Annotation of rpl/lapack/lapack/dgeqr2.f, revision 1.10
1.10 ! bertrand 1: *> \brief \b DGEQR2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGEQR2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGEQR2( 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: *> DGEQR2 computes a QR factorization of a real m by n matrix A:
! 37: *> A = Q * R.
! 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, the elements on and above the diagonal of the array
! 60: *> contain the min(m,n) by n upper trapezoidal matrix R (R is
! 61: *> upper triangular if m >= n); the elements below the diagonal,
! 62: *> with the array TAU, represent the orthogonal matrix Q as a
! 63: *> product of elementary reflectors (see Further Details).
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in] LDA
! 67: *> \verbatim
! 68: *> LDA is INTEGER
! 69: *> The leading dimension of the array A. LDA >= max(1,M).
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[out] TAU
! 73: *> \verbatim
! 74: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
! 75: *> The scalar factors of the elementary reflectors (see Further
! 76: *> Details).
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[out] WORK
! 80: *> \verbatim
! 81: *> WORK is DOUBLE PRECISION array, dimension (N)
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[out] INFO
! 85: *> \verbatim
! 86: *> INFO is INTEGER
! 87: *> = 0: successful exit
! 88: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 89: *> \endverbatim
! 90: *
! 91: * Authors:
! 92: * ========
! 93: *
! 94: *> \author Univ. of Tennessee
! 95: *> \author Univ. of California Berkeley
! 96: *> \author Univ. of Colorado Denver
! 97: *> \author NAG Ltd.
! 98: *
! 99: *> \date November 2011
! 100: *
! 101: *> \ingroup doubleGEcomputational
! 102: *
! 103: *> \par Further Details:
! 104: * =====================
! 105: *>
! 106: *> \verbatim
! 107: *>
! 108: *> The matrix Q is represented as a product of elementary reflectors
! 109: *>
! 110: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 111: *>
! 112: *> Each H(i) has the form
! 113: *>
! 114: *> H(i) = I - tau * v * v**T
! 115: *>
! 116: *> where tau is a real scalar, and v is a real vector with
! 117: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
! 118: *> and tau in TAU(i).
! 119: *> \endverbatim
! 120: *>
! 121: * =====================================================================
1.1 bertrand 122: SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
123: *
1.10 ! bertrand 124: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 ! bertrand 127: * November 2011
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: INTEGER INFO, LDA, M, N
131: * ..
132: * .. Array Arguments ..
133: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
134: * ..
135: *
136: * =====================================================================
137: *
138: * .. Parameters ..
139: DOUBLE PRECISION ONE
140: PARAMETER ( ONE = 1.0D+0 )
141: * ..
142: * .. Local Scalars ..
143: INTEGER I, K
144: DOUBLE PRECISION AII
145: * ..
146: * .. External Subroutines ..
1.5 bertrand 147: EXTERNAL DLARF, DLARFG, XERBLA
1.1 bertrand 148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC MAX, MIN
151: * ..
152: * .. Executable Statements ..
153: *
154: * Test the input arguments
155: *
156: INFO = 0
157: IF( M.LT.0 ) THEN
158: INFO = -1
159: ELSE IF( N.LT.0 ) THEN
160: INFO = -2
161: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
162: INFO = -4
163: END IF
164: IF( INFO.NE.0 ) THEN
165: CALL XERBLA( 'DGEQR2', -INFO )
166: RETURN
167: END IF
168: *
169: K = MIN( M, N )
170: *
171: DO 10 I = 1, K
172: *
173: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
174: *
1.5 bertrand 175: CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
1.1 bertrand 176: $ TAU( I ) )
177: IF( I.LT.N ) THEN
178: *
179: * Apply H(i) to A(i:m,i+1:n) from the left
180: *
181: AII = A( I, I )
182: A( I, I ) = ONE
183: CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
184: $ A( I, I+1 ), LDA, WORK )
185: A( I, I ) = AII
186: END IF
187: 10 CONTINUE
188: RETURN
189: *
190: * End of DGEQR2
191: *
192: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dgeqr2.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack