1: SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
2: *
3: * -- LAPACK routine (version 3.3.1) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * -- April 2011 --
7: *
8: * .. Scalar Arguments ..
9: INTEGER INFO, LDA, LWORK, M, N
10: * ..
11: * .. Array Arguments ..
12: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13: * ..
14: *
15: * Purpose
16: * =======
17: *
18: * DGEQRFP computes a QR factorization of a real M-by-N matrix A:
19: * A = Q * R.
20: *
21: * Arguments
22: * =========
23: *
24: * M (input) INTEGER
25: * The number of rows of the matrix A. M >= 0.
26: *
27: * N (input) INTEGER
28: * The number of columns of the matrix A. N >= 0.
29: *
30: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
31: * On entry, the M-by-N matrix A.
32: * On exit, the elements on and above the diagonal of the array
33: * contain the min(M,N)-by-N upper trapezoidal matrix R (R is
34: * upper triangular if m >= n); the elements below the diagonal,
35: * with the array TAU, represent the orthogonal matrix Q as a
36: * product of min(m,n) elementary reflectors (see Further
37: * Details).
38: *
39: * LDA (input) INTEGER
40: * The leading dimension of the array A. LDA >= max(1,M).
41: *
42: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
43: * The scalar factors of the elementary reflectors (see Further
44: * Details).
45: *
46: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
47: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
48: *
49: * LWORK (input) INTEGER
50: * The dimension of the array WORK. LWORK >= max(1,N).
51: * For optimum performance LWORK >= N*NB, where NB is
52: * the optimal blocksize.
53: *
54: * If LWORK = -1, then a workspace query is assumed; the routine
55: * only calculates the optimal size of the WORK array, returns
56: * this value as the first entry of the WORK array, and no error
57: * message related to LWORK is issued by XERBLA.
58: *
59: * INFO (output) INTEGER
60: * = 0: successful exit
61: * < 0: if INFO = -i, the i-th argument had an illegal value
62: *
63: * Further Details
64: * ===============
65: *
66: * The matrix Q is represented as a product of elementary reflectors
67: *
68: * Q = H(1) H(2) . . . H(k), where k = min(m,n).
69: *
70: * Each H(i) has the form
71: *
72: * H(i) = I - tau * v * v**T
73: *
74: * where tau is a real scalar, and v is a real vector with
75: * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
76: * and tau in TAU(i).
77: *
78: * =====================================================================
79: *
80: * .. Local Scalars ..
81: LOGICAL LQUERY
82: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
83: $ NBMIN, NX
84: * ..
85: * .. External Subroutines ..
86: EXTERNAL DGEQR2P, DLARFB, DLARFT, XERBLA
87: * ..
88: * .. Intrinsic Functions ..
89: INTRINSIC MAX, MIN
90: * ..
91: * .. External Functions ..
92: INTEGER ILAENV
93: EXTERNAL ILAENV
94: * ..
95: * .. Executable Statements ..
96: *
97: * Test the input arguments
98: *
99: INFO = 0
100: NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
101: LWKOPT = N*NB
102: WORK( 1 ) = LWKOPT
103: LQUERY = ( LWORK.EQ.-1 )
104: IF( M.LT.0 ) THEN
105: INFO = -1
106: ELSE IF( N.LT.0 ) THEN
107: INFO = -2
108: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
109: INFO = -4
110: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
111: INFO = -7
112: END IF
113: IF( INFO.NE.0 ) THEN
114: CALL XERBLA( 'DGEQRFP', -INFO )
115: RETURN
116: ELSE IF( LQUERY ) THEN
117: RETURN
118: END IF
119: *
120: * Quick return if possible
121: *
122: K = MIN( M, N )
123: IF( K.EQ.0 ) THEN
124: WORK( 1 ) = 1
125: RETURN
126: END IF
127: *
128: NBMIN = 2
129: NX = 0
130: IWS = N
131: IF( NB.GT.1 .AND. NB.LT.K ) THEN
132: *
133: * Determine when to cross over from blocked to unblocked code.
134: *
135: NX = MAX( 0, ILAENV( 3, 'DGEQRF', ' ', M, N, -1, -1 ) )
136: IF( NX.LT.K ) THEN
137: *
138: * Determine if workspace is large enough for blocked code.
139: *
140: LDWORK = N
141: IWS = LDWORK*NB
142: IF( LWORK.LT.IWS ) THEN
143: *
144: * Not enough workspace to use optimal NB: reduce NB and
145: * determine the minimum value of NB.
146: *
147: NB = LWORK / LDWORK
148: NBMIN = MAX( 2, ILAENV( 2, 'DGEQRF', ' ', M, N, -1,
149: $ -1 ) )
150: END IF
151: END IF
152: END IF
153: *
154: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
155: *
156: * Use blocked code initially
157: *
158: DO 10 I = 1, K - NX, NB
159: IB = MIN( K-I+1, NB )
160: *
161: * Compute the QR factorization of the current block
162: * A(i:m,i:i+ib-1)
163: *
164: CALL DGEQR2P( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
165: $ IINFO )
166: IF( I+IB.LE.N ) THEN
167: *
168: * Form the triangular factor of the block reflector
169: * H = H(i) H(i+1) . . . H(i+ib-1)
170: *
171: CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
172: $ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
173: *
174: * Apply H**T to A(i:m,i+ib:n) from the left
175: *
176: CALL DLARFB( 'Left', 'Transpose', 'Forward',
177: $ 'Columnwise', M-I+1, N-I-IB+1, IB,
178: $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
179: $ LDA, WORK( IB+1 ), LDWORK )
180: END IF
181: 10 CONTINUE
182: ELSE
183: I = 1
184: END IF
185: *
186: * Use unblocked code to factor the last or only block.
187: *
188: IF( I.LE.K )
189: $ CALL DGEQR2P( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
190: $ IINFO )
191: *
192: WORK( 1 ) = IWS
193: RETURN
194: *
195: * End of DGEQRFP
196: *
197: END
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