Annotation of rpl/lapack/lapack/zunghr.f, revision 1.5
1.1 bertrand 1: SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: INTEGER IHI, ILO, INFO, LDA, LWORK, N
10: * ..
11: * .. Array Arguments ..
12: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13: * ..
14: *
15: * Purpose
16: * =======
17: *
18: * ZUNGHR generates a complex unitary matrix Q which is defined as the
19: * product of IHI-ILO elementary reflectors of order N, as returned by
20: * ZGEHRD:
21: *
22: * Q = H(ilo) H(ilo+1) . . . H(ihi-1).
23: *
24: * Arguments
25: * =========
26: *
27: * N (input) INTEGER
28: * The order of the matrix Q. N >= 0.
29: *
30: * ILO (input) INTEGER
31: * IHI (input) INTEGER
32: * ILO and IHI must have the same values as in the previous call
33: * of ZGEHRD. Q is equal to the unit matrix except in the
34: * submatrix Q(ilo+1:ihi,ilo+1:ihi).
35: * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
36: *
37: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
38: * On entry, the vectors which define the elementary reflectors,
39: * as returned by ZGEHRD.
40: * On exit, the N-by-N unitary matrix Q.
41: *
42: * LDA (input) INTEGER
43: * The leading dimension of the array A. LDA >= max(1,N).
44: *
45: * TAU (input) COMPLEX*16 array, dimension (N-1)
46: * TAU(i) must contain the scalar factor of the elementary
47: * reflector H(i), as returned by ZGEHRD.
48: *
49: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
50: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
51: *
52: * LWORK (input) INTEGER
53: * The dimension of the array WORK. LWORK >= IHI-ILO.
54: * For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
55: * the optimal blocksize.
56: *
57: * If LWORK = -1, then a workspace query is assumed; the routine
58: * only calculates the optimal size of the WORK array, returns
59: * this value as the first entry of the WORK array, and no error
60: * message related to LWORK is issued by XERBLA.
61: *
62: * INFO (output) INTEGER
63: * = 0: successful exit
64: * < 0: if INFO = -i, the i-th argument had an illegal value
65: *
66: * =====================================================================
67: *
68: * .. Parameters ..
69: COMPLEX*16 ZERO, ONE
70: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
71: $ ONE = ( 1.0D+0, 0.0D+0 ) )
72: * ..
73: * .. Local Scalars ..
74: LOGICAL LQUERY
75: INTEGER I, IINFO, J, LWKOPT, NB, NH
76: * ..
77: * .. External Subroutines ..
78: EXTERNAL XERBLA, ZUNGQR
79: * ..
80: * .. External Functions ..
81: INTEGER ILAENV
82: EXTERNAL ILAENV
83: * ..
84: * .. Intrinsic Functions ..
85: INTRINSIC MAX, MIN
86: * ..
87: * .. Executable Statements ..
88: *
89: * Test the input arguments
90: *
91: INFO = 0
92: NH = IHI - ILO
93: LQUERY = ( LWORK.EQ.-1 )
94: IF( N.LT.0 ) THEN
95: INFO = -1
96: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
97: INFO = -2
98: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
99: INFO = -3
100: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
101: INFO = -5
102: ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
103: INFO = -8
104: END IF
105: *
106: IF( INFO.EQ.0 ) THEN
107: NB = ILAENV( 1, 'ZUNGQR', ' ', NH, NH, NH, -1 )
108: LWKOPT = MAX( 1, NH )*NB
109: WORK( 1 ) = LWKOPT
110: END IF
111: *
112: IF( INFO.NE.0 ) THEN
113: CALL XERBLA( 'ZUNGHR', -INFO )
114: RETURN
115: ELSE IF( LQUERY ) THEN
116: RETURN
117: END IF
118: *
119: * Quick return if possible
120: *
121: IF( N.EQ.0 ) THEN
122: WORK( 1 ) = 1
123: RETURN
124: END IF
125: *
126: * Shift the vectors which define the elementary reflectors one
127: * column to the right, and set the first ilo and the last n-ihi
128: * rows and columns to those of the unit matrix
129: *
130: DO 40 J = IHI, ILO + 1, -1
131: DO 10 I = 1, J - 1
132: A( I, J ) = ZERO
133: 10 CONTINUE
134: DO 20 I = J + 1, IHI
135: A( I, J ) = A( I, J-1 )
136: 20 CONTINUE
137: DO 30 I = IHI + 1, N
138: A( I, J ) = ZERO
139: 30 CONTINUE
140: 40 CONTINUE
141: DO 60 J = 1, ILO
142: DO 50 I = 1, N
143: A( I, J ) = ZERO
144: 50 CONTINUE
145: A( J, J ) = ONE
146: 60 CONTINUE
147: DO 80 J = IHI + 1, N
148: DO 70 I = 1, N
149: A( I, J ) = ZERO
150: 70 CONTINUE
151: A( J, J ) = ONE
152: 80 CONTINUE
153: *
154: IF( NH.GT.0 ) THEN
155: *
156: * Generate Q(ilo+1:ihi,ilo+1:ihi)
157: *
158: CALL ZUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
159: $ WORK, LWORK, IINFO )
160: END IF
161: WORK( 1 ) = LWKOPT
162: RETURN
163: *
164: * End of ZUNGHR
165: *
166: END
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