slaed0(l) [redhat man page]
SLAED0(l) ) SLAED0(l) NAME
SLAED0 - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method SYNOPSIS
SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO ) INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ INTEGER IWORK( * ) REAL D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), WORK( * ) PURPOSE
SLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. ARGUMENTS
ICOMPQ (input) INTEGER = 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 2: Compute eigenvalues and eigenvectors of tridiagonal matrix. QSIZ (input) INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. N (input) INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. D (input/output) REAL array, dimension (N) On entry, the main diagonal of the tridiagonal matrix. On exit, its eigenvalues. E (input) REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed. Q (input/output) REAL array, dimension (LDQ, N) On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ = 0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a sub- set of the columns of the orthogonal matrix used to reduce the full matrix to tridiagonal form corresponding to the subset of the full matrix which is being decomposed at this time. If ICOMPQ = 2 On entry, Q will be the identity matrix. On exit, Q contains the eigenvectors of the tridiagonal matrix. LDQ (input) INTEGER The leading dimension of the array Q. If eigenvectors are desired, then LDQ >= max(1,N). In any case, LDQ >= 1. QSTORE (workspace) REAL array, dimension (LDQS, N) Referenced only when ICOMPQ = 1. Used to store parts of the eigenvector matrix when the updating matrix multiplies take place. LDQS (input) INTEGER The leading dimension of the array QSTORE. If ICOMPQ = 1, then LDQS >= max(1,N). In any case, LDQS >= 1. WORK (workspace) REAL array, If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 + 3*N + 2*N*lg N + 2*N**2 ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must be at least 4*N + N**2. IWORK (workspace) INTEGER array, If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 + 5*N. INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1). FURTHER DETAILS
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA LAPACK version 3.0 15 June 2000 SLAED0(l)
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slaed0.f(3) LAPACK slaed0.f(3) NAME
slaed0.f - SYNOPSIS
Functions/Subroutines subroutine slaed0 (ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) SLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Function/Subroutine Documentation subroutine slaed0 (integerICOMPQ, integerQSIZ, integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( ldq, * )Q, integerLDQ, real, dimension( ldqs, * )QSTORE, integerLDQS, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO) SLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Purpose: SLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. Parameters: ICOMPQ ICOMPQ is INTEGER = 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 2: Compute eigenvalues and eigenvectors of tridiagonal matrix. QSIZ QSIZ is INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. N N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. D D is REAL array, dimension (N) On entry, the main diagonal of the tridiagonal matrix. On exit, its eigenvalues. E E is REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed. Q Q is REAL array, dimension (LDQ, N) On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ = 0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a subset of the columns of the orthogonal matrix used to reduce the full matrix to tridiagonal form corresponding to the subset of the full matrix which is being decomposed at this time. If ICOMPQ = 2 On entry, Q will be the identity matrix. On exit, Q contains the eigenvectors of the tridiagonal matrix. LDQ LDQ is INTEGER The leading dimension of the array Q. If eigenvectors are desired, then LDQ >= max(1,N). In any case, LDQ >= 1. QSTORE QSTORE is REAL array, dimension (LDQS, N) Referenced only when ICOMPQ = 1. Used to store parts of the eigenvector matrix when the updating matrix multiplies take place. LDQS LDQS is INTEGER The leading dimension of the array QSTORE. If ICOMPQ = 1, then LDQS >= max(1,N). In any case, LDQS >= 1. WORK WORK is REAL array, If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must be at least 4*N + N**2. IWORK IWORK is INTEGER array, If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 + 5*N. INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1). Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Contributors: Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Definition at line 172 of file slaed0.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slaed0.f(3)