Annotation of rpl/lapack/lapack/dgerq2.f, revision 1.10
1.10 ! bertrand 1: *> \brief \b DGERQ2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGERQ2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgerq2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgerq2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgerq2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DGERQ2 computes an RQ factorization of a real m by n matrix A:
! 37: *> A = R * 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,out] A
! 56: *> \verbatim
! 57: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 58: *> On entry, the m by n matrix A.
! 59: *> On exit, if m <= n, the upper triangle of the subarray
! 60: *> A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
! 61: *> if m >= n, the elements on and above the (m-n)-th subdiagonal
! 62: *> contain the m by n upper trapezoidal matrix R; the remaining
! 63: *> elements, with the array TAU, represent the orthogonal matrix
! 64: *> Q as a product of elementary reflectors (see Further
! 65: *> Details).
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] LDA
! 69: *> \verbatim
! 70: *> LDA is INTEGER
! 71: *> The leading dimension of the array A. LDA >= max(1,M).
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[out] TAU
! 75: *> \verbatim
! 76: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
! 77: *> The scalar factors of the elementary reflectors (see Further
! 78: *> Details).
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[out] WORK
! 82: *> \verbatim
! 83: *> WORK is DOUBLE PRECISION array, dimension (M)
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[out] INFO
! 87: *> \verbatim
! 88: *> INFO is INTEGER
! 89: *> = 0: successful exit
! 90: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 91: *> \endverbatim
! 92: *
! 93: * Authors:
! 94: * ========
! 95: *
! 96: *> \author Univ. of Tennessee
! 97: *> \author Univ. of California Berkeley
! 98: *> \author Univ. of Colorado Denver
! 99: *> \author NAG Ltd.
! 100: *
! 101: *> \date November 2011
! 102: *
! 103: *> \ingroup doubleGEcomputational
! 104: *
! 105: *> \par Further Details:
! 106: * =====================
! 107: *>
! 108: *> \verbatim
! 109: *>
! 110: *> The matrix Q is represented as a product of elementary reflectors
! 111: *>
! 112: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 113: *>
! 114: *> Each H(i) has the form
! 115: *>
! 116: *> H(i) = I - tau * v * v**T
! 117: *>
! 118: *> where tau is a real scalar, and v is a real vector with
! 119: *> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
! 120: *> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
! 121: *> \endverbatim
! 122: *>
! 123: * =====================================================================
1.1 bertrand 124: SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
125: *
1.10 ! bertrand 126: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 127: * -- LAPACK is a software package provided by Univ. of Tennessee, --
128: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 ! bertrand 129: * November 2011
1.1 bertrand 130: *
131: * .. Scalar Arguments ..
132: INTEGER INFO, LDA, M, N
133: * ..
134: * .. Array Arguments ..
135: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
136: * ..
137: *
138: * =====================================================================
139: *
140: * .. Parameters ..
141: DOUBLE PRECISION ONE
142: PARAMETER ( ONE = 1.0D+0 )
143: * ..
144: * .. Local Scalars ..
145: INTEGER I, K
146: DOUBLE PRECISION AII
147: * ..
148: * .. External Subroutines ..
1.5 bertrand 149: EXTERNAL DLARF, DLARFG, XERBLA
1.1 bertrand 150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC MAX, MIN
153: * ..
154: * .. Executable Statements ..
155: *
156: * Test the input arguments
157: *
158: INFO = 0
159: IF( M.LT.0 ) THEN
160: INFO = -1
161: ELSE IF( N.LT.0 ) THEN
162: INFO = -2
163: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
164: INFO = -4
165: END IF
166: IF( INFO.NE.0 ) THEN
167: CALL XERBLA( 'DGERQ2', -INFO )
168: RETURN
169: END IF
170: *
171: K = MIN( M, N )
172: *
173: DO 10 I = K, 1, -1
174: *
175: * Generate elementary reflector H(i) to annihilate
176: * A(m-k+i,1:n-k+i-1)
177: *
1.5 bertrand 178: CALL DLARFG( N-K+I, A( M-K+I, N-K+I ), A( M-K+I, 1 ), LDA,
1.1 bertrand 179: $ TAU( I ) )
180: *
181: * Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
182: *
183: AII = A( M-K+I, N-K+I )
184: A( M-K+I, N-K+I ) = ONE
185: CALL DLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
186: $ TAU( I ), A, LDA, WORK )
187: A( M-K+I, N-K+I ) = AII
188: 10 CONTINUE
189: RETURN
190: *
191: * End of DGERQ2
192: *
193: END
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