Annotation of rpl/lapack/lapack/dsytrd_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DSYTRD_2STAGE
! 2: *
! 3: * @generated from zhetrd_2stage.f, fortran z -> d, Sun Nov 6 19:34:06 2016
! 4: *
! 5: * =========== DOCUMENTATION ===========
! 6: *
! 7: * Online html documentation available at
! 8: * http://www.netlib.org/lapack/explore-html/
! 9: *
! 10: *> \htmlonly
! 11: *> Download DSYTRD_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrd_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrd_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrd_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE DSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
! 24: * HOUS2, LHOUS2, WORK, LWORK, INFO )
! 25: *
! 26: * IMPLICIT NONE
! 27: *
! 28: * .. Scalar Arguments ..
! 29: * CHARACTER VECT, UPLO
! 30: * INTEGER N, LDA, LWORK, LHOUS2, INFO
! 31: * ..
! 32: * .. Array Arguments ..
! 33: * DOUBLE PRECISION D( * ), E( * )
! 34: * DOUBLE PRECISION A( LDA, * ), TAU( * ),
! 35: * HOUS2( * ), WORK( * )
! 36: * ..
! 37: *
! 38: *
! 39: *> \par Purpose:
! 40: * =============
! 41: *>
! 42: *> \verbatim
! 43: *>
! 44: *> DSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric
! 45: *> tridiagonal form T by a orthogonal similarity transformation:
! 46: *> Q1**T Q2**T* A * Q2 * Q1 = T.
! 47: *> \endverbatim
! 48: *
! 49: * Arguments:
! 50: * ==========
! 51: *
! 52: *> \param[in] VECT
! 53: *> \verbatim
! 54: *> VECT is CHARACTER*1
! 55: *> = 'N': No need for the Housholder representation,
! 56: *> in particular for the second stage (Band to
! 57: *> tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
! 58: *> = 'V': the Householder representation is needed to
! 59: *> either generate Q1 Q2 or to apply Q1 Q2,
! 60: *> then LHOUS2 is to be queried and computed.
! 61: *> (NOT AVAILABLE IN THIS RELEASE).
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] UPLO
! 65: *> \verbatim
! 66: *> UPLO is CHARACTER*1
! 67: *> = 'U': Upper triangle of A is stored;
! 68: *> = 'L': Lower triangle of A is stored.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] N
! 72: *> \verbatim
! 73: *> N is INTEGER
! 74: *> The order of the matrix A. N >= 0.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in,out] A
! 78: *> \verbatim
! 79: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 80: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 81: *> N-by-N upper triangular part of A contains the upper
! 82: *> triangular part of the matrix A, and the strictly lower
! 83: *> triangular part of A is not referenced. If UPLO = 'L', the
! 84: *> leading N-by-N lower triangular part of A contains the lower
! 85: *> triangular part of the matrix A, and the strictly upper
! 86: *> triangular part of A is not referenced.
! 87: *> On exit, if UPLO = 'U', the band superdiagonal
! 88: *> of A are overwritten by the corresponding elements of the
! 89: *> internal band-diagonal matrix AB, and the elements above
! 90: *> the KD superdiagonal, with the array TAU, represent the orthogonal
! 91: *> matrix Q1 as a product of elementary reflectors; if UPLO
! 92: *> = 'L', the diagonal and band subdiagonal of A are over-
! 93: *> written by the corresponding elements of the internal band-diagonal
! 94: *> matrix AB, and the elements below the KD subdiagonal, with
! 95: *> the array TAU, represent the orthogonal matrix Q1 as a product
! 96: *> of elementary reflectors. See Further Details.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] LDA
! 100: *> \verbatim
! 101: *> LDA is INTEGER
! 102: *> The leading dimension of the array A. LDA >= max(1,N).
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[out] D
! 106: *> \verbatim
! 107: *> D is DOUBLE PRECISION array, dimension (N)
! 108: *> The diagonal elements of the tridiagonal matrix T.
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[out] E
! 112: *> \verbatim
! 113: *> E is DOUBLE PRECISION array, dimension (N-1)
! 114: *> The off-diagonal elements of the tridiagonal matrix T.
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[out] TAU
! 118: *> \verbatim
! 119: *> TAU is DOUBLE PRECISION array, dimension (N-KD)
! 120: *> The scalar factors of the elementary reflectors of
! 121: *> the first stage (see Further Details).
! 122: *> \endverbatim
! 123: *>
! 124: *> \param[out] HOUS2
! 125: *> \verbatim
! 126: *> HOUS2 is DOUBLE PRECISION array, dimension LHOUS2, that
! 127: *> store the Householder representation of the stage2
! 128: *> band to tridiagonal.
! 129: *> \endverbatim
! 130: *>
! 131: *> \param[in] LHOUS2
! 132: *> \verbatim
! 133: *> LHOUS2 is INTEGER
! 134: *> The dimension of the array HOUS2. LHOUS2 = MAX(1, dimension)
! 135: *> If LWORK = -1, or LHOUS2=-1,
! 136: *> then a query is assumed; the routine
! 137: *> only calculates the optimal size of the HOUS2 array, returns
! 138: *> this value as the first entry of the HOUS2 array, and no error
! 139: *> message related to LHOUS2 is issued by XERBLA.
! 140: *> LHOUS2 = MAX(1, dimension) where
! 141: *> dimension = 4*N if VECT='N'
! 142: *> not available now if VECT='H'
! 143: *> \endverbatim
! 144: *>
! 145: *> \param[out] WORK
! 146: *> \verbatim
! 147: *> WORK is DOUBLE PRECISION array, dimension LWORK.
! 148: *> \endverbatim
! 149: *>
! 150: *> \param[in] LWORK
! 151: *> \verbatim
! 152: *> LWORK is INTEGER
! 153: *> The dimension of the array WORK. LWORK = MAX(1, dimension)
! 154: *> If LWORK = -1, or LHOUS2=-1,
! 155: *> then a workspace query is assumed; the routine
! 156: *> only calculates the optimal size of the WORK array, returns
! 157: *> this value as the first entry of the WORK array, and no error
! 158: *> message related to LWORK is issued by XERBLA.
! 159: *> LWORK = MAX(1, dimension) where
! 160: *> dimension = max(stage1,stage2) + (KD+1)*N
! 161: *> = N*KD + N*max(KD+1,FACTOPTNB)
! 162: *> + max(2*KD*KD, KD*NTHREADS)
! 163: *> + (KD+1)*N
! 164: *> where KD is the blocking size of the reduction,
! 165: *> FACTOPTNB is the blocking used by the QR or LQ
! 166: *> algorithm, usually FACTOPTNB=128 is a good choice
! 167: *> NTHREADS is the number of threads used when
! 168: *> openMP compilation is enabled, otherwise =1.
! 169: *> \endverbatim
! 170: *>
! 171: *> \param[out] INFO
! 172: *> \verbatim
! 173: *> INFO is INTEGER
! 174: *> = 0: successful exit
! 175: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 176: *> \endverbatim
! 177: *
! 178: * Authors:
! 179: * ========
! 180: *
! 181: *> \author Univ. of Tennessee
! 182: *> \author Univ. of California Berkeley
! 183: *> \author Univ. of Colorado Denver
! 184: *> \author NAG Ltd.
! 185: *
! 186: *> \date December 2016
! 187: *
! 188: *> \ingroup doubleSYcomputational
! 189: *
! 190: *> \par Further Details:
! 191: * =====================
! 192: *>
! 193: *> \verbatim
! 194: *>
! 195: *> Implemented by Azzam Haidar.
! 196: *>
! 197: *> All details are available on technical report, SC11, SC13 papers.
! 198: *>
! 199: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 200: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 201: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 202: *> of 2011 International Conference for High Performance Computing,
! 203: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 204: *> Article 8 , 11 pages.
! 205: *> http://doi.acm.org/10.1145/2063384.2063394
! 206: *>
! 207: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 208: *> An improved parallel singular value algorithm and its implementation
! 209: *> for multicore hardware, In Proceedings of 2013 International Conference
! 210: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 211: *> Denver, Colorado, USA, 2013.
! 212: *> Article 90, 12 pages.
! 213: *> http://doi.acm.org/10.1145/2503210.2503292
! 214: *>
! 215: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 216: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 217: *> calculations based on fine-grained memory aware tasks.
! 218: *> International Journal of High Performance Computing Applications.
! 219: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 220: *> http://hpc.sagepub.com/content/28/2/196
! 221: *>
! 222: *> \endverbatim
! 223: *>
! 224: * =====================================================================
! 225: SUBROUTINE DSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
! 226: $ HOUS2, LHOUS2, WORK, LWORK, INFO )
! 227: *
! 228: IMPLICIT NONE
! 229: *
! 230: * -- LAPACK computational routine (version 3.7.0) --
! 231: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 232: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 233: * December 2016
! 234: *
! 235: * .. Scalar Arguments ..
! 236: CHARACTER VECT, UPLO
! 237: INTEGER N, LDA, LWORK, LHOUS2, INFO
! 238: * ..
! 239: * .. Array Arguments ..
! 240: DOUBLE PRECISION D( * ), E( * )
! 241: DOUBLE PRECISION A( LDA, * ), TAU( * ),
! 242: $ HOUS2( * ), WORK( * )
! 243: * ..
! 244: *
! 245: * =====================================================================
! 246: * ..
! 247: * .. Local Scalars ..
! 248: LOGICAL LQUERY, UPPER, WANTQ
! 249: INTEGER KD, IB, LWMIN, LHMIN, LWRK, LDAB, WPOS, ABPOS
! 250: * ..
! 251: * .. External Subroutines ..
! 252: EXTERNAL XERBLA, DSYTRD_SY2SB, DSYTRD_SB2ST
! 253: * ..
! 254: * .. External Functions ..
! 255: LOGICAL LSAME
! 256: INTEGER ILAENV
! 257: EXTERNAL LSAME, ILAENV
! 258: * ..
! 259: * .. Executable Statements ..
! 260: *
! 261: * Test the input parameters
! 262: *
! 263: INFO = 0
! 264: WANTQ = LSAME( VECT, 'V' )
! 265: UPPER = LSAME( UPLO, 'U' )
! 266: LQUERY = ( LWORK.EQ.-1 ) .OR. ( LHOUS2.EQ.-1 )
! 267: *
! 268: * Determine the block size, the workspace size and the hous size.
! 269: *
! 270: KD = ILAENV( 17, 'DSYTRD_2STAGE', VECT, N, -1, -1, -1 )
! 271: IB = ILAENV( 18, 'DSYTRD_2STAGE', VECT, N, KD, -1, -1 )
! 272: LHMIN = ILAENV( 19, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
! 273: LWMIN = ILAENV( 20, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
! 274: * WRITE(*,*),'DSYTRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
! 275: * $ LHMIN, LWMIN
! 276: *
! 277: IF( .NOT.LSAME( VECT, 'N' ) ) THEN
! 278: INFO = -1
! 279: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 280: INFO = -2
! 281: ELSE IF( N.LT.0 ) THEN
! 282: INFO = -3
! 283: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 284: INFO = -5
! 285: ELSE IF( LHOUS2.LT.LHMIN .AND. .NOT.LQUERY ) THEN
! 286: INFO = -10
! 287: ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 288: INFO = -12
! 289: END IF
! 290: *
! 291: IF( INFO.EQ.0 ) THEN
! 292: HOUS2( 1 ) = LHMIN
! 293: WORK( 1 ) = LWMIN
! 294: END IF
! 295: *
! 296: IF( INFO.NE.0 ) THEN
! 297: CALL XERBLA( 'DSYTRD_2STAGE', -INFO )
! 298: RETURN
! 299: ELSE IF( LQUERY ) THEN
! 300: RETURN
! 301: END IF
! 302: *
! 303: * Quick return if possible
! 304: *
! 305: IF( N.EQ.0 ) THEN
! 306: WORK( 1 ) = 1
! 307: RETURN
! 308: END IF
! 309: *
! 310: * Determine pointer position
! 311: *
! 312: LDAB = KD+1
! 313: LWRK = LWORK-LDAB*N
! 314: ABPOS = 1
! 315: WPOS = ABPOS + LDAB*N
! 316: CALL DSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
! 317: $ TAU, WORK( WPOS ), LWRK, INFO )
! 318: IF( INFO.NE.0 ) THEN
! 319: CALL XERBLA( 'DSYTRD_SY2SB', -INFO )
! 320: RETURN
! 321: END IF
! 322: CALL DSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD,
! 323: $ WORK( ABPOS ), LDAB, D, E,
! 324: $ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
! 325: IF( INFO.NE.0 ) THEN
! 326: CALL XERBLA( 'DSYTRD_SB2ST', -INFO )
! 327: RETURN
! 328: END IF
! 329: *
! 330: *
! 331: HOUS2( 1 ) = LHMIN
! 332: WORK( 1 ) = LWMIN
! 333: RETURN
! 334: *
! 335: * End of DSYTRD_2STAGE
! 336: *
! 337: END
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