LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
cgeqr2p.f
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1 *> \brief \b CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDA, M, N
25 * ..
26 * .. Array Arguments ..
27 * COMPLEX A( LDA, * ), TAU( * ), WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> CGEQR2P computes a QR factorization of a complex m-by-n matrix A:
37 *>
38 *> A = Q * ( R ),
39 *> ( 0 )
40 *>
41 *> where:
42 *>
43 *> Q is a m-by-m orthogonal matrix;
44 *> R is an upper-triangular n-by-n matrix with nonnegative diagonal
45 *> entries;
46 *> 0 is a (m-n)-by-n zero matrix, if m > n.
47 *>
48 *> \endverbatim
49 *
50 * Arguments:
51 * ==========
52 *
53 *> \param[in] M
54 *> \verbatim
55 *> M is INTEGER
56 *> The number of rows of the matrix A. M >= 0.
57 *> \endverbatim
58 *>
59 *> \param[in] N
60 *> \verbatim
61 *> N is INTEGER
62 *> The number of columns of the matrix A. N >= 0.
63 *> \endverbatim
64 *>
65 *> \param[in,out] A
66 *> \verbatim
67 *> A is COMPLEX array, dimension (LDA,N)
68 *> On entry, the m by n matrix A.
69 *> On exit, the elements on and above the diagonal of the array
70 *> contain the min(m,n) by n upper trapezoidal matrix R (R is
71 *> upper triangular if m >= n). The diagonal entries of R are
72 *> real and nonnegative; the elements below the diagonal,
73 *> with the array TAU, represent the unitary matrix Q as a
74 *> product of elementary reflectors (see Further Details).
75 *> \endverbatim
76 *>
77 *> \param[in] LDA
78 *> \verbatim
79 *> LDA is INTEGER
80 *> The leading dimension of the array A. LDA >= max(1,M).
81 *> \endverbatim
82 *>
83 *> \param[out] TAU
84 *> \verbatim
85 *> TAU is COMPLEX array, dimension (min(M,N))
86 *> The scalar factors of the elementary reflectors (see Further
87 *> Details).
88 *> \endverbatim
89 *>
90 *> \param[out] WORK
91 *> \verbatim
92 *> WORK is COMPLEX array, dimension (N)
93 *> \endverbatim
94 *>
95 *> \param[out] INFO
96 *> \verbatim
97 *> INFO is INTEGER
98 *> = 0: successful exit
99 *> < 0: if INFO = -i, the i-th argument had an illegal value
100 *> \endverbatim
101 *
102 * Authors:
103 * ========
104 *
105 *> \author Univ. of Tennessee
106 *> \author Univ. of California Berkeley
107 *> \author Univ. of Colorado Denver
108 *> \author NAG Ltd.
109 *
110 *> \ingroup complexGEcomputational
111 *
112 *> \par Further Details:
113 * =====================
114 *>
115 *> \verbatim
116 *>
117 *> The matrix Q is represented as a product of elementary reflectors
118 *>
119 *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
120 *>
121 *> Each H(i) has the form
122 *>
123 *> H(i) = I - tau * v * v**H
124 *>
125 *> where tau is a complex scalar, and v is a complex vector with
126 *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
127 *> and tau in TAU(i).
128 *>
129 *> See Lapack Working Note 203 for details
130 *> \endverbatim
131 *>
132 * =====================================================================
133  SUBROUTINE cgeqr2p( M, N, A, LDA, TAU, WORK, INFO )
134 *
135 * -- LAPACK computational routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  INTEGER INFO, LDA, M, N
141 * ..
142 * .. Array Arguments ..
143  COMPLEX A( LDA, * ), TAU( * ), WORK( * )
144 * ..
145 *
146 * =====================================================================
147 *
148 * .. Parameters ..
149  COMPLEX ONE
150  parameter( one = ( 1.0e+0, 0.0e+0 ) )
151 * ..
152 * .. Local Scalars ..
153  INTEGER I, K
154  COMPLEX ALPHA
155 * ..
156 * .. External Subroutines ..
157  EXTERNAL clarf, clarfgp, xerbla
158 * ..
159 * .. Intrinsic Functions ..
160  INTRINSIC conjg, max, min
161 * ..
162 * .. Executable Statements ..
163 *
164 * Test the input arguments
165 *
166  info = 0
167  IF( m.LT.0 ) THEN
168  info = -1
169  ELSE IF( n.LT.0 ) THEN
170  info = -2
171  ELSE IF( lda.LT.max( 1, m ) ) THEN
172  info = -4
173  END IF
174  IF( info.NE.0 ) THEN
175  CALL xerbla( 'CGEQR2P', -info )
176  RETURN
177  END IF
178 *
179  k = min( m, n )
180 *
181  DO 10 i = 1, k
182 *
183 * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
184 *
185  CALL clarfgp( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
186  \$ tau( i ) )
187  IF( i.LT.n ) THEN
188 *
189 * Apply H(i)**H to A(i:m,i+1:n) from the left
190 *
191  alpha = a( i, i )
192  a( i, i ) = one
193  CALL clarf( 'Left', m-i+1, n-i, a( i, i ), 1,
194  \$ conjg( tau( i ) ), a( i, i+1 ), lda, work )
195  a( i, i ) = alpha
196  END IF
197  10 CONTINUE
198  RETURN
199 *
200 * End of CGEQR2P
201 *
202  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgeqr2p(M, N, A, LDA, TAU, WORK, INFO)
CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elem...
Definition: cgeqr2p.f:134
subroutine clarfgp(N, ALPHA, X, INCX, TAU)
CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Definition: clarfgp.f:104
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:128