1 SUBROUTINE ZSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK,
2 $ RESULT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER KBAND, LDU, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
13 $ SD( * ), SE( * )
14 COMPLEX*16 U( LDU, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZSTT21 checks a decomposition of the form
21 *
22 * A = U S U*
23 *
24 * where * means conjugate transpose, A is real symmetric tridiagonal,
25 * U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
26 * tridiagonal (if KBAND=1). Two tests are performed:
27 *
28 * RESULT(1) = | A - U S U* | / ( |A| n ulp )
29 *
30 * RESULT(2) = | I - UU* | / ( n ulp )
31 *
32 * Arguments
33 * =========
34 *
35 * N (input) INTEGER
36 * The size of the matrix. If it is zero, ZSTT21 does nothing.
37 * It must be at least zero.
38 *
39 * KBAND (input) INTEGER
40 * The bandwidth of the matrix S. It may only be zero or one.
41 * If zero, then S is diagonal, and SE is not referenced. If
42 * one, then S is symmetric tri-diagonal.
43 *
44 * AD (input) DOUBLE PRECISION array, dimension (N)
45 * The diagonal of the original (unfactored) matrix A. A is
46 * assumed to be real symmetric tridiagonal.
47 *
48 * AE (input) DOUBLE PRECISION array, dimension (N-1)
49 * The off-diagonal of the original (unfactored) matrix A. A
50 * is assumed to be symmetric tridiagonal. AE(1) is the (1,2)
51 * and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
52 *
53 * SD (input) DOUBLE PRECISION array, dimension (N)
54 * The diagonal of the real (symmetric tri-) diagonal matrix S.
55 *
56 * SE (input) DOUBLE PRECISION array, dimension (N-1)
57 * The off-diagonal of the (symmetric tri-) diagonal matrix S.
58 * Not referenced if KBSND=0. If KBAND=1, then AE(1) is the
59 * (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
60 * element, etc.
61 *
62 * U (input) COMPLEX*16 array, dimension (LDU, N)
63 * The unitary matrix in the decomposition.
64 *
65 * LDU (input) INTEGER
66 * The leading dimension of U. LDU must be at least N.
67 *
68 * WORK (workspace) COMPLEX*16 array, dimension (N**2)
69 *
70 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
71 *
72 * RESULT (output) DOUBLE PRECISION array, dimension (2)
73 * The values computed by the two tests described above. The
74 * values are currently limited to 1/ulp, to avoid overflow.
75 * RESULT(1) is always modified.
76 *
77 * =====================================================================
78 *
79 * .. Parameters ..
80 DOUBLE PRECISION ZERO, ONE
81 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
82 COMPLEX*16 CZERO, CONE
83 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
84 $ CONE = ( 1.0D+0, 0.0D+0 ) )
85 * ..
86 * .. Local Scalars ..
87 INTEGER J
88 DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
89 * ..
90 * .. External Functions ..
91 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
92 EXTERNAL DLAMCH, ZLANGE, ZLANHE
93 * ..
94 * .. External Subroutines ..
95 EXTERNAL ZGEMM, ZHER, ZHER2, ZLASET
96 * ..
97 * .. Intrinsic Functions ..
98 INTRINSIC ABS, DBLE, DCMPLX, MAX, MIN
99 * ..
100 * .. Executable Statements ..
101 *
102 * 1) Constants
103 *
104 RESULT( 1 ) = ZERO
105 RESULT( 2 ) = ZERO
106 IF( N.LE.0 )
107 $ RETURN
108 *
109 UNFL = DLAMCH( 'Safe minimum' )
110 ULP = DLAMCH( 'Precision' )
111 *
112 * Do Test 1
113 *
114 * Copy A & Compute its 1-Norm:
115 *
116 CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
117 *
118 ANORM = ZERO
119 TEMP1 = ZERO
120 *
121 DO 10 J = 1, N - 1
122 WORK( ( N+1 )*( J-1 )+1 ) = AD( J )
123 WORK( ( N+1 )*( J-1 )+2 ) = AE( J )
124 TEMP2 = ABS( AE( J ) )
125 ANORM = MAX( ANORM, ABS( AD( J ) )+TEMP1+TEMP2 )
126 TEMP1 = TEMP2
127 10 CONTINUE
128 *
129 WORK( N**2 ) = AD( N )
130 ANORM = MAX( ANORM, ABS( AD( N ) )+TEMP1, UNFL )
131 *
132 * Norm of A - USU*
133 *
134 DO 20 J = 1, N
135 CALL ZHER( 'L', N, -SD( J ), U( 1, J ), 1, WORK, N )
136 20 CONTINUE
137 *
138 IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
139 DO 30 J = 1, N - 1
140 CALL ZHER2( 'L', N, -DCMPLX( SE( J ) ), U( 1, J ), 1,
141 $ U( 1, J+1 ), 1, WORK, N )
142 30 CONTINUE
143 END IF
144 *
145 WNORM = ZLANHE( '1', 'L', N, WORK, N, RWORK )
146 *
147 IF( ANORM.GT.WNORM ) THEN
148 RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
149 ELSE
150 IF( ANORM.LT.ONE ) THEN
151 RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
152 ELSE
153 RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
154 END IF
155 END IF
156 *
157 * Do Test 2
158 *
159 * Compute UU* - I
160 *
161 CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
162 $ N )
163 *
164 DO 40 J = 1, N
165 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
166 40 CONTINUE
167 *
168 RESULT( 2 ) = MIN( DBLE( N ), ZLANGE( '1', N, N, WORK, N,
169 $ RWORK ) ) / ( N*ULP )
170 *
171 RETURN
172 *
173 * End of ZSTT21
174 *
175 END
2 $ RESULT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER KBAND, LDU, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
13 $ SD( * ), SE( * )
14 COMPLEX*16 U( LDU, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZSTT21 checks a decomposition of the form
21 *
22 * A = U S U*
23 *
24 * where * means conjugate transpose, A is real symmetric tridiagonal,
25 * U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
26 * tridiagonal (if KBAND=1). Two tests are performed:
27 *
28 * RESULT(1) = | A - U S U* | / ( |A| n ulp )
29 *
30 * RESULT(2) = | I - UU* | / ( n ulp )
31 *
32 * Arguments
33 * =========
34 *
35 * N (input) INTEGER
36 * The size of the matrix. If it is zero, ZSTT21 does nothing.
37 * It must be at least zero.
38 *
39 * KBAND (input) INTEGER
40 * The bandwidth of the matrix S. It may only be zero or one.
41 * If zero, then S is diagonal, and SE is not referenced. If
42 * one, then S is symmetric tri-diagonal.
43 *
44 * AD (input) DOUBLE PRECISION array, dimension (N)
45 * The diagonal of the original (unfactored) matrix A. A is
46 * assumed to be real symmetric tridiagonal.
47 *
48 * AE (input) DOUBLE PRECISION array, dimension (N-1)
49 * The off-diagonal of the original (unfactored) matrix A. A
50 * is assumed to be symmetric tridiagonal. AE(1) is the (1,2)
51 * and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
52 *
53 * SD (input) DOUBLE PRECISION array, dimension (N)
54 * The diagonal of the real (symmetric tri-) diagonal matrix S.
55 *
56 * SE (input) DOUBLE PRECISION array, dimension (N-1)
57 * The off-diagonal of the (symmetric tri-) diagonal matrix S.
58 * Not referenced if KBSND=0. If KBAND=1, then AE(1) is the
59 * (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
60 * element, etc.
61 *
62 * U (input) COMPLEX*16 array, dimension (LDU, N)
63 * The unitary matrix in the decomposition.
64 *
65 * LDU (input) INTEGER
66 * The leading dimension of U. LDU must be at least N.
67 *
68 * WORK (workspace) COMPLEX*16 array, dimension (N**2)
69 *
70 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
71 *
72 * RESULT (output) DOUBLE PRECISION array, dimension (2)
73 * The values computed by the two tests described above. The
74 * values are currently limited to 1/ulp, to avoid overflow.
75 * RESULT(1) is always modified.
76 *
77 * =====================================================================
78 *
79 * .. Parameters ..
80 DOUBLE PRECISION ZERO, ONE
81 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
82 COMPLEX*16 CZERO, CONE
83 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
84 $ CONE = ( 1.0D+0, 0.0D+0 ) )
85 * ..
86 * .. Local Scalars ..
87 INTEGER J
88 DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
89 * ..
90 * .. External Functions ..
91 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
92 EXTERNAL DLAMCH, ZLANGE, ZLANHE
93 * ..
94 * .. External Subroutines ..
95 EXTERNAL ZGEMM, ZHER, ZHER2, ZLASET
96 * ..
97 * .. Intrinsic Functions ..
98 INTRINSIC ABS, DBLE, DCMPLX, MAX, MIN
99 * ..
100 * .. Executable Statements ..
101 *
102 * 1) Constants
103 *
104 RESULT( 1 ) = ZERO
105 RESULT( 2 ) = ZERO
106 IF( N.LE.0 )
107 $ RETURN
108 *
109 UNFL = DLAMCH( 'Safe minimum' )
110 ULP = DLAMCH( 'Precision' )
111 *
112 * Do Test 1
113 *
114 * Copy A & Compute its 1-Norm:
115 *
116 CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
117 *
118 ANORM = ZERO
119 TEMP1 = ZERO
120 *
121 DO 10 J = 1, N - 1
122 WORK( ( N+1 )*( J-1 )+1 ) = AD( J )
123 WORK( ( N+1 )*( J-1 )+2 ) = AE( J )
124 TEMP2 = ABS( AE( J ) )
125 ANORM = MAX( ANORM, ABS( AD( J ) )+TEMP1+TEMP2 )
126 TEMP1 = TEMP2
127 10 CONTINUE
128 *
129 WORK( N**2 ) = AD( N )
130 ANORM = MAX( ANORM, ABS( AD( N ) )+TEMP1, UNFL )
131 *
132 * Norm of A - USU*
133 *
134 DO 20 J = 1, N
135 CALL ZHER( 'L', N, -SD( J ), U( 1, J ), 1, WORK, N )
136 20 CONTINUE
137 *
138 IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
139 DO 30 J = 1, N - 1
140 CALL ZHER2( 'L', N, -DCMPLX( SE( J ) ), U( 1, J ), 1,
141 $ U( 1, J+1 ), 1, WORK, N )
142 30 CONTINUE
143 END IF
144 *
145 WNORM = ZLANHE( '1', 'L', N, WORK, N, RWORK )
146 *
147 IF( ANORM.GT.WNORM ) THEN
148 RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
149 ELSE
150 IF( ANORM.LT.ONE ) THEN
151 RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
152 ELSE
153 RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
154 END IF
155 END IF
156 *
157 * Do Test 2
158 *
159 * Compute UU* - I
160 *
161 CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
162 $ N )
163 *
164 DO 40 J = 1, N
165 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
166 40 CONTINUE
167 *
168 RESULT( 2 ) = MIN( DBLE( N ), ZLANGE( '1', N, N, WORK, N,
169 $ RWORK ) ) / ( N*ULP )
170 *
171 RETURN
172 *
173 * End of ZSTT21
174 *
175 END