LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clagsy.f
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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
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