Annotation of rpl/lapack/lapack/dtpmqrt.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DTPMQRT
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DTPMQRT + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpmqrt.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtpmqrt.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtpmqrt.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
! 22: * A, LDA, B, LDB, WORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER SIDE, TRANS
! 26: * INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION V( LDV, * ), A( LDA, * ), B( LDB, * ),
! 30: * $ T( LDT, * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> DTPMQRT applies a real orthogonal matrix Q obtained from a
! 40: *> "triangular-pentagonal" real block reflector H to a general
! 41: *> real matrix C, which consists of two blocks A and B.
! 42: *> \endverbatim
! 43: *
! 44: * Arguments:
! 45: * ==========
! 46: *
! 47: *> \param[in] SIDE
! 48: *> \verbatim
! 49: *> SIDE is CHARACTER*1
! 50: *> = 'L': apply Q or Q**T from the Left;
! 51: *> = 'R': apply Q or Q**T from the Right.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] TRANS
! 55: *> \verbatim
! 56: *> TRANS is CHARACTER*1
! 57: *> = 'N': No transpose, apply Q;
! 58: *> = 'C': Transpose, apply Q**T.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] M
! 62: *> \verbatim
! 63: *> M is INTEGER
! 64: *> The number of rows of the matrix B. M >= 0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] N
! 68: *> \verbatim
! 69: *> N is INTEGER
! 70: *> The number of columns of the matrix B. N >= 0.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] K
! 74: *> \verbatim
! 75: *> K is INTEGER
! 76: *> The number of elementary reflectors whose product defines
! 77: *> the matrix Q.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] L
! 81: *> \verbatim
! 82: *> L is INTEGER
! 83: *> The order of the trapezoidal part of V.
! 84: *> K >= L >= 0. See Further Details.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] NB
! 88: *> \verbatim
! 89: *> NB is INTEGER
! 90: *> The block size used for the storage of T. K >= NB >= 1.
! 91: *> This must be the same value of NB used to generate T
! 92: *> in CTPQRT.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] V
! 96: *> \verbatim
! 97: *> V is DOUBLE PRECISION array, dimension (LDA,K)
! 98: *> The i-th column must contain the vector which defines the
! 99: *> elementary reflector H(i), for i = 1,2,...,k, as returned by
! 100: *> CTPQRT in B. See Further Details.
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] LDV
! 104: *> \verbatim
! 105: *> LDV is INTEGER
! 106: *> The leading dimension of the array V.
! 107: *> If SIDE = 'L', LDV >= max(1,M);
! 108: *> if SIDE = 'R', LDV >= max(1,N).
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in] T
! 112: *> \verbatim
! 113: *> T is DOUBLE PRECISION array, dimension (LDT,K)
! 114: *> The upper triangular factors of the block reflectors
! 115: *> as returned by CTPQRT, stored as a NB-by-K matrix.
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[in] LDT
! 119: *> \verbatim
! 120: *> LDT is INTEGER
! 121: *> The leading dimension of the array T. LDT >= NB.
! 122: *> \endverbatim
! 123: *>
! 124: *> \param[in,out] A
! 125: *> \verbatim
! 126: *> A is DOUBLE PRECISION array, dimension
! 127: *> (LDA,N) if SIDE = 'L' or
! 128: *> (LDA,K) if SIDE = 'R'
! 129: *> On entry, the K-by-N or M-by-K matrix A.
! 130: *> On exit, A is overwritten by the corresponding block of
! 131: *> Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.
! 132: *> \endverbatim
! 133: *>
! 134: *> \param[in] LDA
! 135: *> \verbatim
! 136: *> LDA is INTEGER
! 137: *> The leading dimension of the array A.
! 138: *> If SIDE = 'L', LDC >= max(1,K);
! 139: *> If SIDE = 'R', LDC >= max(1,M).
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in,out] B
! 143: *> \verbatim
! 144: *> B is DOUBLE PRECISION array, dimension (LDB,N)
! 145: *> On entry, the M-by-N matrix B.
! 146: *> On exit, B is overwritten by the corresponding block of
! 147: *> Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.
! 148: *> \endverbatim
! 149: *>
! 150: *> \param[in] LDB
! 151: *> \verbatim
! 152: *> LDB is INTEGER
! 153: *> The leading dimension of the array B.
! 154: *> LDB >= max(1,M).
! 155: *> \endverbatim
! 156: *>
! 157: *> \param[out] WORK
! 158: *> \verbatim
! 159: *> WORK is DOUBLE PRECISION array. The dimension of WORK is
! 160: *> N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
! 161: *> \endverbatim
! 162: *>
! 163: *> \param[out] INFO
! 164: *> \verbatim
! 165: *> INFO is INTEGER
! 166: *> = 0: successful exit
! 167: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 168: *> \endverbatim
! 169: *
! 170: * Authors:
! 171: * ========
! 172: *
! 173: *> \author Univ. of Tennessee
! 174: *> \author Univ. of California Berkeley
! 175: *> \author Univ. of Colorado Denver
! 176: *> \author NAG Ltd.
! 177: *
! 178: *> \date April 2012
! 179: *
! 180: *> \ingroup doubleOTHERcomputational
! 181: *
! 182: *> \par Further Details:
! 183: * =====================
! 184: *>
! 185: *> \verbatim
! 186: *>
! 187: *> The columns of the pentagonal matrix V contain the elementary reflectors
! 188: *> H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
! 189: *> trapezoidal block V2:
! 190: *>
! 191: *> V = [V1]
! 192: *> [V2].
! 193: *>
! 194: *> The size of the trapezoidal block V2 is determined by the parameter L,
! 195: *> where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
! 196: *> rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangular;
! 197: *> if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
! 198: *>
! 199: *> If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K.
! 200: *> [B]
! 201: *>
! 202: *> If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
! 203: *>
! 204: *> The real orthogonal matrix Q is formed from V and T.
! 205: *>
! 206: *> If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
! 207: *>
! 208: *> If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.
! 209: *>
! 210: *> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
! 211: *>
! 212: *> If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.
! 213: *> \endverbatim
! 214: *>
! 215: * =====================================================================
! 216: SUBROUTINE DTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
! 217: $ A, LDA, B, LDB, WORK, INFO )
! 218: *
! 219: * -- LAPACK computational routine (version 3.4.1) --
! 220: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 221: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 222: * April 2012
! 223: *
! 224: * .. Scalar Arguments ..
! 225: CHARACTER SIDE, TRANS
! 226: INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT
! 227: * ..
! 228: * .. Array Arguments ..
! 229: DOUBLE PRECISION V( LDV, * ), A( LDA, * ), B( LDB, * ),
! 230: $ T( LDT, * ), WORK( * )
! 231: * ..
! 232: *
! 233: * =====================================================================
! 234: *
! 235: * ..
! 236: * .. Local Scalars ..
! 237: LOGICAL LEFT, RIGHT, TRAN, NOTRAN
! 238: INTEGER I, IB, MB, LB, KF, Q
! 239: * ..
! 240: * .. External Functions ..
! 241: LOGICAL LSAME
! 242: EXTERNAL LSAME
! 243: * ..
! 244: * .. External Subroutines ..
! 245: EXTERNAL XERBLA, DLARFB
! 246: * ..
! 247: * .. Intrinsic Functions ..
! 248: INTRINSIC MAX, MIN
! 249: * ..
! 250: * .. Executable Statements ..
! 251: *
! 252: * .. Test the input arguments ..
! 253: *
! 254: INFO = 0
! 255: LEFT = LSAME( SIDE, 'L' )
! 256: RIGHT = LSAME( SIDE, 'R' )
! 257: TRAN = LSAME( TRANS, 'T' )
! 258: NOTRAN = LSAME( TRANS, 'N' )
! 259: *
! 260: IF( LEFT ) THEN
! 261: Q = M
! 262: ELSE IF ( RIGHT ) THEN
! 263: Q = N
! 264: END IF
! 265: IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
! 266: INFO = -1
! 267: ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
! 268: INFO = -2
! 269: ELSE IF( M.LT.0 ) THEN
! 270: INFO = -3
! 271: ELSE IF( N.LT.0 ) THEN
! 272: INFO = -4
! 273: ELSE IF( K.LT.0 ) THEN
! 274: INFO = -5
! 275: ELSE IF( L.LT.0 .OR. L.GT.K ) THEN
! 276: INFO = -6
! 277: ELSE IF( NB.LT.1 .OR. NB.GT.K ) THEN
! 278: INFO = -7
! 279: ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
! 280: INFO = -9
! 281: ELSE IF( LDT.LT.NB ) THEN
! 282: INFO = -11
! 283: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 284: INFO = -13
! 285: ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
! 286: INFO = -15
! 287: END IF
! 288: *
! 289: IF( INFO.NE.0 ) THEN
! 290: CALL XERBLA( 'DTPMQRT', -INFO )
! 291: RETURN
! 292: END IF
! 293: *
! 294: * .. Quick return if possible ..
! 295: *
! 296: IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN
! 297: *
! 298: IF( LEFT .AND. TRAN ) THEN
! 299: *
! 300: DO I = 1, K, NB
! 301: IB = MIN( NB, K-I+1 )
! 302: MB = MIN( M-L+I+IB-1, M )
! 303: IF( I.GE.L ) THEN
! 304: LB = 0
! 305: ELSE
! 306: LB = MB-M+L-I+1
! 307: END IF
! 308: CALL DTPRFB( 'L', 'T', 'F', 'C', MB, N, IB, LB,
! 309: $ V( 1, I ), LDV, T( 1, I ), LDT,
! 310: $ A( I, 1 ), LDA, B, LDB, WORK, IB )
! 311: END DO
! 312: *
! 313: ELSE IF( RIGHT .AND. NOTRAN ) THEN
! 314: *
! 315: DO I = 1, K, NB
! 316: IB = MIN( NB, K-I+1 )
! 317: MB = MIN( N-L+I+IB-1, N )
! 318: IF( I.GE.L ) THEN
! 319: LB = 0
! 320: ELSE
! 321: LB = MB-N+L-I+1
! 322: END IF
! 323: CALL DTPRFB( 'R', 'N', 'F', 'C', M, MB, IB, LB,
! 324: $ V( 1, I ), LDV, T( 1, I ), LDT,
! 325: $ A( 1, I ), LDA, B, LDB, WORK, M )
! 326: END DO
! 327: *
! 328: ELSE IF( LEFT .AND. NOTRAN ) THEN
! 329: *
! 330: KF = ((K-1)/NB)*NB+1
! 331: DO I = KF, 1, -NB
! 332: IB = MIN( NB, K-I+1 )
! 333: MB = MIN( M-L+I+IB-1, M )
! 334: IF( I.GE.L ) THEN
! 335: LB = 0
! 336: ELSE
! 337: LB = MB-M+L-I+1
! 338: END IF
! 339: CALL DTPRFB( 'L', 'N', 'F', 'C', MB, N, IB, LB,
! 340: $ V( 1, I ), LDV, T( 1, I ), LDT,
! 341: $ A( I, 1 ), LDA, B, LDB, WORK, IB )
! 342: END DO
! 343: *
! 344: ELSE IF( RIGHT .AND. TRAN ) THEN
! 345: *
! 346: KF = ((K-1)/NB)*NB+1
! 347: DO I = KF, 1, -NB
! 348: IB = MIN( NB, K-I+1 )
! 349: MB = MIN( N-L+I+IB-1, N )
! 350: IF( I.GE.L ) THEN
! 351: LB = 0
! 352: ELSE
! 353: LB = MB-N+L-I+1
! 354: END IF
! 355: CALL DTPRFB( 'R', 'T', 'F', 'C', M, MB, IB, LB,
! 356: $ V( 1, I ), LDV, T( 1, I ), LDT,
! 357: $ A( 1, I ), LDA, B, LDB, WORK, M )
! 358: END DO
! 359: *
! 360: END IF
! 361: *
! 362: RETURN
! 363: *
! 364: * End of DTPMQRT
! 365: *
! 366: END
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