|
|
complib/zhsein(3) -- use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
|
|
ZHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y. |
|
complib/zhseqr(3) -- compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the
|
|
ZHSEQR computes the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors. Optionally Z may be postmultiplied into an input unitary matrix Q, so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H.... |
|
complib/zlabrd(3) -- reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal fo
|
|
ZLABRD reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A. If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form. This is an auxiliary routine called by ZGEBRD |
|
complib/zlacgv(3) -- conjugate a complex vector of length N
|
|
ZLACGV conjugates a complex vector of length N. |
|
complib/zlacon(3) -- estimate the 1-norm of a square, complex matrix A
|
|
ZLACON estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products. |
|
complib/zlacpy(3) -- copie all or part of a two-dimensional matrix A to another matrix B
|
|
ZLACPY copies all or part of a two-dimensional matrix A to another matrix B. |
|
complib/zlacrm(3) -- perform a very simple matrix-matrix multiplication
|
|
ZLACRM performs a very simple matrix-matrix multiplication: C := A * B, where A is M by N and complex; B is N by N and real; C is M by N and complex. |
|
complib/zlacrt(3) -- applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex
|
|
ZLACRT applies a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex. |
|
complib/zladiv(3) -- := X / Y, where X and Y are complex
|
|
ZLADIV := X / Y, where X and Y are complex. The computation of X / Y will not overflow on an intermediary step unless the results overflows. |
|
complib/zlaed0(3) -- the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one
|
|
Using the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix. |
|
complib/zlaed7(3) -- modification by a rank-one symmetric matrix
|
|
ZLAED7 computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and optionally eigenvectors of a dense or banded Hermitian matrix that has been reduced to tridiagonal form. T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) where Z = Q'u, u is a vector of length N with ones in the CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. The eigenvectors... |
|
complib/zlaed8(3) -- merge the two sets of eigenvalues together into a single sorted set
|
|
ZLAED8 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one. |
|
complib/zlaein(3) -- use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper
|
|
ZLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H. |
