Annotation of rpl/lapack/lapack/zlamswlq.f, revision 1.1
1.1 ! bertrand 1: *
! 2: * Definition:
! 3: * ===========
! 4: *
! 5: * SUBROUTINE ZLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
! 6: * $ LDT, C, LDC, WORK, LWORK, INFO )
! 7: *
! 8: *
! 9: * .. Scalar Arguments ..
! 10: * CHARACTER SIDE, TRANS
! 11: * INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
! 12: * ..
! 13: * .. Array Arguments ..
! 14: * COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ),
! 15: * $ T( LDT, * )
! 16: *> \par Purpose:
! 17: * =============
! 18: *>
! 19: *> \verbatim
! 20: *>
! 21: *> ZLAMQRTS overwrites the general real M-by-N matrix C with
! 22: *>
! 23: *>
! 24: *> SIDE = 'L' SIDE = 'R'
! 25: *> TRANS = 'N': Q * C C * Q
! 26: *> TRANS = 'T': Q**T * C C * Q**T
! 27: *> where Q is a real orthogonal matrix defined as the product of blocked
! 28: *> elementary reflectors computed by short wide LQ
! 29: *> factorization (ZLASWLQ)
! 30: *> \endverbatim
! 31: *
! 32: * Arguments:
! 33: * ==========
! 34: *
! 35: *> \param[in] SIDE
! 36: *> \verbatim
! 37: *> SIDE is CHARACTER*1
! 38: *> = 'L': apply Q or Q**T from the Left;
! 39: *> = 'R': apply Q or Q**T from the Right.
! 40: *> \endverbatim
! 41: *>
! 42: *> \param[in] TRANS
! 43: *> \verbatim
! 44: *> TRANS is CHARACTER*1
! 45: *> = 'N': No transpose, apply Q;
! 46: *> = 'T': Transpose, apply Q**T.
! 47: *> \endverbatim
! 48: *>
! 49: *> \param[in] M
! 50: *> \verbatim
! 51: *> M is INTEGER
! 52: *> The number of rows of the matrix A. M >=0.
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] N
! 56: *> \verbatim
! 57: *> N is INTEGER
! 58: *> The number of columns of the matrix C. N >= M.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] K
! 62: *> \verbatim
! 63: *> K is INTEGER
! 64: *> The number of elementary reflectors whose product defines
! 65: *> the matrix Q.
! 66: *> M >= K >= 0;
! 67: *>
! 68: *> \endverbatim
! 69: *> \param[in] MB
! 70: *> \verbatim
! 71: *> MB is INTEGER
! 72: *> The row block size to be used in the blocked QR.
! 73: *> M >= MB >= 1
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] NB
! 77: *> \verbatim
! 78: *> NB is INTEGER
! 79: *> The column block size to be used in the blocked QR.
! 80: *> NB > M.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] NB
! 84: *> \verbatim
! 85: *> NB is INTEGER
! 86: *> The block size to be used in the blocked QR.
! 87: *> MB > M.
! 88: *>
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[in,out] A
! 92: *> \verbatim
! 93: *> A is COMPLEX*16 array, dimension (LDA,K)
! 94: *> The i-th row must contain the vector which defines the blocked
! 95: *> elementary reflector H(i), for i = 1,2,...,k, as returned by
! 96: *> DLASWLQ in the first k rows of its array argument A.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] LDA
! 100: *> \verbatim
! 101: *> LDA is INTEGER
! 102: *> The leading dimension of the array A.
! 103: *> If SIDE = 'L', LDA >= max(1,M);
! 104: *> if SIDE = 'R', LDA >= max(1,N).
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[in] T
! 108: *> \verbatim
! 109: *> T is COMPLEX*16 array, dimension
! 110: *> ( M * Number of blocks(CEIL(N-K/NB-K)),
! 111: *> The blocked upper triangular block reflectors stored in compact form
! 112: *> as a sequence of upper triangular blocks. See below
! 113: *> for further details.
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[in] LDT
! 117: *> \verbatim
! 118: *> LDT is INTEGER
! 119: *> The leading dimension of the array T. LDT >= MB.
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[in,out] C
! 123: *> \verbatim
! 124: *> C is COMPLEX*16 array, dimension (LDC,N)
! 125: *> On entry, the M-by-N matrix C.
! 126: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in] LDC
! 130: *> \verbatim
! 131: *> LDC is INTEGER
! 132: *> The leading dimension of the array C. LDC >= max(1,M).
! 133: *> \endverbatim
! 134: *>
! 135: *> \param[out] WORK
! 136: *> \verbatim
! 137: *> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 138: *> \endverbatim
! 139: *>
! 140: *> \param[in] LWORK
! 141: *> \verbatim
! 142: *> LWORK is INTEGER
! 143: *> The dimension of the array WORK.
! 144: *> If SIDE = 'L', LWORK >= max(1,NB) * MB;
! 145: *> if SIDE = 'R', LWORK >= max(1,M) * MB.
! 146: *> If LWORK = -1, then a workspace query is assumed; the routine
! 147: *> only calculates the optimal size of the WORK array, returns
! 148: *> this value as the first entry of the WORK array, and no error
! 149: *> message related to LWORK is issued by XERBLA.
! 150: *> \endverbatim
! 151: *>
! 152: *> \param[out] INFO
! 153: *> \verbatim
! 154: *> INFO is INTEGER
! 155: *> = 0: successful exit
! 156: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 157: *> \endverbatim
! 158: *
! 159: * Authors:
! 160: * ========
! 161: *
! 162: *> \author Univ. of Tennessee
! 163: *> \author Univ. of California Berkeley
! 164: *> \author Univ. of Colorado Denver
! 165: *> \author NAG Ltd.
! 166: *
! 167: *> \par Further Details:
! 168: * =====================
! 169: *>
! 170: *> \verbatim
! 171: *> Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
! 172: *> representing Q as a product of other orthogonal matrices
! 173: *> Q = Q(1) * Q(2) * . . . * Q(k)
! 174: *> where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
! 175: *> Q(1) zeros out the upper diagonal entries of rows 1:NB of A
! 176: *> Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
! 177: *> Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
! 178: *> . . .
! 179: *>
! 180: *> Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
! 181: *> stored under the diagonal of rows 1:MB of A, and by upper triangular
! 182: *> block reflectors, stored in array T(1:LDT,1:N).
! 183: *> For more information see Further Details in GELQT.
! 184: *>
! 185: *> Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
! 186: *> stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
! 187: *> block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
! 188: *> The last Q(k) may use fewer rows.
! 189: *> For more information see Further Details in TPQRT.
! 190: *>
! 191: *> For more details of the overall algorithm, see the description of
! 192: *> Sequential TSQR in Section 2.2 of [1].
! 193: *>
! 194: *> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
! 195: *> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
! 196: *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
! 197: *> \endverbatim
! 198: *>
! 199: * =====================================================================
! 200: SUBROUTINE ZLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
! 201: $ LDT, C, LDC, WORK, LWORK, INFO )
! 202: *
! 203: * -- LAPACK computational routine (version 3.7.0) --
! 204: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 205: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 206: * December 2016
! 207: *
! 208: * .. Scalar Arguments ..
! 209: CHARACTER SIDE, TRANS
! 210: INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC, LW
! 211: * ..
! 212: * .. Array Arguments ..
! 213: COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ),
! 214: $ T( LDT, * )
! 215: * ..
! 216: *
! 217: * =====================================================================
! 218: *
! 219: * ..
! 220: * .. Local Scalars ..
! 221: LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
! 222: INTEGER I, II, KK, CTR
! 223: * ..
! 224: * .. External Functions ..
! 225: LOGICAL LSAME
! 226: EXTERNAL LSAME
! 227: * .. External Subroutines ..
! 228: EXTERNAL ZTPMLQT, ZGEMLQT, XERBLA
! 229: * ..
! 230: * .. Executable Statements ..
! 231: *
! 232: * Test the input arguments
! 233: *
! 234: LQUERY = LWORK.LT.0
! 235: NOTRAN = LSAME( TRANS, 'N' )
! 236: TRAN = LSAME( TRANS, 'C' )
! 237: LEFT = LSAME( SIDE, 'L' )
! 238: RIGHT = LSAME( SIDE, 'R' )
! 239: IF (LEFT) THEN
! 240: LW = N * MB
! 241: ELSE
! 242: LW = M * MB
! 243: END IF
! 244: *
! 245: INFO = 0
! 246: IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
! 247: INFO = -1
! 248: ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
! 249: INFO = -2
! 250: ELSE IF( M.LT.0 ) THEN
! 251: INFO = -3
! 252: ELSE IF( N.LT.0 ) THEN
! 253: INFO = -4
! 254: ELSE IF( K.LT.0 ) THEN
! 255: INFO = -5
! 256: ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
! 257: INFO = -9
! 258: ELSE IF( LDT.LT.MAX( 1, MB) ) THEN
! 259: INFO = -11
! 260: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
! 261: INFO = -13
! 262: ELSE IF(( LWORK.LT.MAX(1,LW)).AND.(.NOT.LQUERY)) THEN
! 263: INFO = -15
! 264: END IF
! 265: *
! 266: IF( INFO.NE.0 ) THEN
! 267: CALL XERBLA( 'ZLAMSWLQ', -INFO )
! 268: WORK(1) = LW
! 269: RETURN
! 270: ELSE IF (LQUERY) THEN
! 271: WORK(1) = LW
! 272: RETURN
! 273: END IF
! 274: *
! 275: * Quick return if possible
! 276: *
! 277: IF( MIN(M,N,K).EQ.0 ) THEN
! 278: RETURN
! 279: END IF
! 280: *
! 281: IF((NB.LE.K).OR.(NB.GE.MAX(M,N,K))) THEN
! 282: CALL ZGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA,
! 283: $ T, LDT, C, LDC, WORK, INFO)
! 284: RETURN
! 285: END IF
! 286: *
! 287: IF(LEFT.AND.TRAN) THEN
! 288: *
! 289: * Multiply Q to the last block of C
! 290: *
! 291: KK = MOD((M-K),(NB-K))
! 292: CTR = (M-K)/(NB-K)
! 293: *
! 294: IF (KK.GT.0) THEN
! 295: II=M-KK+1
! 296: CALL ZTPMLQT('L','C',KK , N, K, 0, MB, A(1,II), LDA,
! 297: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
! 298: $ C(II,1), LDC, WORK, INFO )
! 299: ELSE
! 300: II=M+1
! 301: END IF
! 302: *
! 303: DO I=II-(NB-K),NB+1,-(NB-K)
! 304: *
! 305: * Multiply Q to the current block of C (1:M,I:I+NB)
! 306: *
! 307: CTR = CTR - 1
! 308: CALL ZTPMLQT('L','C',NB-K , N, K, 0,MB, A(1,I), LDA,
! 309: $ T(1,CTR*K+1),LDT, C(1,1), LDC,
! 310: $ C(I,1), LDC, WORK, INFO )
! 311:
! 312: END DO
! 313: *
! 314: * Multiply Q to the first block of C (1:M,1:NB)
! 315: *
! 316: CALL ZGEMLQT('L','C',NB , N, K, MB, A(1,1), LDA, T
! 317: $ ,LDT ,C(1,1), LDC, WORK, INFO )
! 318: *
! 319: ELSE IF (LEFT.AND.NOTRAN) THEN
! 320: *
! 321: * Multiply Q to the first block of C
! 322: *
! 323: KK = MOD((M-K),(NB-K))
! 324: II=M-KK+1
! 325: CTR = 1
! 326: CALL ZGEMLQT('L','N',NB , N, K, MB, A(1,1), LDA, T
! 327: $ ,LDT ,C(1,1), LDC, WORK, INFO )
! 328: *
! 329: DO I=NB+1,II-NB+K,(NB-K)
! 330: *
! 331: * Multiply Q to the current block of C (I:I+NB,1:N)
! 332: *
! 333: CALL ZTPMLQT('L','N',NB-K , N, K, 0,MB, A(1,I), LDA,
! 334: $ T(1, CTR * K + 1), LDT, C(1,1), LDC,
! 335: $ C(I,1), LDC, WORK, INFO )
! 336: CTR = CTR + 1
! 337: *
! 338: END DO
! 339: IF(II.LE.M) THEN
! 340: *
! 341: * Multiply Q to the last block of C
! 342: *
! 343: CALL ZTPMLQT('L','N',KK , N, K, 0, MB, A(1,II), LDA,
! 344: $ T(1, CTR * K + 1), LDT, C(1,1), LDC,
! 345: $ C(II,1), LDC, WORK, INFO )
! 346: *
! 347: END IF
! 348: *
! 349: ELSE IF(RIGHT.AND.NOTRAN) THEN
! 350: *
! 351: * Multiply Q to the last block of C
! 352: *
! 353: KK = MOD((N-K),(NB-K))
! 354: CTR = (N-K)/(NB-K)
! 355: IF (KK.GT.0) THEN
! 356: II=N-KK+1
! 357: CALL ZTPMLQT('R','N',M , KK, K, 0, MB, A(1, II), LDA,
! 358: $ T(1, CTR * K + 1), LDT, C(1,1), LDC,
! 359: $ C(1,II), LDC, WORK, INFO )
! 360: ELSE
! 361: II=N+1
! 362: END IF
! 363: *
! 364: DO I=II-(NB-K),NB+1,-(NB-K)
! 365: *
! 366: * Multiply Q to the current block of C (1:M,I:I+MB)
! 367: *
! 368: CTR = CTR - 1
! 369: CALL ZTPMLQT('R','N', M, NB-K, K, 0, MB, A(1, I), LDA,
! 370: $ T(1, CTR * K + 1), LDT, C(1,1), LDC,
! 371: $ C(1,I), LDC, WORK, INFO )
! 372:
! 373: END DO
! 374: *
! 375: * Multiply Q to the first block of C (1:M,1:MB)
! 376: *
! 377: CALL ZGEMLQT('R','N',M , NB, K, MB, A(1,1), LDA, T
! 378: $ ,LDT ,C(1,1), LDC, WORK, INFO )
! 379: *
! 380: ELSE IF (RIGHT.AND.TRAN) THEN
! 381: *
! 382: * Multiply Q to the first block of C
! 383: *
! 384: KK = MOD((N-K),(NB-K))
! 385: II=N-KK+1
! 386: CALL ZGEMLQT('R','C',M , NB, K, MB, A(1,1), LDA, T
! 387: $ ,LDT ,C(1,1), LDC, WORK, INFO )
! 388: CTR = 1
! 389: *
! 390: DO I=NB+1,II-NB+K,(NB-K)
! 391: *
! 392: * Multiply Q to the current block of C (1:M,I:I+MB)
! 393: *
! 394: CALL ZTPMLQT('R','C',M , NB-K, K, 0,MB, A(1,I), LDA,
! 395: $ T(1,CTR *K+1), LDT, C(1,1), LDC,
! 396: $ C(1,I), LDC, WORK, INFO )
! 397: CTR = CTR + 1
! 398: *
! 399: END DO
! 400: IF(II.LE.N) THEN
! 401: *
! 402: * Multiply Q to the last block of C
! 403: *
! 404: CALL ZTPMLQT('R','C',M , KK, K, 0,MB, A(1,II), LDA,
! 405: $ T(1, CTR * K + 1),LDT, C(1,1), LDC,
! 406: $ C(1,II), LDC, WORK, INFO )
! 407: *
! 408: END IF
! 409: *
! 410: END IF
! 411: *
! 412: WORK(1) = LW
! 413: RETURN
! 414: *
! 415: * End of ZLAMSWLQ
! 416: *
! 417: END
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