SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, $ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) * * -- LAPACK routine (version 3.2.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2010 * * .. Scalar Arguments .. INTEGER CURLVL, CURPBM, INFO, N, TLVLS * .. * .. Array Arguments .. INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), $ PRMPTR( * ), QPTR( * ) DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) * .. * * Purpose * ======= * * DLAEDA computes the Z vector corresponding to the merge step in the * CURLVLth step of the merge process with TLVLS steps for the CURPBMth * problem. * * Arguments * ========= * * N (input) INTEGER * The dimension of the symmetric tridiagonal matrix. N >= 0. * * TLVLS (input) INTEGER * The total number of merging levels in the overall divide and * conquer tree. * * CURLVL (input) INTEGER * The current level in the overall merge routine, * 0 <= curlvl <= tlvls. * * CURPBM (input) INTEGER * The current problem in the current level in the overall * merge routine (counting from upper left to lower right). * * PRMPTR (input) INTEGER array, dimension (N lg N) * Contains a list of pointers which indicate where in PERM a * level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) * indicates the size of the permutation and incidentally the * size of the full, non-deflated problem. * * PERM (input) INTEGER array, dimension (N lg N) * Contains the permutations (from deflation and sorting) to be * applied to each eigenblock. * * GIVPTR (input) INTEGER array, dimension (N lg N) * Contains a list of pointers which indicate where in GIVCOL a * level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) * indicates the number of Givens rotations. * * GIVCOL (input) INTEGER array, dimension (2, N lg N) * Each pair of numbers indicates a pair of columns to take place * in a Givens rotation. * * GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N) * Each number indicates the S value to be used in the * corresponding Givens rotation. * * Q (input) DOUBLE PRECISION array, dimension (N**2) * Contains the square eigenblocks from previous levels, the * starting positions for blocks are given by QPTR. * * QPTR (input) INTEGER array, dimension (N+2) * Contains a list of pointers which indicate where in Q an * eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates * the size of the block. * * Z (output) DOUBLE PRECISION array, dimension (N) * On output this vector contains the updating vector (the last * row of the first sub-eigenvector matrix and the first row of * the second sub-eigenvector matrix). * * ZTEMP (workspace) DOUBLE PRECISION array, dimension (N) * * INFO (output) INTEGER * = 0: successful exit. * < 0: if INFO = -i, the i-th argument had an illegal value. * * Further Details * =============== * * Based on contributions by * Jeff Rutter, Computer Science Division, University of California * at Berkeley, USA * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, HALF, ONE PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER BSIZ1, BSIZ2, CURR, I, K, MID, PSIZ1, PSIZ2, $ PTR, ZPTR1 * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMV, DROT, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, INT, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( N.LT.0 ) THEN INFO = -1 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAEDA', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Determine location of first number in second half. * MID = N / 2 + 1 * * Gather last/first rows of appropriate eigenblocks into center of Z * PTR = 1 * * Determine location of lowest level subproblem in the full storage * scheme * CURR = PTR + CURPBM*2**CURLVL + 2**( CURLVL-1 ) - 1 * * Determine size of these matrices. We add HALF to the value of * the SQRT in case the machine underestimates one of these square * roots. * BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) ) BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+1 ) ) ) ) DO 10 K = 1, MID - BSIZ1 - 1 Z( K ) = ZERO 10 CONTINUE CALL DCOPY( BSIZ1, Q( QPTR( CURR )+BSIZ1-1 ), BSIZ1, $ Z( MID-BSIZ1 ), 1 ) CALL DCOPY( BSIZ2, Q( QPTR( CURR+1 ) ), BSIZ2, Z( MID ), 1 ) DO 20 K = MID + BSIZ2, N Z( K ) = ZERO 20 CONTINUE * * Loop through remaining levels 1 -> CURLVL applying the Givens * rotations and permutation and then multiplying the center matrices * against the current Z. * PTR = 2**TLVLS + 1 DO 70 K = 1, CURLVL - 1 CURR = PTR + CURPBM*2**( CURLVL-K ) + 2**( CURLVL-K-1 ) - 1 PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR ) PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 ) ZPTR1 = MID - PSIZ1 * * Apply Givens at CURR and CURR+1 * DO 30 I = GIVPTR( CURR ), GIVPTR( CURR+1 ) - 1 CALL DROT( 1, Z( ZPTR1+GIVCOL( 1, I )-1 ), 1, $ Z( ZPTR1+GIVCOL( 2, I )-1 ), 1, GIVNUM( 1, I ), $ GIVNUM( 2, I ) ) 30 CONTINUE DO 40 I = GIVPTR( CURR+1 ), GIVPTR( CURR+2 ) - 1 CALL DROT( 1, Z( MID-1+GIVCOL( 1, I ) ), 1, $ Z( MID-1+GIVCOL( 2, I ) ), 1, GIVNUM( 1, I ), $ GIVNUM( 2, I ) ) 40 CONTINUE PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR ) PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 ) DO 50 I = 0, PSIZ1 - 1 ZTEMP( I+1 ) = Z( ZPTR1+PERM( PRMPTR( CURR )+I )-1 ) 50 CONTINUE DO 60 I = 0, PSIZ2 - 1 ZTEMP( PSIZ1+I+1 ) = Z( MID+PERM( PRMPTR( CURR+1 )+I )-1 ) 60 CONTINUE * * Multiply Blocks at CURR and CURR+1 * * Determine size of these matrices. We add HALF to the value of * the SQRT in case the machine underestimates one of these * square roots. * BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) ) BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+ $ 1 ) ) ) ) IF( BSIZ1.GT.0 ) THEN CALL DGEMV( 'T', BSIZ1, BSIZ1, ONE, Q( QPTR( CURR ) ), $ BSIZ1, ZTEMP( 1 ), 1, ZERO, Z( ZPTR1 ), 1 ) END IF CALL DCOPY( PSIZ1-BSIZ1, ZTEMP( BSIZ1+1 ), 1, Z( ZPTR1+BSIZ1 ), $ 1 ) IF( BSIZ2.GT.0 ) THEN CALL DGEMV( 'T', BSIZ2, BSIZ2, ONE, Q( QPTR( CURR+1 ) ), $ BSIZ2, ZTEMP( PSIZ1+1 ), 1, ZERO, Z( MID ), 1 ) END IF CALL DCOPY( PSIZ2-BSIZ2, ZTEMP( PSIZ1+BSIZ2+1 ), 1, $ Z( MID+BSIZ2 ), 1 ) * PTR = PTR + 2**( TLVLS-K ) 70 CONTINUE * RETURN * * End of DLAEDA * END