
NAMEzlaed8.f SYNOPSISFunctions/Subroutinessubroutine zlaed8 (K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO) Function/Subroutine Documentationsubroutine zlaed8 (integerK, integerN, integerQSIZ, complex*16, dimension( ldq, * )Q, integerLDQ, double precision, dimension( * )D, double precisionRHO, integerCUTPNT, double precision, dimension( * )Z, double precision, dimension( * )DLAMDA, complex*16, dimension( ldq2, * )Q2, integerLDQ2, double precision, dimension( * )W, integer, dimension( * )INDXP, integer, dimension( * )INDX, integer, dimension( * )INDXQ, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( 2, * )GIVCOL, double precision, dimension( 2, * )GIVNUM, integerINFO)ZLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. Purpose: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. K
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K is INTEGER Contains the number of nondeflated eigenvalues. This is the order of the related secular equation.N N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.QSIZ QSIZ is INTEGER The dimension of the unitary matrix used to reduce the dense or band matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.Q Q is COMPLEX*16 array, dimension (LDQ,N) On entry, Q contains the eigenvectors of the partially solved system which has been previously updated in matrix multiplies with other partially solved eigensystems. On exit, Q contains the trailing (NK) updated eigenvectors (those which were deflated) in its last NK columns.LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max( 1, N ).D D is DOUBLE PRECISION array, dimension (N) On entry, D contains the eigenvalues of the two submatrices to be combined. On exit, D contains the trailing (NK) updated eigenvalues (those which were deflated) sorted into increasing order.RHO RHO is DOUBLE PRECISION Contains the off diagonal element associated with the rank1 cut which originally split the two submatrices which are now being recombined. RHO is modified during the computation to the value required by DLAED3.CUTPNT CUTPNT is INTEGER Contains the location of the last eigenvalue in the leading submatrix. MIN(1,N) <= CUTPNT <= N.Z Z is DOUBLE PRECISION array, dimension (N) On input this vector contains the updating vector (the last row of the first subeigenvector matrix and the first row of the second subeigenvector matrix). The contents of Z are destroyed during the updating process.DLAMDA DLAMDA is DOUBLE PRECISION array, dimension (N) Contains a copy of the first K eigenvalues which will be used by DLAED3 to form the secular equation.Q2 Q2 is COMPLEX*16 array, dimension (LDQ2,N) If ICOMPQ = 0, Q2 is not referenced. Otherwise, Contains a copy of the first K eigenvectors which will be used by DLAED7 in a matrix multiply (DGEMM) to update the new eigenvectors.LDQ2 LDQ2 is INTEGER The leading dimension of the array Q2. LDQ2 >= max( 1, N ).W W is DOUBLE PRECISION array, dimension (N) This will hold the first k values of the final deflationaltered zvector and will be passed to DLAED3.INDXP INDXP is INTEGER array, dimension (N) This will contain the permutation used to place deflated values of D at the end of the array. On output INDXP(1:K) points to the nondeflated Dvalues and INDXP(K+1:N) points to the deflated eigenvalues.INDX INDX is INTEGER array, dimension (N) This will contain the permutation used to sort the contents of D into ascending order.INDXQ INDXQ is INTEGER array, dimension (N) This contains the permutation which separately sorts the two subproblems in D into ascending order. Note that elements in the second half of this permutation must first have CUTPNT added to their values in order to be accurate.PERM PERM is INTEGER array, dimension (N) Contains the permutations (from deflation and sorting) to be applied to each eigenblock.GIVPTR GIVPTR is INTEGER Contains the number of Givens rotations which took place in this subproblem.GIVCOL GIVCOL is INTEGER array, dimension (2, N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation.GIVNUM GIVNUM is DOUBLE PRECISION array, dimension (2, N) Each number indicates the S value to be used in the corresponding Givens rotation.INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Definition at line 227 of file zlaed8.f.
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