Annotation of rpl/lapack/lapack/dgelqt.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DGELQT
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGEQRT + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgelqt.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgelqt.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgelqt.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, LDT, M, N, MB
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
! 37: *> using the compact WY representation of Q.
! 38: *> \endverbatim
! 39: *
! 40: * Arguments:
! 41: * ==========
! 42: *
! 43: *> \param[in] M
! 44: *> \verbatim
! 45: *> M is INTEGER
! 46: *> The number of rows of the matrix A. M >= 0.
! 47: *> \endverbatim
! 48: *>
! 49: *> \param[in] N
! 50: *> \verbatim
! 51: *> N is INTEGER
! 52: *> The number of columns of the matrix A. N >= 0.
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] MB
! 56: *> \verbatim
! 57: *> MB is INTEGER
! 58: *> The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in,out] A
! 62: *> \verbatim
! 63: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 64: *> On entry, the M-by-N matrix A.
! 65: *> On exit, the elements on and below the diagonal of the array
! 66: *> contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
! 67: *> lower triangular if M <= N); the elements above the diagonal
! 68: *> are the rows of V.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] LDA
! 72: *> \verbatim
! 73: *> LDA is INTEGER
! 74: *> The leading dimension of the array A. LDA >= max(1,M).
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[out] T
! 78: *> \verbatim
! 79: *> T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
! 80: *> The upper triangular block reflectors stored in compact form
! 81: *> as a sequence of upper triangular blocks. See below
! 82: *> for further details.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] LDT
! 86: *> \verbatim
! 87: *> LDT is INTEGER
! 88: *> The leading dimension of the array T. LDT >= MB.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[out] WORK
! 92: *> \verbatim
! 93: *> WORK is DOUBLE PRECISION array, dimension (MB*N)
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[out] INFO
! 97: *> \verbatim
! 98: *> INFO is INTEGER
! 99: *> = 0: successful exit
! 100: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 101: *> \endverbatim
! 102: *
! 103: * Authors:
! 104: * ========
! 105: *
! 106: *> \author Univ. of Tennessee
! 107: *> \author Univ. of California Berkeley
! 108: *> \author Univ. of Colorado Denver
! 109: *> \author NAG Ltd.
! 110: *
! 111: *> \date December 2016
! 112: *
! 113: *> \ingroup doubleGEcomputational
! 114: *
! 115: *> \par Further Details:
! 116: * =====================
! 117: *>
! 118: *> \verbatim
! 119: *>
! 120: *> The matrix V stores the elementary reflectors H(i) in the i-th column
! 121: *> below the diagonal. For example, if M=5 and N=3, the matrix V is
! 122: *>
! 123: *> V = ( 1 v1 v1 v1 v1 )
! 124: *> ( 1 v2 v2 v2 )
! 125: *> ( 1 v3 v3 )
! 126: *>
! 127: *>
! 128: *> where the vi's represent the vectors which define H(i), which are returned
! 129: *> in the matrix A. The 1's along the diagonal of V are not stored in A.
! 130: *> Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each
! 131: *> block is of order NB except for the last block, which is of order
! 132: *> IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block
! 133: *> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
! 134: *> for the last block) T's are stored in the NB-by-N matrix T as
! 135: *>
! 136: *> T = (T1 T2 ... TB).
! 137: *> \endverbatim
! 138: *>
! 139: * =====================================================================
! 140: SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
! 141: *
! 142: * -- LAPACK computational routine (version 3.7.0) --
! 143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 145: * December 2016
! 146: *
! 147: * .. Scalar Arguments ..
! 148: INTEGER INFO, LDA, LDT, M, N, MB
! 149: * ..
! 150: * .. Array Arguments ..
! 151: DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
! 152: * ..
! 153: *
! 154: * =====================================================================
! 155: *
! 156: * ..
! 157: * .. Local Scalars ..
! 158: INTEGER I, IB, IINFO, K
! 159: * ..
! 160: * .. External Subroutines ..
! 161: EXTERNAL DGEQRT2, DGEQRT3, DLARFB, XERBLA
! 162: * ..
! 163: * .. Executable Statements ..
! 164: *
! 165: * Test the input arguments
! 166: *
! 167: INFO = 0
! 168: IF( M.LT.0 ) THEN
! 169: INFO = -1
! 170: ELSE IF( N.LT.0 ) THEN
! 171: INFO = -2
! 172: ELSE IF( MB.LT.1 .OR. ( MB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN
! 173: INFO = -3
! 174: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 175: INFO = -5
! 176: ELSE IF( LDT.LT.MB ) THEN
! 177: INFO = -7
! 178: END IF
! 179: IF( INFO.NE.0 ) THEN
! 180: CALL XERBLA( 'DGELQT', -INFO )
! 181: RETURN
! 182: END IF
! 183: *
! 184: * Quick return if possible
! 185: *
! 186: K = MIN( M, N )
! 187: IF( K.EQ.0 ) RETURN
! 188: *
! 189: * Blocked loop of length K
! 190: *
! 191: DO I = 1, K, MB
! 192: IB = MIN( K-I+1, MB )
! 193: *
! 194: * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
! 195: *
! 196: CALL DGELQT3( IB, N-I+1, A(I,I), LDA, T(1,I), LDT, IINFO )
! 197: IF( I+IB.LE.M ) THEN
! 198: *
! 199: * Update by applying H**T to A(I:M,I+IB:N) from the right
! 200: *
! 201: CALL DLARFB( 'R', 'N', 'F', 'R', M-I-IB+1, N-I+1, IB,
! 202: $ A( I, I ), LDA, T( 1, I ), LDT,
! 203: $ A( I+IB, I ), LDA, WORK , M-I-IB+1 )
! 204: END IF
! 205: END DO
! 206: RETURN
! 207: *
! 208: * End of DGELQT
! 209: *
! 210: END
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