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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) 00002 * 00003 * -- LAPACK auxiliary test routine (version 3.1) -- 00004 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00005 * November 2006 00006 * 00007 * .. Scalar Arguments .. 00008 INTEGER INFO, KL, KU, LDA, M, N 00009 * .. 00010 * .. Array Arguments .. 00011 INTEGER ISEED( 4 ) 00012 DOUBLE PRECISION D( * ) 00013 COMPLEX*16 A( LDA, * ), WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * ZLAGGE generates a complex general m by n matrix A, by pre- and post- 00020 * multiplying a real diagonal matrix D with random unitary matrices: 00021 * A = U*D*V. The lower and upper bandwidths may then be reduced to 00022 * kl and ku by additional unitary transformations. 00023 * 00024 * Arguments 00025 * ========= 00026 * 00027 * M (input) INTEGER 00028 * The number of rows of the matrix A. M >= 0. 00029 * 00030 * N (input) INTEGER 00031 * The number of columns of the matrix A. N >= 0. 00032 * 00033 * KL (input) INTEGER 00034 * The number of nonzero subdiagonals within the band of A. 00035 * 0 <= KL <= M-1. 00036 * 00037 * KU (input) INTEGER 00038 * The number of nonzero superdiagonals within the band of A. 00039 * 0 <= KU <= N-1. 00040 * 00041 * D (input) DOUBLE PRECISION array, dimension (min(M,N)) 00042 * The diagonal elements of the diagonal matrix D. 00043 * 00044 * A (output) COMPLEX*16 array, dimension (LDA,N) 00045 * The generated m by n matrix A. 00046 * 00047 * LDA (input) INTEGER 00048 * The leading dimension of the array A. LDA >= M. 00049 * 00050 * ISEED (input/output) INTEGER array, dimension (4) 00051 * On entry, the seed of the random number generator; the array 00052 * elements must be between 0 and 4095, and ISEED(4) must be 00053 * odd. 00054 * On exit, the seed is updated. 00055 * 00056 * WORK (workspace) COMPLEX*16 array, dimension (M+N) 00057 * 00058 * INFO (output) INTEGER 00059 * = 0: successful exit 00060 * < 0: if INFO = -i, the i-th argument had an illegal value 00061 * 00062 * ===================================================================== 00063 * 00064 * .. Parameters .. 00065 COMPLEX*16 ZERO, ONE 00066 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), 00067 $ ONE = ( 1.0D+0, 0.0D+0 ) ) 00068 * .. 00069 * .. Local Scalars .. 00070 INTEGER I, J 00071 DOUBLE PRECISION WN 00072 COMPLEX*16 TAU, WA, WB 00073 * .. 00074 * .. External Subroutines .. 00075 EXTERNAL XERBLA, ZGEMV, ZGERC, ZLACGV, ZLARNV, ZSCAL 00076 * .. 00077 * .. Intrinsic Functions .. 00078 INTRINSIC ABS, DBLE, MAX, MIN 00079 * .. 00080 * .. External Functions .. 00081 DOUBLE PRECISION DZNRM2 00082 EXTERNAL DZNRM2 00083 * .. 00084 * .. Executable Statements .. 00085 * 00086 * Test the input arguments 00087 * 00088 INFO = 0 00089 IF( M.LT.0 ) THEN 00090 INFO = -1 00091 ELSE IF( N.LT.0 ) THEN 00092 INFO = -2 00093 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN 00094 INFO = -3 00095 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN 00096 INFO = -4 00097 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00098 INFO = -7 00099 END IF 00100 IF( INFO.LT.0 ) THEN 00101 CALL XERBLA( 'ZLAGGE', -INFO ) 00102 RETURN 00103 END IF 00104 * 00105 * initialize A to diagonal matrix 00106 * 00107 DO 20 J = 1, N 00108 DO 10 I = 1, M 00109 A( I, J ) = ZERO 00110 10 CONTINUE 00111 20 CONTINUE 00112 DO 30 I = 1, MIN( M, N ) 00113 A( I, I ) = D( I ) 00114 30 CONTINUE 00115 * 00116 * pre- and post-multiply A by random unitary matrices 00117 * 00118 DO 40 I = MIN( M, N ), 1, -1 00119 IF( I.LT.M ) THEN 00120 * 00121 * generate random reflection 00122 * 00123 CALL ZLARNV( 3, ISEED, M-I+1, WORK ) 00124 WN = DZNRM2( M-I+1, WORK, 1 ) 00125 WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 ) 00126 IF( WN.EQ.ZERO ) THEN 00127 TAU = ZERO 00128 ELSE 00129 WB = WORK( 1 ) + WA 00130 CALL ZSCAL( M-I, ONE / WB, WORK( 2 ), 1 ) 00131 WORK( 1 ) = ONE 00132 TAU = DBLE( WB / WA ) 00133 END IF 00134 * 00135 * multiply A(i:m,i:n) by random reflection from the left 00136 * 00137 CALL ZGEMV( 'Conjugate transpose', M-I+1, N-I+1, ONE, 00138 $ A( I, I ), LDA, WORK, 1, ZERO, WORK( M+1 ), 1 ) 00139 CALL ZGERC( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1, 00140 $ A( I, I ), LDA ) 00141 END IF 00142 IF( I.LT.N ) THEN 00143 * 00144 * generate random reflection 00145 * 00146 CALL ZLARNV( 3, ISEED, N-I+1, WORK ) 00147 WN = DZNRM2( N-I+1, WORK, 1 ) 00148 WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 ) 00149 IF( WN.EQ.ZERO ) THEN 00150 TAU = ZERO 00151 ELSE 00152 WB = WORK( 1 ) + WA 00153 CALL ZSCAL( N-I, ONE / WB, WORK( 2 ), 1 ) 00154 WORK( 1 ) = ONE 00155 TAU = DBLE( WB / WA ) 00156 END IF 00157 * 00158 * multiply A(i:m,i:n) by random reflection from the right 00159 * 00160 CALL ZGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ), 00161 $ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 ) 00162 CALL ZGERC( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, 00163 $ A( I, I ), LDA ) 00164 END IF 00165 40 CONTINUE 00166 * 00167 * Reduce number of subdiagonals to KL and number of superdiagonals 00168 * to KU 00169 * 00170 DO 70 I = 1, MAX( M-1-KL, N-1-KU ) 00171 IF( KL.LE.KU ) THEN 00172 * 00173 * annihilate subdiagonal elements first (necessary if KL = 0) 00174 * 00175 IF( I.LE.MIN( M-1-KL, N ) ) THEN 00176 * 00177 * generate reflection to annihilate A(kl+i+1:m,i) 00178 * 00179 WN = DZNRM2( M-KL-I+1, A( KL+I, I ), 1 ) 00180 WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I ) 00181 IF( WN.EQ.ZERO ) THEN 00182 TAU = ZERO 00183 ELSE 00184 WB = A( KL+I, I ) + WA 00185 CALL ZSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) 00186 A( KL+I, I ) = ONE 00187 TAU = DBLE( WB / WA ) 00188 END IF 00189 * 00190 * apply reflection to A(kl+i:m,i+1:n) from the left 00191 * 00192 CALL ZGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE, 00193 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, 00194 $ WORK, 1 ) 00195 CALL ZGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 00196 $ 1, A( KL+I, I+1 ), LDA ) 00197 A( KL+I, I ) = -WA 00198 END IF 00199 * 00200 IF( I.LE.MIN( N-1-KU, M ) ) THEN 00201 * 00202 * generate reflection to annihilate A(i,ku+i+1:n) 00203 * 00204 WN = DZNRM2( N-KU-I+1, A( I, KU+I ), LDA ) 00205 WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I ) 00206 IF( WN.EQ.ZERO ) THEN 00207 TAU = ZERO 00208 ELSE 00209 WB = A( I, KU+I ) + WA 00210 CALL ZSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) 00211 A( I, KU+I ) = ONE 00212 TAU = DBLE( WB / WA ) 00213 END IF 00214 * 00215 * apply reflection to A(i+1:m,ku+i:n) from the right 00216 * 00217 CALL ZLACGV( N-KU-I+1, A( I, KU+I ), LDA ) 00218 CALL ZGEMV( 'No transpose', M-I, N-KU-I+1, ONE, 00219 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, 00220 $ WORK, 1 ) 00221 CALL ZGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), 00222 $ LDA, A( I+1, KU+I ), LDA ) 00223 A( I, KU+I ) = -WA 00224 END IF 00225 ELSE 00226 * 00227 * annihilate superdiagonal elements first (necessary if 00228 * KU = 0) 00229 * 00230 IF( I.LE.MIN( N-1-KU, M ) ) THEN 00231 * 00232 * generate reflection to annihilate A(i,ku+i+1:n) 00233 * 00234 WN = DZNRM2( N-KU-I+1, A( I, KU+I ), LDA ) 00235 WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I ) 00236 IF( WN.EQ.ZERO ) THEN 00237 TAU = ZERO 00238 ELSE 00239 WB = A( I, KU+I ) + WA 00240 CALL ZSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) 00241 A( I, KU+I ) = ONE 00242 TAU = DBLE( WB / WA ) 00243 END IF 00244 * 00245 * apply reflection to A(i+1:m,ku+i:n) from the right 00246 * 00247 CALL ZLACGV( N-KU-I+1, A( I, KU+I ), LDA ) 00248 CALL ZGEMV( 'No transpose', M-I, N-KU-I+1, ONE, 00249 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, 00250 $ WORK, 1 ) 00251 CALL ZGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), 00252 $ LDA, A( I+1, KU+I ), LDA ) 00253 A( I, KU+I ) = -WA 00254 END IF 00255 * 00256 IF( I.LE.MIN( M-1-KL, N ) ) THEN 00257 * 00258 * generate reflection to annihilate A(kl+i+1:m,i) 00259 * 00260 WN = DZNRM2( M-KL-I+1, A( KL+I, I ), 1 ) 00261 WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I ) 00262 IF( WN.EQ.ZERO ) THEN 00263 TAU = ZERO 00264 ELSE 00265 WB = A( KL+I, I ) + WA 00266 CALL ZSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) 00267 A( KL+I, I ) = ONE 00268 TAU = DBLE( WB / WA ) 00269 END IF 00270 * 00271 * apply reflection to A(kl+i:m,i+1:n) from the left 00272 * 00273 CALL ZGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE, 00274 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, 00275 $ WORK, 1 ) 00276 CALL ZGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 00277 $ 1, A( KL+I, I+1 ), LDA ) 00278 A( KL+I, I ) = -WA 00279 END IF 00280 END IF 00281 * 00282 DO 50 J = KL + I + 1, M 00283 A( J, I ) = ZERO 00284 50 CONTINUE 00285 * 00286 DO 60 J = KU + I + 1, N 00287 A( I, J ) = ZERO 00288 60 CONTINUE 00289 70 CONTINUE 00290 RETURN 00291 * 00292 * End of ZLAGGE 00293 * 00294 END
1.7.3 
