1 DOUBLE COMPLEX FUNCTION ZLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
2 $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
3 $ SPARSE )
4 *
5 * -- LAPACK auxiliary test routine (version 3.1) --
6 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
7 * June 2010
8 *
9 * .. Scalar Arguments ..
10 *
11 INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
12 $ KU, M, N
13 DOUBLE PRECISION SPARSE
14 * ..
15 *
16 * .. Array Arguments ..
17 *
18 INTEGER ISEED( 4 ), IWORK( * )
19 COMPLEX*16 D( * ), DL( * ), DR( * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of
26 * dimension (M, N) described by the other paramters. (ISUB,JSUB)
27 * is the final position of the (I,J) entry after pivoting
28 * according to IPVTNG and IWORK. ZLATM3 is called by the
29 * ZLATMR routine in order to build random test matrices. No error
30 * checking on parameters is done, because this routine is called in
31 * a tight loop by ZLATMR which has already checked the parameters.
32 *
33 * Use of ZLATM3 differs from CLATM2 in the order in which the random
34 * number generator is called to fill in random matrix entries.
35 * With ZLATM2, the generator is called to fill in the pivoted matrix
36 * columnwise. With ZLATM3, the generator is called to fill in the
37 * matrix columnwise, after which it is pivoted. Thus, ZLATM3 can
38 * be used to construct random matrices which differ only in their
39 * order of rows and/or columns. ZLATM2 is used to construct band
40 * matrices while avoiding calling the random number generator for
41 * entries outside the band (and therefore generating random numbers
42 * in different orders for different pivot orders).
43 *
44 * The matrix whose (ISUB,JSUB) entry is returned is constructed as
45 * follows (this routine only computes one entry):
46 *
47 * If ISUB is outside (1..M) or JSUB is outside (1..N), return zero
48 * (this is convenient for generating matrices in band format).
49 *
50 * Generate a matrix A with random entries of distribution IDIST.
51 *
52 * Set the diagonal to D.
53 *
54 * Grade the matrix, if desired, from the left (by DL) and/or
55 * from the right (by DR or DL) as specified by IGRADE.
56 *
57 * Permute, if desired, the rows and/or columns as specified by
58 * IPVTNG and IWORK.
59 *
60 * Band the matrix to have lower bandwidth KL and upper
61 * bandwidth KU.
62 *
63 * Set random entries to zero as specified by SPARSE.
64 *
65 * Arguments
66 * =========
67 *
68 * M (input) INTEGER
69 * Number of rows of matrix. Not modified.
70 *
71 * N (input) INTEGER
72 * Number of columns of matrix. Not modified.
73 *
74 * I (input) INTEGER
75 * Row of unpivoted entry to be returned. Not modified.
76 *
77 * J (input) INTEGER
78 * Column of unpivoted entry to be returned. Not modified.
79 *
80 * ISUB (input/output) INTEGER
81 * Row of pivoted entry to be returned. Changed on exit.
82 *
83 * JSUB (input/output) INTEGER
84 * Column of pivoted entry to be returned. Changed on exit.
85 *
86 * KL (input) INTEGER
87 * Lower bandwidth. Not modified.
88 *
89 * KU (input) INTEGER
90 * Upper bandwidth. Not modified.
91 *
92 * IDIST (input) INTEGER
93 * On entry, IDIST specifies the type of distribution to be
94 * used to generate a random matrix .
95 * 1 => real and imaginary parts each UNIFORM( 0, 1 )
96 * 2 => real and imaginary parts each UNIFORM( -1, 1 )
97 * 3 => real and imaginary parts each NORMAL( 0, 1 )
98 * 4 => complex number uniform in DISK( 0 , 1 )
99 * Not modified.
100 *
101 * ISEED (input/output) INTEGER array of dimension ( 4 )
102 * Seed for random number generator.
103 * Changed on exit.
104 *
105 * D (input) COMPLEX*16 array of dimension ( MIN( I , J ) )
106 * Diagonal entries of matrix. Not modified.
107 *
108 * IGRADE (input) INTEGER
109 * Specifies grading of matrix as follows:
110 * 0 => no grading
111 * 1 => matrix premultiplied by diag( DL )
112 * 2 => matrix postmultiplied by diag( DR )
113 * 3 => matrix premultiplied by diag( DL ) and
114 * postmultiplied by diag( DR )
115 * 4 => matrix premultiplied by diag( DL ) and
116 * postmultiplied by inv( diag( DL ) )
117 * 5 => matrix premultiplied by diag( DL ) and
118 * postmultiplied by diag( CONJG(DL) )
119 * 6 => matrix premultiplied by diag( DL ) and
120 * postmultiplied by diag( DL )
121 * Not modified.
122 *
123 * DL (input) COMPLEX*16 array ( I or J, as appropriate )
124 * Left scale factors for grading matrix. Not modified.
125 *
126 * DR (input) COMPLEX*16 array ( I or J, as appropriate )
127 * Right scale factors for grading matrix. Not modified.
128 *
129 * IPVTNG (input) INTEGER
130 * On entry specifies pivoting permutations as follows:
131 * 0 => none.
132 * 1 => row pivoting.
133 * 2 => column pivoting.
134 * 3 => full pivoting, i.e., on both sides.
135 * Not modified.
136 *
137 * IWORK (input) INTEGER array ( I or J, as appropriate )
138 * This array specifies the permutation used. The
139 * row (or column) originally in position K is in
140 * position IWORK( K ) after pivoting.
141 * This differs from IWORK for ZLATM2. Not modified.
142 *
143 * SPARSE (input) DOUBLE PRECISION between 0. and 1.
144 * On entry specifies the sparsity of the matrix
145 * if sparse matix is to be generated.
146 * SPARSE should lie between 0 and 1.
147 * A uniform ( 0, 1 ) random number x is generated and
148 * compared to SPARSE; if x is larger the matrix entry
149 * is unchanged and if x is smaller the entry is set
150 * to zero. Thus on the average a fraction SPARSE of the
151 * entries will be set to zero.
152 * Not modified.
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157 *
158 DOUBLE PRECISION ZERO
159 PARAMETER ( ZERO = 0.0D0 )
160 COMPLEX*16 CZERO
161 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ) )
162 * ..
163 *
164 * .. Local Scalars ..
165 *
166 COMPLEX*16 CTEMP
167 * ..
168 *
169 * .. External Functions ..
170 *
171 DOUBLE PRECISION DLARAN
172 COMPLEX*16 ZLARND
173 EXTERNAL DLARAN, ZLARND
174 * ..
175 *
176 * .. Intrinsic Functions ..
177 *
178 INTRINSIC DCONJG
179 * ..
180 *
181 *-----------------------------------------------------------------------
182 *
183 * .. Executable Statements ..
184 *
185 *
186 * Check for I and J in range
187 *
188 IF( I.LT.1 .OR. I.GT.M .OR. J.LT.1 .OR. J.GT.N ) THEN
189 ISUB = I
190 JSUB = J
191 ZLATM3 = CZERO
192 RETURN
193 END IF
194 *
195 * Compute subscripts depending on IPVTNG
196 *
197 IF( IPVTNG.EQ.0 ) THEN
198 ISUB = I
199 JSUB = J
200 ELSE IF( IPVTNG.EQ.1 ) THEN
201 ISUB = IWORK( I )
202 JSUB = J
203 ELSE IF( IPVTNG.EQ.2 ) THEN
204 ISUB = I
205 JSUB = IWORK( J )
206 ELSE IF( IPVTNG.EQ.3 ) THEN
207 ISUB = IWORK( I )
208 JSUB = IWORK( J )
209 END IF
210 *
211 * Check for banding
212 *
213 IF( JSUB.GT.ISUB+KU .OR. JSUB.LT.ISUB-KL ) THEN
214 ZLATM3 = CZERO
215 RETURN
216 END IF
217 *
218 * Check for sparsity
219 *
220 IF( SPARSE.GT.ZERO ) THEN
221 IF( DLARAN( ISEED ).LT.SPARSE ) THEN
222 ZLATM3 = CZERO
223 RETURN
224 END IF
225 END IF
226 *
227 * Compute entry and grade it according to IGRADE
228 *
229 IF( I.EQ.J ) THEN
230 CTEMP = D( I )
231 ELSE
232 CTEMP = ZLARND( IDIST, ISEED )
233 END IF
234 IF( IGRADE.EQ.1 ) THEN
235 CTEMP = CTEMP*DL( I )
236 ELSE IF( IGRADE.EQ.2 ) THEN
237 CTEMP = CTEMP*DR( J )
238 ELSE IF( IGRADE.EQ.3 ) THEN
239 CTEMP = CTEMP*DL( I )*DR( J )
240 ELSE IF( IGRADE.EQ.4 .AND. I.NE.J ) THEN
241 CTEMP = CTEMP*DL( I ) / DL( J )
242 ELSE IF( IGRADE.EQ.5 ) THEN
243 CTEMP = CTEMP*DL( I )*DCONJG( DL( J ) )
244 ELSE IF( IGRADE.EQ.6 ) THEN
245 CTEMP = CTEMP*DL( I )*DL( J )
246 END IF
247 ZLATM3 = CTEMP
248 RETURN
249 *
250 * End of ZLATM3
251 *
252 END
2 $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
3 $ SPARSE )
4 *
5 * -- LAPACK auxiliary test routine (version 3.1) --
6 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
7 * June 2010
8 *
9 * .. Scalar Arguments ..
10 *
11 INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
12 $ KU, M, N
13 DOUBLE PRECISION SPARSE
14 * ..
15 *
16 * .. Array Arguments ..
17 *
18 INTEGER ISEED( 4 ), IWORK( * )
19 COMPLEX*16 D( * ), DL( * ), DR( * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of
26 * dimension (M, N) described by the other paramters. (ISUB,JSUB)
27 * is the final position of the (I,J) entry after pivoting
28 * according to IPVTNG and IWORK. ZLATM3 is called by the
29 * ZLATMR routine in order to build random test matrices. No error
30 * checking on parameters is done, because this routine is called in
31 * a tight loop by ZLATMR which has already checked the parameters.
32 *
33 * Use of ZLATM3 differs from CLATM2 in the order in which the random
34 * number generator is called to fill in random matrix entries.
35 * With ZLATM2, the generator is called to fill in the pivoted matrix
36 * columnwise. With ZLATM3, the generator is called to fill in the
37 * matrix columnwise, after which it is pivoted. Thus, ZLATM3 can
38 * be used to construct random matrices which differ only in their
39 * order of rows and/or columns. ZLATM2 is used to construct band
40 * matrices while avoiding calling the random number generator for
41 * entries outside the band (and therefore generating random numbers
42 * in different orders for different pivot orders).
43 *
44 * The matrix whose (ISUB,JSUB) entry is returned is constructed as
45 * follows (this routine only computes one entry):
46 *
47 * If ISUB is outside (1..M) or JSUB is outside (1..N), return zero
48 * (this is convenient for generating matrices in band format).
49 *
50 * Generate a matrix A with random entries of distribution IDIST.
51 *
52 * Set the diagonal to D.
53 *
54 * Grade the matrix, if desired, from the left (by DL) and/or
55 * from the right (by DR or DL) as specified by IGRADE.
56 *
57 * Permute, if desired, the rows and/or columns as specified by
58 * IPVTNG and IWORK.
59 *
60 * Band the matrix to have lower bandwidth KL and upper
61 * bandwidth KU.
62 *
63 * Set random entries to zero as specified by SPARSE.
64 *
65 * Arguments
66 * =========
67 *
68 * M (input) INTEGER
69 * Number of rows of matrix. Not modified.
70 *
71 * N (input) INTEGER
72 * Number of columns of matrix. Not modified.
73 *
74 * I (input) INTEGER
75 * Row of unpivoted entry to be returned. Not modified.
76 *
77 * J (input) INTEGER
78 * Column of unpivoted entry to be returned. Not modified.
79 *
80 * ISUB (input/output) INTEGER
81 * Row of pivoted entry to be returned. Changed on exit.
82 *
83 * JSUB (input/output) INTEGER
84 * Column of pivoted entry to be returned. Changed on exit.
85 *
86 * KL (input) INTEGER
87 * Lower bandwidth. Not modified.
88 *
89 * KU (input) INTEGER
90 * Upper bandwidth. Not modified.
91 *
92 * IDIST (input) INTEGER
93 * On entry, IDIST specifies the type of distribution to be
94 * used to generate a random matrix .
95 * 1 => real and imaginary parts each UNIFORM( 0, 1 )
96 * 2 => real and imaginary parts each UNIFORM( -1, 1 )
97 * 3 => real and imaginary parts each NORMAL( 0, 1 )
98 * 4 => complex number uniform in DISK( 0 , 1 )
99 * Not modified.
100 *
101 * ISEED (input/output) INTEGER array of dimension ( 4 )
102 * Seed for random number generator.
103 * Changed on exit.
104 *
105 * D (input) COMPLEX*16 array of dimension ( MIN( I , J ) )
106 * Diagonal entries of matrix. Not modified.
107 *
108 * IGRADE (input) INTEGER
109 * Specifies grading of matrix as follows:
110 * 0 => no grading
111 * 1 => matrix premultiplied by diag( DL )
112 * 2 => matrix postmultiplied by diag( DR )
113 * 3 => matrix premultiplied by diag( DL ) and
114 * postmultiplied by diag( DR )
115 * 4 => matrix premultiplied by diag( DL ) and
116 * postmultiplied by inv( diag( DL ) )
117 * 5 => matrix premultiplied by diag( DL ) and
118 * postmultiplied by diag( CONJG(DL) )
119 * 6 => matrix premultiplied by diag( DL ) and
120 * postmultiplied by diag( DL )
121 * Not modified.
122 *
123 * DL (input) COMPLEX*16 array ( I or J, as appropriate )
124 * Left scale factors for grading matrix. Not modified.
125 *
126 * DR (input) COMPLEX*16 array ( I or J, as appropriate )
127 * Right scale factors for grading matrix. Not modified.
128 *
129 * IPVTNG (input) INTEGER
130 * On entry specifies pivoting permutations as follows:
131 * 0 => none.
132 * 1 => row pivoting.
133 * 2 => column pivoting.
134 * 3 => full pivoting, i.e., on both sides.
135 * Not modified.
136 *
137 * IWORK (input) INTEGER array ( I or J, as appropriate )
138 * This array specifies the permutation used. The
139 * row (or column) originally in position K is in
140 * position IWORK( K ) after pivoting.
141 * This differs from IWORK for ZLATM2. Not modified.
142 *
143 * SPARSE (input) DOUBLE PRECISION between 0. and 1.
144 * On entry specifies the sparsity of the matrix
145 * if sparse matix is to be generated.
146 * SPARSE should lie between 0 and 1.
147 * A uniform ( 0, 1 ) random number x is generated and
148 * compared to SPARSE; if x is larger the matrix entry
149 * is unchanged and if x is smaller the entry is set
150 * to zero. Thus on the average a fraction SPARSE of the
151 * entries will be set to zero.
152 * Not modified.
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157 *
158 DOUBLE PRECISION ZERO
159 PARAMETER ( ZERO = 0.0D0 )
160 COMPLEX*16 CZERO
161 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ) )
162 * ..
163 *
164 * .. Local Scalars ..
165 *
166 COMPLEX*16 CTEMP
167 * ..
168 *
169 * .. External Functions ..
170 *
171 DOUBLE PRECISION DLARAN
172 COMPLEX*16 ZLARND
173 EXTERNAL DLARAN, ZLARND
174 * ..
175 *
176 * .. Intrinsic Functions ..
177 *
178 INTRINSIC DCONJG
179 * ..
180 *
181 *-----------------------------------------------------------------------
182 *
183 * .. Executable Statements ..
184 *
185 *
186 * Check for I and J in range
187 *
188 IF( I.LT.1 .OR. I.GT.M .OR. J.LT.1 .OR. J.GT.N ) THEN
189 ISUB = I
190 JSUB = J
191 ZLATM3 = CZERO
192 RETURN
193 END IF
194 *
195 * Compute subscripts depending on IPVTNG
196 *
197 IF( IPVTNG.EQ.0 ) THEN
198 ISUB = I
199 JSUB = J
200 ELSE IF( IPVTNG.EQ.1 ) THEN
201 ISUB = IWORK( I )
202 JSUB = J
203 ELSE IF( IPVTNG.EQ.2 ) THEN
204 ISUB = I
205 JSUB = IWORK( J )
206 ELSE IF( IPVTNG.EQ.3 ) THEN
207 ISUB = IWORK( I )
208 JSUB = IWORK( J )
209 END IF
210 *
211 * Check for banding
212 *
213 IF( JSUB.GT.ISUB+KU .OR. JSUB.LT.ISUB-KL ) THEN
214 ZLATM3 = CZERO
215 RETURN
216 END IF
217 *
218 * Check for sparsity
219 *
220 IF( SPARSE.GT.ZERO ) THEN
221 IF( DLARAN( ISEED ).LT.SPARSE ) THEN
222 ZLATM3 = CZERO
223 RETURN
224 END IF
225 END IF
226 *
227 * Compute entry and grade it according to IGRADE
228 *
229 IF( I.EQ.J ) THEN
230 CTEMP = D( I )
231 ELSE
232 CTEMP = ZLARND( IDIST, ISEED )
233 END IF
234 IF( IGRADE.EQ.1 ) THEN
235 CTEMP = CTEMP*DL( I )
236 ELSE IF( IGRADE.EQ.2 ) THEN
237 CTEMP = CTEMP*DR( J )
238 ELSE IF( IGRADE.EQ.3 ) THEN
239 CTEMP = CTEMP*DL( I )*DR( J )
240 ELSE IF( IGRADE.EQ.4 .AND. I.NE.J ) THEN
241 CTEMP = CTEMP*DL( I ) / DL( J )
242 ELSE IF( IGRADE.EQ.5 ) THEN
243 CTEMP = CTEMP*DL( I )*DCONJG( DL( J ) )
244 ELSE IF( IGRADE.EQ.6 ) THEN
245 CTEMP = CTEMP*DL( I )*DL( J )
246 END IF
247 ZLATM3 = CTEMP
248 RETURN
249 *
250 * End of ZLATM3
251 *
252 END