KTH framework for Nek5000 toolboxes; testing version  0.0.1
dgehd2.f
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1  SUBROUTINE dgehd2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
2 *
3 * -- LAPACK routine (version 3.0) --
4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
5 * Courant Institute, Argonne National Lab, and Rice University
6 * October 31, 1992
7 *
8 * .. Scalar Arguments ..
9  INTEGER IHI, ILO, INFO, LDA, N
10 * ..
11 * .. Array Arguments ..
12  DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
19 * an orthogonal similarity transformation: Q' * A * Q = H .
20 *
21 * Arguments
22 * =========
23 *
24 * N (input) INTEGER
25 * The order of the matrix A. N >= 0.
26 *
27 * ILO (input) INTEGER
28 * IHI (input) INTEGER
29 * It is assumed that A is already upper triangular in rows
30 * and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
31 * set by a previous call to DGEBAL; otherwise they should be
32 * set to 1 and N respectively. See Further Details.
33 * 1 <= ILO <= IHI <= max(1,N).
34 *
35 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
36 * On entry, the n by n general matrix to be reduced.
37 * On exit, the upper triangle and the first subdiagonal of A
38 * are overwritten with the upper Hessenberg matrix H, and the
39 * elements below the first subdiagonal, with the array TAU,
40 * represent the orthogonal matrix Q as a product of elementary
41 * reflectors. See Further Details.
42 *
43 * LDA (input) INTEGER
44 * The leading dimension of the array A. LDA >= max(1,N).
45 *
46 * TAU (output) DOUBLE PRECISION array, dimension (N-1)
47 * The scalar factors of the elementary reflectors (see Further
48 * Details).
49 *
50 * WORK (workspace) DOUBLE PRECISION array, dimension (N)
51 *
52 * INFO (output) INTEGER
53 * = 0: successful exit.
54 * < 0: if INFO = -i, the i-th argument had an illegal value.
55 *
56 * Further Details
57 * ===============
58 *
59 * The matrix Q is represented as a product of (ihi-ilo) elementary
60 * reflectors
61 *
62 * Q = H(ilo) H(ilo+1) . . . H(ihi-1).
63 *
64 * Each H(i) has the form
65 *
66 * H(i) = I - tau * v * v'
67 *
68 * where tau is a real scalar, and v is a real vector with
69 * v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
70 * exit in A(i+2:ihi,i), and tau in TAU(i).
71 *
72 * The contents of A are illustrated by the following example, with
73 * n = 7, ilo = 2 and ihi = 6:
74 *
75 * on entry, on exit,
76 *
77 * ( a a a a a a a ) ( a a h h h h a )
78 * ( a a a a a a ) ( a h h h h a )
79 * ( a a a a a a ) ( h h h h h h )
80 * ( a a a a a a ) ( v2 h h h h h )
81 * ( a a a a a a ) ( v2 v3 h h h h )
82 * ( a a a a a a ) ( v2 v3 v4 h h h )
83 * ( a ) ( a )
84 *
85 * where a denotes an element of the original matrix A, h denotes a
86 * modified element of the upper Hessenberg matrix H, and vi denotes an
87 * element of the vector defining H(i).
88 *
89 * =====================================================================
90 *
91 * .. Parameters ..
92  DOUBLE PRECISION ONE
93  parameter( one = 1.0d+0 )
94 * ..
95 * .. Local Scalars ..
96  INTEGER I
97  DOUBLE PRECISION AII
98 * ..
99 * .. External Subroutines ..
100  EXTERNAL dlarf, dlarfg, xerbla
101 * ..
102 * .. Intrinsic Functions ..
103  INTRINSIC max, min
104 * ..
105 * .. Executable Statements ..
106 *
107 * Test the input parameters
108 *
109  info = 0
110  IF( n.LT.0 ) THEN
111  info = -1
112  ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
113  info = -2
114  ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
115  info = -3
116  ELSE IF( lda.LT.max( 1, n ) ) THEN
117  info = -5
118  END IF
119  IF( info.NE.0 ) THEN
120  CALL xerbla( 'DGEHD2', -info )
121  RETURN
122  END IF
123 *
124  DO 10 i = ilo, ihi - 1
125 *
126 * Compute elementary reflector H(i) to annihilate A(i+2:ihi,i)
127 *
128  CALL dlarfg( ihi-i, a( i+1, i ), a( min( i+2, n ), i ), 1,
129  $ tau( i ) )
130  aii = a( i+1, i )
131  a( i+1, i ) = one
132 *
133 * Apply H(i) to A(1:ihi,i+1:ihi) from the right
134 *
135  CALL dlarf( 'Right', ihi, ihi-i, a( i+1, i ), 1, tau( i ),
136  $ a( 1, i+1 ), lda, work )
137 *
138 * Apply H(i) to A(i+1:ihi,i+1:n) from the left
139 *
140  CALL dlarf( 'Left', ihi-i, n-i, a( i+1, i ), 1, tau( i ),
141  $ a( i+1, i+1 ), lda, work )
142 *
143  a( i+1, i ) = aii
144  10 CONTINUE
145 *
146  RETURN
147 *
148 * End of DGEHD2
149 *
150  END
subroutine dgehd2(N, ILO, IHI, A, LDA, TAU, WORK, INFO)
Definition: dgehd2.f:2
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
Definition: dlarf.f:2
subroutine dlarfg(N, ALPHA, X, INCX, TAU)
Definition: dlarfg.f:2
subroutine xerbla(SRNAME, INFO)
Definition: xerbla.f:2