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