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