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SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
$ WORK, IWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), $ WORK( * ) * .. * * Purpose * ======= * * DLAED0 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) DOUBLE PRECISION array, dimension (N) * On entry, the main diagonal of the tridiagonal matrix. * On exit, its eigenvalues. * * E (input) DOUBLE PRECISION array, dimension (N-1) * The off-diagonal elements of the tridiagonal matrix. * On exit, E has been destroyed. * * Q (input/output) DOUBLE PRECISION 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 (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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.D0, ONE = 1.D0, TWO = 2.D0 ) * .. * .. Local Scalars .. INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM, $ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM, $ J, K, LGN, MATSIZ, MSD2, SMLSIZ, SMM1, SPM1, $ SPM2, SUBMAT, SUBPBS, TLVLS DOUBLE PRECISION TEMP * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMM, DLACPY, DLAED1, DLAED7, DSTEQR, $ XERBLA * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, INT, LOG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.2 ) THEN INFO = -1 ELSE IF( ( ICOMPQ.EQ.1 ) .AND. ( QSIZ.LT.MAX( 0, N ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED0', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * SMLSIZ = ILAENV( 9, 'DLAED0', ' ', 0, 0, 0, 0 ) * * Determine the size and placement of the submatrices, and save in * the leading elements of IWORK. * IWORK( 1 ) = N SUBPBS = 1 TLVLS = 0 10 CONTINUE IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN DO 20 J = SUBPBS, 1, -1 IWORK( 2*J ) = ( IWORK( J )+1 ) / 2 IWORK( 2*J-1 ) = IWORK( J ) / 2 20 CONTINUE TLVLS = TLVLS + 1 SUBPBS = 2*SUBPBS GO TO 10 END IF DO 30 J = 2, SUBPBS IWORK( J ) = IWORK( J ) + IWORK( J-1 ) 30 CONTINUE * * Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 * using rank-1 modifications (cuts). * SPM1 = SUBPBS - 1 DO 40 I = 1, SPM1 SUBMAT = IWORK( I ) + 1 SMM1 = SUBMAT - 1 D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) ) D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) ) 40 CONTINUE * INDXQ = 4*N + 3 IF( ICOMPQ.NE.2 ) THEN * * Set up workspaces for eigenvalues only/accumulate new vectors * routine * TEMP = LOG( DBLE( N ) ) / LOG( TWO ) LGN = INT( TEMP ) IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IPRMPT = INDXQ + N + 1 IPERM = IPRMPT + N*LGN IQPTR = IPERM + N*LGN IGIVPT = IQPTR + N + 2 IGIVCL = IGIVPT + N*LGN * IGIVNM = 1 IQ = IGIVNM + 2*N*LGN IWREM = IQ + N**2 + 1 * * Initialize pointers * DO 50 I = 0, SUBPBS IWORK( IPRMPT+I ) = 1 IWORK( IGIVPT+I ) = 1 50 CONTINUE IWORK( IQPTR ) = 1 END IF * * Solve each submatrix eigenproblem at the bottom of the divide and * conquer tree. * CURR = 0 DO 70 I = 0, SPM1 IF( I.EQ.0 ) THEN SUBMAT = 1 MATSIZ = IWORK( 1 ) ELSE SUBMAT = IWORK( I ) + 1 MATSIZ = IWORK( I+1 ) - IWORK( I ) END IF IF( ICOMPQ.EQ.2 ) THEN CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), $ Q( SUBMAT, SUBMAT ), LDQ, WORK, INFO ) IF( INFO.NE.0 ) $ GO TO 130 ELSE CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), $ WORK( IQ-1+IWORK( IQPTR+CURR ) ), MATSIZ, WORK, $ INFO ) IF( INFO.NE.0 ) $ GO TO 130 IF( ICOMPQ.EQ.1 ) THEN CALL DGEMM( 'N', 'N', QSIZ, MATSIZ, MATSIZ, ONE, $ Q( 1, SUBMAT ), LDQ, WORK( IQ-1+IWORK( IQPTR+ $ CURR ) ), MATSIZ, ZERO, QSTORE( 1, SUBMAT ), $ LDQS ) END IF IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2 CURR = CURR + 1 END IF K = 1 DO 60 J = SUBMAT, IWORK( I+1 ) IWORK( INDXQ+J ) = K K = K + 1 60 CONTINUE 70 CONTINUE * * Successively merge eigensystems of adjacent submatrices * into eigensystem for the corresponding larger matrix. * * while ( SUBPBS > 1 ) * CURLVL = 1 80 CONTINUE IF( SUBPBS.GT.1 ) THEN SPM2 = SUBPBS - 2 DO 90 I = 0, SPM2, 2 IF( I.EQ.0 ) THEN SUBMAT = 1 MATSIZ = IWORK( 2 ) MSD2 = IWORK( 1 ) CURPRB = 0 ELSE SUBMAT = IWORK( I ) + 1 MATSIZ = IWORK( I+2 ) - IWORK( I ) MSD2 = MATSIZ / 2 CURPRB = CURPRB + 1 END IF * * Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) * into an eigensystem of size MATSIZ. * DLAED1 is used only for the full eigensystem of a tridiagonal * matrix. * DLAED7 handles the cases in which eigenvalues only or eigenvalues * and eigenvectors of a full symmetric matrix (which was reduced to * tridiagonal form) are desired. * IF( ICOMPQ.EQ.2 ) THEN CALL DLAED1( MATSIZ, D( SUBMAT ), Q( SUBMAT, SUBMAT ), $ LDQ, IWORK( INDXQ+SUBMAT ), $ E( SUBMAT+MSD2-1 ), MSD2, WORK, $ IWORK( SUBPBS+1 ), INFO ) ELSE CALL DLAED7( ICOMPQ, MATSIZ, QSIZ, TLVLS, CURLVL, CURPRB, $ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS, $ IWORK( INDXQ+SUBMAT ), E( SUBMAT+MSD2-1 ), $ MSD2, WORK( IQ ), IWORK( IQPTR ), $ IWORK( IPRMPT ), IWORK( IPERM ), $ IWORK( IGIVPT ), IWORK( IGIVCL ), $ WORK( IGIVNM ), WORK( IWREM ), $ IWORK( SUBPBS+1 ), INFO ) END IF IF( INFO.NE.0 ) $ GO TO 130 IWORK( I / 2+1 ) = IWORK( I+2 ) 90 CONTINUE SUBPBS = SUBPBS / 2 CURLVL = CURLVL + 1 GO TO 80 END IF * * end while * * Re-merge the eigenvalues/vectors which were deflated at the final * merge step. * IF( ICOMPQ.EQ.1 ) THEN DO 100 I = 1, N J = IWORK( INDXQ+I ) WORK( I ) = D( J ) CALL DCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 ) 100 CONTINUE CALL DCOPY( N, WORK, 1, D, 1 ) ELSE IF( ICOMPQ.EQ.2 ) THEN DO 110 I = 1, N J = IWORK( INDXQ+I ) WORK( I ) = D( J ) CALL DCOPY( N, Q( 1, J ), 1, WORK( N*I+1 ), 1 ) 110 CONTINUE CALL DCOPY( N, WORK, 1, D, 1 ) CALL DLACPY( 'A', N, N, WORK( N+1 ), N, Q, LDQ ) ELSE DO 120 I = 1, N J = IWORK( INDXQ+I ) WORK( I ) = D( J ) 120 CONTINUE CALL DCOPY( N, WORK, 1, D, 1 ) END IF GO TO 140 * 130 CONTINUE INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1 * 140 CONTINUE RETURN * * End of DLAED0 * END |