*> \brief \b DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAEDA + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, * GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) * * .. Scalar Arguments .. * INTEGER CURLVL, CURPBM, INFO, N, TLVLS * .. * .. Array Arguments .. * INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), * \$ PRMPTR( * ), QPTR( * ) * DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in] TLVLS *> \verbatim *> TLVLS is INTEGER *> The total number of merging levels in the overall divide and *> conquer tree. *> \endverbatim *> *> \param[in] CURLVL *> \verbatim *> CURLVL is INTEGER *> The current level in the overall merge routine, *> 0 <= curlvl <= tlvls. *> \endverbatim *> *> \param[in] CURPBM *> \verbatim *> CURPBM is INTEGER *> The current problem in the current level in the overall *> merge routine (counting from upper left to lower right). *> \endverbatim *> *> \param[in] PRMPTR *> \verbatim *> PRMPTR is 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. *> \endverbatim *> *> \param[in] PERM *> \verbatim *> PERM is INTEGER array, dimension (N lg N) *> Contains the permutations (from deflation and sorting) to be *> applied to each eigenblock. *> \endverbatim *> *> \param[in] GIVPTR *> \verbatim *> GIVPTR is 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. *> \endverbatim *> *> \param[in] GIVCOL *> \verbatim *> GIVCOL is INTEGER array, dimension (2, N lg N) *> Each pair of numbers indicates a pair of columns to take place *> in a Givens rotation. *> \endverbatim *> *> \param[in] GIVNUM *> \verbatim *> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) *> Each number indicates the S value to be used in the *> corresponding Givens rotation. *> \endverbatim *> *> \param[in] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (N**2) *> Contains the square eigenblocks from previous levels, the *> starting positions for blocks are given by QPTR. *> \endverbatim *> *> \param[in] QPTR *> \verbatim *> QPTR is 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. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is 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). *> \endverbatim *> *> \param[out] ZTEMP *> \verbatim *> ZTEMP is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA * * ===================================================================== SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, \$ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER CURLVL, CURPBM, INFO, N, TLVLS * .. * .. Array Arguments .. INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), \$ PRMPTR( * ), QPTR( * ) DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) * .. * * ===================================================================== * * .. 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