex, Array1DTComplex, Int32) 
Computes an RQ factorization of a complex MbyN matrix A:
A = R * Q. 
 RQDecompose(Int32, Int32, Array2DTReal, Array1DTReal, Int32) 
Computes an RQ factorization of a real MbyN matrix A:
A = R * Q. 
 RQOrthogonalMultiply 
Overwrites the general real MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . 
 RQUnitaryMultiply 
Overwrites the general complex MbyN matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(1)**H H(2)**H . 
 SingularValueDecompose(Char, Int32, Int32, Array2DTComplex, Array1DTReal, Array2DTComplex, Array2DTComplex, Int32) 
Computes the singular value decomposition (SVD) of a complex
MbyN matrix A, optionally computing the left and/or right singular
vectors, by using divideandconquer method. 
 SingularValueDecompose(Char, Int32, Int32, Array2DTReal, Array1DTReal, Array2DTReal, Array2DTReal, Int32) 
Computes the singular value decomposition (SVD) of a real
MbyN matrix A, optionally computing the left and right singular
vectors. 
 SymmetricDecompose 
Computes the factorization of a real symmetric matrix A using
the BunchKaufman diagonal pivoting method. 
 SymmetricEigenvalueDecompose 
Computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A. 
 SymmetricEstimateCondition 
Estimates the reciprocal of the condition number (in the
1norm) of a real symmetric matrix A using the factorization
A = U*D*U^{T} or A = L*D*L^{T} computed by DSYTRF. 
 SymmetricGeneralizedEigenvalueDecompose 
Computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetricdefinite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. 
 SymmetricInvert 
Computes the inverse of a real symmetric indefinite matrix
A using the factorization A = U*D*U^{T} or A = L*D*L^{T} computed by
DSYTRF. 
 SymmetricSolve 
Solves a system of linear equations A*X = B with a real
symmetric matrix A using the factorization A = U*D*U^{T} or
A = L*D*L^{T} computed by DSYTRF. 
 ToString  Returns a string that represents the current object. (Inherited from Object.) 
 TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Array2DTComplex, TReal, Int32) 
Approximates the reciprocal of the condition number of a complex triangular matrix.

 TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Array2DTReal, TReal, Int32) 
Estimates the reciprocal of the condition number of a
triangular matrix A, in either the 1norm or the infinitynorm. 
 TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Array2DTComplex, Int32) 
Computes the inverse of a complex triangular matrix.

 TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Array2DTReal, Int32) 
Computes the inverse of a real upper or lower triangular
matrix A. 
 TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2DTComplex, Array2DTComplex, Int32) 
Solves a complex triangular system of equations.

 TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2DTReal, Array2DTReal, Int32) 
Solves a triangular system of the form
A * X = B or A^{T} * X = B,
where A is a triangular matrix of order N, and B is an NbyNRHS
matrix. 