|
|
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. |
|
complib/zlaesy(3) -- compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the mat
|
|
ZLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value. RT1 is the eigenvalue of larger absolute value, and RT2 of smaller absolute value. If the eigenvectors are computed, then on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ] [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]... |
|
complib/zlaev2(3) -- compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
|
|
ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] [- SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. |
|
complib/zlags2(3) -- compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0
|
|
ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV ) Q = ( CSQ SNQ ) ( -CONJG(SNQ) CSQ ) Z' denotes the conjugate transpose of Z. The rows of the transformed A and B are parallel. Moreover, if the input 2-by-2 matrix A is not zero, then the transformed (1,1) entry of A is not zero. If the input matrices A and B are both not zero, then the transformed (2,2) element of B is not zero, except when the first rows of input A and B are... |
|
complib/zlagtm(3) -- perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of o
|
|
ZLAGTM performs a matrix-vector product of the form |
|
complib/zlahef(3) -- using the Bunch-Kaufman diagonal pivoting method
|
|
ZLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12' U22' ) A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U' denotes the conjugate trans... |
|
complib/zlahqr(3) -- i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by
|
|
ZLAHQR is an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI. |
|
complib/zlahrd(3) -- matrix A so that elements below the k-th subdiagonal are zero
|
|
ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero. The reduction is performed by a unitary similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T. This is an auxiliary routine called by ZGEHRD. |
