SUBROUTINE SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
$ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER CURLVL, CURPBM, INFO, N, TLVLS
* ..
* .. Array Arguments ..
INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ),
$ PRMPTR( * ), QPTR( * )
REAL GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )
* ..
*
* Purpose
* =======
*
* SLAEDA 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) REAL array, dimension (2, N lg N)
* Each number indicates the S value to be used in the
* corresponding Givens rotation.
*
* Q (input) REAL 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) REAL 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) REAL 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 ..
REAL ZERO, HALF, ONE
PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER BSIZ1, BSIZ2, CURR, I, K, MID, PSIZ1, PSIZ2,
$ PTR, ZPTR1
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SGEMV, SROT, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC INT, REAL, 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( 'SLAEDA', -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( REAL( QPTR( CURR+1 )-QPTR( CURR ) ) ) )
BSIZ2 = INT( HALF+SQRT( REAL( QPTR( CURR+2 )-QPTR( CURR+1 ) ) ) )
DO 10 K = 1, MID - BSIZ1 - 1
Z( K ) = ZERO
10 CONTINUE
CALL SCOPY( BSIZ1, Q( QPTR( CURR )+BSIZ1-1 ), BSIZ1,
$ Z( MID-BSIZ1 ), 1 )
CALL SCOPY( BSIZ2, Q( QPTR( CURR+1 ) ), BSIZ2, Z( MID ), 1 )
DO 20 K = MID + BSIZ2, N
Z( K ) = ZERO
20 CONTINUE
*
* Loop thru 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 SROT( 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 SROT( 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( REAL( QPTR( CURR+1 )-QPTR( CURR ) ) ) )
BSIZ2 = INT( HALF+SQRT( REAL( QPTR( CURR+2 )-QPTR( CURR+
$ 1 ) ) ) )
IF( BSIZ1.GT.0 ) THEN
CALL SGEMV( 'T', BSIZ1, BSIZ1, ONE, Q( QPTR( CURR ) ),
$ BSIZ1, ZTEMP( 1 ), 1, ZERO, Z( ZPTR1 ), 1 )
END IF
CALL SCOPY( PSIZ1-BSIZ1, ZTEMP( BSIZ1+1 ), 1, Z( ZPTR1+BSIZ1 ),
$ 1 )
IF( BSIZ2.GT.0 ) THEN
CALL SGEMV( 'T', BSIZ2, BSIZ2, ONE, Q( QPTR( CURR+1 ) ),
$ BSIZ2, ZTEMP( PSIZ1+1 ), 1, ZERO, Z( MID ), 1 )
END IF
CALL SCOPY( PSIZ2-BSIZ2, ZTEMP( PSIZ1+BSIZ2+1 ), 1,
$ Z( MID+BSIZ2 ), 1 )
*
PTR = PTR + 2**( TLVLS-K )
70 CONTINUE
*
RETURN
*
* End of SLAEDA
*
END