# FreeBSD Manual Pages

PDLAED1(l) ) PDLAED1(l)NAMEPDLAED1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix,SYNOPSISSUBROUTINE PDLAED1( N, N1, D, ID, Q, IQ, JQ, DESCQ, RHO, WORK, IWORK, INFO ) INTEGER ID, INFO, IQ, JQ, N, N1 DOUBLE PRECISION RHO INTEGER DESCQ( * ), IWORK( * ) DOUBLE PRECISION D( * ), Q( * ), WORK( * )PURPOSEPDLAED1 computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix, in parallel. 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 N1 and N1 + 1 th elements and zeros elsewhere. The eigenvectors of the original matrix are stored in Q, and the eigenvalues are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero in the Z vector. For each such occurence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine PDLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine SLAED4 (as called by PDLAED3). This routine also calculates the eigenvectors of the current problem. The final stage consists of computing the updated eigenvectors directly using the updated eigenvalues. The eigenvectors for the current problem are multiplied with the eigenvectors from the overall problem.ARGUMENTSN (global input) INTEGER The order of the tridiagonal matrix T. N >= 0. N1 (input) INTEGER The location of the last eigenvalue in the leading sub-matrix. min(1,N) <= N1 <= N. D (global input/output) DOUBLE PRECISION array, dimension (N) On entry,the eigenvalues of the rank-1-perturbed matrix. On exit, the eigenvalues of the repaired matrix. ID (global input) INTEGER Q's global row/col index, which points to the beginning of the submatrix which is to be operated on. Q (local output) DOUBLE PRECISION array, global dimension (N, N), local dimension ( LLD_Q, LOCc(JQ+N-1)) Q contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. IQ (global input) INTEGER Q's global row index, which points to the beginning of the sub- matrix which is to be operated on. JQ (global input) INTEGER Q's global column index, which points to the beginning of the submatrix which is to be operated on. DESCQ (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix Z. RHO (input) DOUBLE PRECISION The subdiagonal entry used to create the rank-1 modification. WORK (local workspace/output) DOUBLE PRECISION array, dimension 6*N + 2*NP*NQ IWORK (local workspace/output) INTEGER array, dimension 7*N + 8*NPCOL + 2 INFO (global output) INTEGER = 0: successful exit < 0: If the i-th argument is an array and the j-entry had an illegal value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an illegal value, then INFO = -i. > 0: The algorithm failed to compute the ith eigenvalue. ScaLAPACK version 1.7 13 August 2001 PDLAED1(l)

NAME | SYNOPSIS | PURPOSE | ARGUMENTS

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