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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLAGSY 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE CLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) 00012 * 00013 * .. Scalar Arguments .. 00014 * INTEGER INFO, K, LDA, N 00015 * .. 00016 * .. Array Arguments .. 00017 * INTEGER ISEED( 4 ) 00018 * REAL D( * ) 00019 * COMPLEX A( LDA, * ), WORK( * ) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> CLAGSY generates a complex symmetric matrix A, by pre- and post- 00029 *> multiplying a real diagonal matrix D with a random unitary matrix: 00030 *> A = U*D*U**T. The semi-bandwidth may then be reduced to k by 00031 *> additional unitary transformations. 00032 *> \endverbatim 00033 * 00034 * Arguments: 00035 * ========== 00036 * 00037 *> \param[in] N 00038 *> \verbatim 00039 *> N is INTEGER 00040 *> The order of the matrix A. N >= 0. 00041 *> \endverbatim 00042 *> 00043 *> \param[in] K 00044 *> \verbatim 00045 *> K is INTEGER 00046 *> The number of nonzero subdiagonals within the band of A. 00047 *> 0 <= K <= N-1. 00048 *> \endverbatim 00049 *> 00050 *> \param[in] D 00051 *> \verbatim 00052 *> D is REAL array, dimension (N) 00053 *> The diagonal elements of the diagonal matrix D. 00054 *> \endverbatim 00055 *> 00056 *> \param[out] A 00057 *> \verbatim 00058 *> A is COMPLEX array, dimension (LDA,N) 00059 *> The generated n by n symmetric matrix A (the full matrix is 00060 *> stored). 00061 *> \endverbatim 00062 *> 00063 *> \param[in] LDA 00064 *> \verbatim 00065 *> LDA is INTEGER 00066 *> The leading dimension of the array A. LDA >= N. 00067 *> \endverbatim 00068 *> 00069 *> \param[in,out] ISEED 00070 *> \verbatim 00071 *> ISEED is INTEGER array, dimension (4) 00072 *> On entry, the seed of the random number generator; the array 00073 *> elements must be between 0 and 4095, and ISEED(4) must be 00074 *> odd. 00075 *> On exit, the seed is updated. 00076 *> \endverbatim 00077 *> 00078 *> \param[out] WORK 00079 *> \verbatim 00080 *> WORK is COMPLEX array, dimension (2*N) 00081 *> \endverbatim 00082 *> 00083 *> \param[out] INFO 00084 *> \verbatim 00085 *> INFO is INTEGER 00086 *> = 0: successful exit 00087 *> < 0: if INFO = -i, the i-th argument had an illegal value 00088 *> \endverbatim 00089 * 00090 * Authors: 00091 * ======== 00092 * 00093 *> \author Univ. of Tennessee 00094 *> \author Univ. of California Berkeley 00095 *> \author Univ. of Colorado Denver 00096 *> \author NAG Ltd. 00097 * 00098 *> \date November 2011 00099 * 00100 *> \ingroup complex_matgen 00101 * 00102 * ===================================================================== 00103 SUBROUTINE CLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) 00104 * 00105 * -- LAPACK auxiliary routine (version 3.4.0) -- 00106 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00108 * November 2011 00109 * 00110 * .. Scalar Arguments .. 00111 INTEGER INFO, K, LDA, N 00112 * .. 00113 * .. Array Arguments .. 00114 INTEGER ISEED( 4 ) 00115 REAL D( * ) 00116 COMPLEX A( LDA, * ), WORK( * ) 00117 * .. 00118 * 00119 * ===================================================================== 00120 * 00121 * .. Parameters .. 00122 COMPLEX ZERO, ONE, HALF 00123 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ), 00124 $ ONE = ( 1.0E+0, 0.0E+0 ), 00125 $ HALF = ( 0.5E+0, 0.0E+0 ) ) 00126 * .. 00127 * .. Local Scalars .. 00128 INTEGER I, II, J, JJ 00129 REAL WN 00130 COMPLEX ALPHA, TAU, WA, WB 00131 * .. 00132 * .. External Subroutines .. 00133 EXTERNAL CAXPY, CGEMV, CGERC, CLACGV, CLARNV, CSCAL, 00134 $ CSYMV, XERBLA 00135 * .. 00136 * .. External Functions .. 00137 REAL SCNRM2 00138 COMPLEX CDOTC 00139 EXTERNAL SCNRM2, CDOTC 00140 * .. 00141 * .. Intrinsic Functions .. 00142 INTRINSIC ABS, MAX, REAL 00143 * .. 00144 * .. Executable Statements .. 00145 * 00146 * Test the input arguments 00147 * 00148 INFO = 0 00149 IF( N.LT.0 ) THEN 00150 INFO = -1 00151 ELSE IF( K.LT.0 .OR. K.GT.N-1 ) THEN 00152 INFO = -2 00153 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00154 INFO = -5 00155 END IF 00156 IF( INFO.LT.0 ) THEN 00157 CALL XERBLA( 'CLAGSY', -INFO ) 00158 RETURN 00159 END IF 00160 * 00161 * initialize lower triangle of A to diagonal matrix 00162 * 00163 DO 20 J = 1, N 00164 DO 10 I = J + 1, N 00165 A( I, J ) = ZERO 00166 10 CONTINUE 00167 20 CONTINUE 00168 DO 30 I = 1, N 00169 A( I, I ) = D( I ) 00170 30 CONTINUE 00171 * 00172 * Generate lower triangle of symmetric matrix 00173 * 00174 DO 60 I = N - 1, 1, -1 00175 * 00176 * generate random reflection 00177 * 00178 CALL CLARNV( 3, ISEED, N-I+1, WORK ) 00179 WN = SCNRM2( N-I+1, WORK, 1 ) 00180 WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 ) 00181 IF( WN.EQ.ZERO ) THEN 00182 TAU = ZERO 00183 ELSE 00184 WB = WORK( 1 ) + WA 00185 CALL CSCAL( N-I, ONE / WB, WORK( 2 ), 1 ) 00186 WORK( 1 ) = ONE 00187 TAU = REAL( WB / WA ) 00188 END IF 00189 * 00190 * apply random reflection to A(i:n,i:n) from the left 00191 * and the right 00192 * 00193 * compute y := tau * A * conjg(u) 00194 * 00195 CALL CLACGV( N-I+1, WORK, 1 ) 00196 CALL CSYMV( 'Lower', N-I+1, TAU, A( I, I ), LDA, WORK, 1, ZERO, 00197 $ WORK( N+1 ), 1 ) 00198 CALL CLACGV( N-I+1, WORK, 1 ) 00199 * 00200 * compute v := y - 1/2 * tau * ( u, y ) * u 00201 * 00202 ALPHA = -HALF*TAU*CDOTC( N-I+1, WORK, 1, WORK( N+1 ), 1 ) 00203 CALL CAXPY( N-I+1, ALPHA, WORK, 1, WORK( N+1 ), 1 ) 00204 * 00205 * apply the transformation as a rank-2 update to A(i:n,i:n) 00206 * 00207 * CALL CSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, 00208 * $ A( I, I ), LDA ) 00209 * 00210 DO 50 JJ = I, N 00211 DO 40 II = JJ, N 00212 A( II, JJ ) = A( II, JJ ) - 00213 $ WORK( II-I+1 )*WORK( N+JJ-I+1 ) - 00214 $ WORK( N+II-I+1 )*WORK( JJ-I+1 ) 00215 40 CONTINUE 00216 50 CONTINUE 00217 60 CONTINUE 00218 * 00219 * Reduce number of subdiagonals to K 00220 * 00221 DO 100 I = 1, N - 1 - K 00222 * 00223 * generate reflection to annihilate A(k+i+1:n,i) 00224 * 00225 WN = SCNRM2( N-K-I+1, A( K+I, I ), 1 ) 00226 WA = ( WN / ABS( A( K+I, I ) ) )*A( K+I, I ) 00227 IF( WN.EQ.ZERO ) THEN 00228 TAU = ZERO 00229 ELSE 00230 WB = A( K+I, I ) + WA 00231 CALL CSCAL( N-K-I, ONE / WB, A( K+I+1, I ), 1 ) 00232 A( K+I, I ) = ONE 00233 TAU = REAL( WB / WA ) 00234 END IF 00235 * 00236 * apply reflection to A(k+i:n,i+1:k+i-1) from the left 00237 * 00238 CALL CGEMV( 'Conjugate transpose', N-K-I+1, K-1, ONE, 00239 $ A( K+I, I+1 ), LDA, A( K+I, I ), 1, ZERO, WORK, 1 ) 00240 CALL CGERC( N-K-I+1, K-1, -TAU, A( K+I, I ), 1, WORK, 1, 00241 $ A( K+I, I+1 ), LDA ) 00242 * 00243 * apply reflection to A(k+i:n,k+i:n) from the left and the right 00244 * 00245 * compute y := tau * A * conjg(u) 00246 * 00247 CALL CLACGV( N-K-I+1, A( K+I, I ), 1 ) 00248 CALL CSYMV( 'Lower', N-K-I+1, TAU, A( K+I, K+I ), LDA, 00249 $ A( K+I, I ), 1, ZERO, WORK, 1 ) 00250 CALL CLACGV( N-K-I+1, A( K+I, I ), 1 ) 00251 * 00252 * compute v := y - 1/2 * tau * ( u, y ) * u 00253 * 00254 ALPHA = -HALF*TAU*CDOTC( N-K-I+1, A( K+I, I ), 1, WORK, 1 ) 00255 CALL CAXPY( N-K-I+1, ALPHA, A( K+I, I ), 1, WORK, 1 ) 00256 * 00257 * apply symmetric rank-2 update to A(k+i:n,k+i:n) 00258 * 00259 * CALL CSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1, 00260 * $ A( K+I, K+I ), LDA ) 00261 * 00262 DO 80 JJ = K + I, N 00263 DO 70 II = JJ, N 00264 A( II, JJ ) = A( II, JJ ) - A( II, I )*WORK( JJ-K-I+1 ) - 00265 $ WORK( II-K-I+1 )*A( JJ, I ) 00266 70 CONTINUE 00267 80 CONTINUE 00268 * 00269 A( K+I, I ) = -WA 00270 DO 90 J = K + I + 1, N 00271 A( J, I ) = ZERO 00272 90 CONTINUE 00273 100 CONTINUE 00274 * 00275 * Store full symmetric matrix 00276 * 00277 DO 120 J = 1, N 00278 DO 110 I = J + 1, N 00279 A( J, I ) = A( I, J ) 00280 110 CONTINUE 00281 120 CONTINUE 00282 RETURN 00283 * 00284 * End of CLAGSY 00285 * 00286 END