Annotation of rpl/lapack/lapack/dgemqrt.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DGEMQRT
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGEMQRT + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgemqrt.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgemqrt.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgemqrt.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
! 22: * C, LDC, WORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER SIDE, TRANS
! 26: * INTEGER INFO, K, LDV, LDC, M, N, NB, LDT
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DGEMQRT overwrites the general real M-by-N matrix C with
! 39: *>
! 40: *> SIDE = 'L' SIDE = 'R'
! 41: *> TRANS = 'N': Q C C Q
! 42: *> TRANS = 'T': Q**T C C Q**T
! 43: *>
! 44: *> where Q is a real orthogonal matrix defined as the product of K
! 45: *> elementary reflectors:
! 46: *>
! 47: *> Q = H(1) H(2) . . . H(K) = I - V T V**T
! 48: *>
! 49: *> generated using the compact WY representation as returned by DGEQRT.
! 50: *>
! 51: *> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
! 52: *> \endverbatim
! 53: *
! 54: * Arguments:
! 55: * ==========
! 56: *
! 57: *> \param[in] SIDE
! 58: *> \verbatim
! 59: *> SIDE is CHARACTER*1
! 60: *> = 'L': apply Q or Q**T from the Left;
! 61: *> = 'R': apply Q or Q**T from the Right.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] TRANS
! 65: *> \verbatim
! 66: *> TRANS is CHARACTER*1
! 67: *> = 'N': No transpose, apply Q;
! 68: *> = 'C': Transpose, apply Q**T.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] M
! 72: *> \verbatim
! 73: *> M is INTEGER
! 74: *> The number of rows of the matrix C. M >= 0.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] N
! 78: *> \verbatim
! 79: *> N is INTEGER
! 80: *> The number of columns of the matrix C. N >= 0.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] K
! 84: *> \verbatim
! 85: *> K is INTEGER
! 86: *> The number of elementary reflectors whose product defines
! 87: *> the matrix Q.
! 88: *> If SIDE = 'L', M >= K >= 0;
! 89: *> if SIDE = 'R', N >= K >= 0.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] NB
! 93: *> \verbatim
! 94: *> NB is INTEGER
! 95: *> The block size used for the storage of T. K >= NB >= 1.
! 96: *> This must be the same value of NB used to generate T
! 97: *> in CGEQRT.
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[in] V
! 101: *> \verbatim
! 102: *> V is DOUBLE PRECISION array, dimension (LDV,K)
! 103: *> The i-th column must contain the vector which defines the
! 104: *> elementary reflector H(i), for i = 1,2,...,k, as returned by
! 105: *> CGEQRT in the first K columns of its array argument A.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in] LDV
! 109: *> \verbatim
! 110: *> LDV is INTEGER
! 111: *> The leading dimension of the array V.
! 112: *> If SIDE = 'L', LDA >= max(1,M);
! 113: *> if SIDE = 'R', LDA >= max(1,N).
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[in] T
! 117: *> \verbatim
! 118: *> T is DOUBLE PRECISION array, dimension (LDT,K)
! 119: *> The upper triangular factors of the block reflectors
! 120: *> as returned by CGEQRT, stored as a NB-by-N matrix.
! 121: *> \endverbatim
! 122: *>
! 123: *> \param[in] LDT
! 124: *> \verbatim
! 125: *> LDT is INTEGER
! 126: *> The leading dimension of the array T. LDT >= NB.
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in,out] C
! 130: *> \verbatim
! 131: *> C is DOUBLE PRECISION array, dimension (LDC,N)
! 132: *> On entry, the M-by-N matrix C.
! 133: *> On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[in] LDC
! 137: *> \verbatim
! 138: *> LDC is INTEGER
! 139: *> The leading dimension of the array C. LDC >= max(1,M).
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[out] WORK
! 143: *> \verbatim
! 144: *> WORK is DOUBLE PRECISION array. The dimension of
! 145: *> WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
! 146: *> \endverbatim
! 147: *>
! 148: *> \param[out] INFO
! 149: *> \verbatim
! 150: *> INFO is INTEGER
! 151: *> = 0: successful exit
! 152: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 153: *> \endverbatim
! 154: *
! 155: * Authors:
! 156: * ========
! 157: *
! 158: *> \author Univ. of Tennessee
! 159: *> \author Univ. of California Berkeley
! 160: *> \author Univ. of Colorado Denver
! 161: *> \author NAG Ltd.
! 162: *
! 163: *> \date November 2011
! 164: *
! 165: *> \ingroup doubleGEcomputational
! 166: *
! 167: * =====================================================================
! 168: SUBROUTINE DGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
! 169: $ C, LDC, WORK, INFO )
! 170: *
! 171: * -- LAPACK computational routine (version 3.4.0) --
! 172: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 173: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 174: * November 2011
! 175: *
! 176: * .. Scalar Arguments ..
! 177: CHARACTER SIDE, TRANS
! 178: INTEGER INFO, K, LDV, LDC, M, N, NB, LDT
! 179: * ..
! 180: * .. Array Arguments ..
! 181: DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
! 182: * ..
! 183: *
! 184: * =====================================================================
! 185: *
! 186: * ..
! 187: * .. Local Scalars ..
! 188: LOGICAL LEFT, RIGHT, TRAN, NOTRAN
! 189: INTEGER I, IB, LDWORK, KF, Q
! 190: * ..
! 191: * .. External Functions ..
! 192: LOGICAL LSAME
! 193: EXTERNAL LSAME
! 194: * ..
! 195: * .. External Subroutines ..
! 196: EXTERNAL XERBLA, DLARFB
! 197: * ..
! 198: * .. Intrinsic Functions ..
! 199: INTRINSIC MAX, MIN
! 200: * ..
! 201: * .. Executable Statements ..
! 202: *
! 203: * .. Test the input arguments ..
! 204: *
! 205: INFO = 0
! 206: LEFT = LSAME( SIDE, 'L' )
! 207: RIGHT = LSAME( SIDE, 'R' )
! 208: TRAN = LSAME( TRANS, 'T' )
! 209: NOTRAN = LSAME( TRANS, 'N' )
! 210: *
! 211: IF( LEFT ) THEN
! 212: LDWORK = MAX( 1, N )
! 213: Q = M
! 214: ELSE IF ( RIGHT ) THEN
! 215: LDWORK = MAX( 1, M )
! 216: Q = N
! 217: END IF
! 218: IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
! 219: INFO = -1
! 220: ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
! 221: INFO = -2
! 222: ELSE IF( M.LT.0 ) THEN
! 223: INFO = -3
! 224: ELSE IF( N.LT.0 ) THEN
! 225: INFO = -4
! 226: ELSE IF( K.LT.0 .OR. K.GT.Q ) THEN
! 227: INFO = -5
! 228: ELSE IF( NB.LT.1 .OR. NB.GT.K ) THEN
! 229: INFO = -6
! 230: ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
! 231: INFO = -8
! 232: ELSE IF( LDT.LT.NB ) THEN
! 233: INFO = -10
! 234: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
! 235: INFO = -12
! 236: END IF
! 237: *
! 238: IF( INFO.NE.0 ) THEN
! 239: CALL XERBLA( 'DGEMQRT', -INFO )
! 240: RETURN
! 241: END IF
! 242: *
! 243: * .. Quick return if possible ..
! 244: *
! 245: IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN
! 246: *
! 247: IF( LEFT .AND. TRAN ) THEN
! 248: *
! 249: DO I = 1, K, NB
! 250: IB = MIN( NB, K-I+1 )
! 251: CALL DLARFB( 'L', 'T', 'F', 'C', M-I+1, N, IB,
! 252: $ V( I, I ), LDV, T( 1, I ), LDT,
! 253: $ C( I, 1 ), LDC, WORK, LDWORK )
! 254: END DO
! 255: *
! 256: ELSE IF( RIGHT .AND. NOTRAN ) THEN
! 257: *
! 258: DO I = 1, K, NB
! 259: IB = MIN( NB, K-I+1 )
! 260: CALL DLARFB( 'R', 'N', 'F', 'C', M, N-I+1, IB,
! 261: $ V( I, I ), LDV, T( 1, I ), LDT,
! 262: $ C( 1, I ), LDC, WORK, LDWORK )
! 263: END DO
! 264: *
! 265: ELSE IF( LEFT .AND. NOTRAN ) THEN
! 266: *
! 267: KF = ((K-1)/NB)*NB+1
! 268: DO I = KF, 1, -NB
! 269: IB = MIN( NB, K-I+1 )
! 270: CALL DLARFB( 'L', 'N', 'F', 'C', M-I+1, N, IB,
! 271: $ V( I, I ), LDV, T( 1, I ), LDT,
! 272: $ C( I, 1 ), LDC, WORK, LDWORK )
! 273: END DO
! 274: *
! 275: ELSE IF( RIGHT .AND. TRAN ) THEN
! 276: *
! 277: KF = ((K-1)/NB)*NB+1
! 278: DO I = KF, 1, -NB
! 279: IB = MIN( NB, K-I+1 )
! 280: CALL DLARFB( 'R', 'T', 'F', 'C', M, N-I+1, IB,
! 281: $ V( I, I ), LDV, T( 1, I ), LDT,
! 282: $ C( 1, I ), LDC, WORK, LDWORK )
! 283: END DO
! 284: *
! 285: END IF
! 286: *
! 287: RETURN
! 288: *
! 289: * End of DGEMQRT
! 290: *
! 291: END
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