Annotation of rpl/lapack/lapack/dlaswlq.f, revision 1.1
1.1 ! bertrand 1: *
! 2: * Definition:
! 3: * ===========
! 4: *
! 5: * SUBROUTINE DLASWLQ( M, N, MB, NB, A, LDA, T, LDT, WORK,
! 6: * LWORK, INFO)
! 7: *
! 8: * .. Scalar Arguments ..
! 9: * INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK
! 10: * ..
! 11: * .. Array Arguments ..
! 12: * DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
! 13: * ..
! 14: *
! 15: *
! 16: *> \par Purpose:
! 17: * =============
! 18: *>
! 19: *> \verbatim
! 20: *>
! 21: *> DLASWLQ computes a blocked Short-Wide LQ factorization of a
! 22: *> M-by-N matrix A, where N >= M:
! 23: *> A = L * Q
! 24: *> \endverbatim
! 25: *
! 26: * Arguments:
! 27: * ==========
! 28: *
! 29: *> \param[in] M
! 30: *> \verbatim
! 31: *> M is INTEGER
! 32: *> The number of rows of the matrix A. M >= 0.
! 33: *> \endverbatim
! 34: *>
! 35: *> \param[in] N
! 36: *> \verbatim
! 37: *> N is INTEGER
! 38: *> The number of columns of the matrix A. N >= M >= 0.
! 39: *> \endverbatim
! 40: *>
! 41: *> \param[in] MB
! 42: *> \verbatim
! 43: *> MB is INTEGER
! 44: *> The row block size to be used in the blocked QR.
! 45: *> M >= MB >= 1
! 46: *> \endverbatim
! 47: *> \param[in] NB
! 48: *> \verbatim
! 49: *> NB is INTEGER
! 50: *> The column block size to be used in the blocked QR.
! 51: *> NB > M.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in,out] A
! 55: *> \verbatim
! 56: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 57: *> On entry, the M-by-N matrix A.
! 58: *> On exit, the elements on and bleow the diagonal
! 59: *> of the array contain the N-by-N lower triangular matrix L;
! 60: *> the elements above the diagonal represent Q by the rows
! 61: *> of blocked V (see Further Details).
! 62: *>
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] LDA
! 66: *> \verbatim
! 67: *> LDA is INTEGER
! 68: *> The leading dimension of the array A. LDA >= max(1,M).
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[out] T
! 72: *> \verbatim
! 73: *> T is DOUBLE PRECISION array,
! 74: *> dimension (LDT, N * Number_of_row_blocks)
! 75: *> where Number_of_row_blocks = CEIL((N-M)/(NB-M))
! 76: *> The blocked upper triangular block reflectors stored in compact form
! 77: *> as a sequence of upper triangular blocks.
! 78: *> See Further Details below.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] LDT
! 82: *> \verbatim
! 83: *> LDT is INTEGER
! 84: *> The leading dimension of the array T. LDT >= MB.
! 85: *> \endverbatim
! 86: *>
! 87: *>
! 88: *> \param[out] WORK
! 89: *> \verbatim
! 90: *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 91: *>
! 92: *> \endverbatim
! 93: *> \param[in] LWORK
! 94: *> \verbatim
! 95: *> The dimension of the array WORK. LWORK >= MB*M.
! 96: *> If LWORK = -1, then a workspace query is assumed; the routine
! 97: *> only calculates the optimal size of the WORK array, returns
! 98: *> this value as the first entry of the WORK array, and no error
! 99: *> message related to LWORK is issued by XERBLA.
! 100: *>
! 101: *> \endverbatim
! 102: *> \param[out] INFO
! 103: *> \verbatim
! 104: *> INFO is INTEGER
! 105: *> = 0: successful exit
! 106: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 107: *> \endverbatim
! 108: *
! 109: * Authors:
! 110: * ========
! 111: *
! 112: *> \author Univ. of Tennessee
! 113: *> \author Univ. of California Berkeley
! 114: *> \author Univ. of Colorado Denver
! 115: *> \author NAG Ltd.
! 116: *
! 117: *> \par Further Details:
! 118: * =====================
! 119: *>
! 120: *> \verbatim
! 121: *> Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
! 122: *> representing Q as a product of other orthogonal matrices
! 123: *> Q = Q(1) * Q(2) * . . . * Q(k)
! 124: *> where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
! 125: *> Q(1) zeros out the upper diagonal entries of rows 1:NB of A
! 126: *> Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
! 127: *> Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
! 128: *> . . .
! 129: *>
! 130: *> Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
! 131: *> stored under the diagonal of rows 1:MB of A, and by upper triangular
! 132: *> block reflectors, stored in array T(1:LDT,1:N).
! 133: *> For more information see Further Details in GELQT.
! 134: *>
! 135: *> Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
! 136: *> stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
! 137: *> block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
! 138: *> The last Q(k) may use fewer rows.
! 139: *> For more information see Further Details in TPQRT.
! 140: *>
! 141: *> For more details of the overall algorithm, see the description of
! 142: *> Sequential TSQR in Section 2.2 of [1].
! 143: *>
! 144: *> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
! 145: *> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
! 146: *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
! 147: *> \endverbatim
! 148: *>
! 149: * =====================================================================
! 150: SUBROUTINE DLASWLQ( M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK,
! 151: $ INFO)
! 152: *
! 153: * -- LAPACK computational routine (version 3.7.0) --
! 154: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 155: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
! 156: * December 2016
! 157: *
! 158: * .. Scalar Arguments ..
! 159: INTEGER INFO, LDA, M, N, MB, NB, LWORK, LDT
! 160: * ..
! 161: * .. Array Arguments ..
! 162: DOUBLE PRECISION A( LDA, * ), WORK( * ), T( LDT, *)
! 163: * ..
! 164: *
! 165: * =====================================================================
! 166: *
! 167: * ..
! 168: * .. Local Scalars ..
! 169: LOGICAL LQUERY
! 170: INTEGER I, II, KK, CTR
! 171: * ..
! 172: * .. EXTERNAL FUNCTIONS ..
! 173: LOGICAL LSAME
! 174: EXTERNAL LSAME
! 175: * .. EXTERNAL SUBROUTINES ..
! 176: EXTERNAL DGELQT, DTPLQT, XERBLA
! 177: * .. INTRINSIC FUNCTIONS ..
! 178: INTRINSIC MAX, MIN, MOD
! 179: * ..
! 180: * .. EXECUTABLE STATEMENTS ..
! 181: *
! 182: * TEST THE INPUT ARGUMENTS
! 183: *
! 184: INFO = 0
! 185: *
! 186: LQUERY = ( LWORK.EQ.-1 )
! 187: *
! 188: IF( M.LT.0 ) THEN
! 189: INFO = -1
! 190: ELSE IF( N.LT.0 .OR. N.LT.M ) THEN
! 191: INFO = -2
! 192: ELSE IF( MB.LT.1 .OR. ( MB.GT.M .AND. M.GT.0 )) THEN
! 193: INFO = -3
! 194: ELSE IF( NB.LE.M ) THEN
! 195: INFO = -4
! 196: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 197: INFO = -5
! 198: ELSE IF( LDT.LT.MB ) THEN
! 199: INFO = -8
! 200: ELSE IF( ( LWORK.LT.M*MB) .AND. (.NOT.LQUERY) ) THEN
! 201: INFO = -10
! 202: END IF
! 203: IF( INFO.EQ.0) THEN
! 204: WORK(1) = MB*M
! 205: END IF
! 206: *
! 207: IF( INFO.NE.0 ) THEN
! 208: CALL XERBLA( 'DLASWLQ', -INFO )
! 209: RETURN
! 210: ELSE IF (LQUERY) THEN
! 211: RETURN
! 212: END IF
! 213: *
! 214: * Quick return if possible
! 215: *
! 216: IF( MIN(M,N).EQ.0 ) THEN
! 217: RETURN
! 218: END IF
! 219: *
! 220: * The LQ Decomposition
! 221: *
! 222: IF((M.GE.N).OR.(NB.LE.M).OR.(NB.GE.N)) THEN
! 223: CALL DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO)
! 224: RETURN
! 225: END IF
! 226: *
! 227: KK = MOD((N-M),(NB-M))
! 228: II=N-KK+1
! 229: *
! 230: * Compute the LQ factorization of the first block A(1:M,1:NB)
! 231: *
! 232: CALL DGELQT( M, NB, MB, A(1,1), LDA, T, LDT, WORK, INFO)
! 233: CTR = 1
! 234: *
! 235: DO I = NB+1, II-NB+M , (NB-M)
! 236: *
! 237: * Compute the QR factorization of the current block A(1:M,I:I+NB-M)
! 238: *
! 239: CALL DTPLQT( M, NB-M, 0, MB, A(1,1), LDA, A( 1, I ),
! 240: $ LDA, T(1, CTR * M + 1),
! 241: $ LDT, WORK, INFO )
! 242: CTR = CTR + 1
! 243: END DO
! 244: *
! 245: * Compute the QR factorization of the last block A(1:M,II:N)
! 246: *
! 247: IF (II.LE.N) THEN
! 248: CALL DTPLQT( M, KK, 0, MB, A(1,1), LDA, A( 1, II ),
! 249: $ LDA, T(1, CTR * M + 1), LDT,
! 250: $ WORK, INFO )
! 251: END IF
! 252: *
! 253: WORK( 1 ) = M * MB
! 254: RETURN
! 255: *
! 256: * End of DLASWLQ
! 257: *
! 258: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dlaswlq.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack