LAPACK 3.3.1
Linear Algebra PACKage

zlaghe.f

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00001       SUBROUTINE ZLAGHE( N, K, 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, K, LDA, 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 *  ZLAGHE generates a complex hermitian matrix A, by pre- and post-
00020 *  multiplying a real diagonal matrix D with a random unitary matrix:
00021 *  A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
00022 *  unitary transformations.
00023 *
00024 *  Arguments
00025 *  =========
00026 *
00027 *  N       (input) INTEGER
00028 *          The order of the matrix A.  N >= 0.
00029 *
00030 *  K       (input) INTEGER
00031 *          The number of nonzero subdiagonals within the band of A.
00032 *          0 <= K <= N-1.
00033 *
00034 *  D       (input) DOUBLE PRECISION array, dimension (N)
00035 *          The diagonal elements of the diagonal matrix D.
00036 *
00037 *  A       (output) COMPLEX*16 array, dimension (LDA,N)
00038 *          The generated n by n hermitian matrix A (the full matrix is
00039 *          stored).
00040 *
00041 *  LDA     (input) INTEGER
00042 *          The leading dimension of the array A.  LDA >= N.
00043 *
00044 *  ISEED   (input/output) INTEGER array, dimension (4)
00045 *          On entry, the seed of the random number generator; the array
00046 *          elements must be between 0 and 4095, and ISEED(4) must be
00047 *          odd.
00048 *          On exit, the seed is updated.
00049 *
00050 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00051 *
00052 *  INFO    (output) INTEGER
00053 *          = 0: successful exit
00054 *          < 0: if INFO = -i, the i-th argument had an illegal value
00055 *
00056 *  =====================================================================
00057 *
00058 *     .. Parameters ..
00059       COMPLEX*16         ZERO, ONE, HALF
00060       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
00061      $                   ONE = ( 1.0D+0, 0.0D+0 ),
00062      $                   HALF = ( 0.5D+0, 0.0D+0 ) )
00063 *     ..
00064 *     .. Local Scalars ..
00065       INTEGER            I, J
00066       DOUBLE PRECISION   WN
00067       COMPLEX*16         ALPHA, TAU, WA, WB
00068 *     ..
00069 *     .. External Subroutines ..
00070       EXTERNAL           XERBLA, ZAXPY, ZGEMV, ZGERC, ZHEMV, ZHER2,
00071      $                   ZLARNV, ZSCAL
00072 *     ..
00073 *     .. External Functions ..
00074       DOUBLE PRECISION   DZNRM2
00075       COMPLEX*16         ZDOTC
00076       EXTERNAL           DZNRM2, ZDOTC
00077 *     ..
00078 *     .. Intrinsic Functions ..
00079       INTRINSIC          ABS, DBLE, DCONJG, MAX
00080 *     ..
00081 *     .. Executable Statements ..
00082 *
00083 *     Test the input arguments
00084 *
00085       INFO = 0
00086       IF( N.LT.0 ) THEN
00087          INFO = -1
00088       ELSE IF( K.LT.0 .OR. K.GT.N-1 ) THEN
00089          INFO = -2
00090       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00091          INFO = -5
00092       END IF
00093       IF( INFO.LT.0 ) THEN
00094          CALL XERBLA( 'ZLAGHE', -INFO )
00095          RETURN
00096       END IF
00097 *
00098 *     initialize lower triangle of A to diagonal matrix
00099 *
00100       DO 20 J = 1, N
00101          DO 10 I = J + 1, N
00102             A( I, J ) = ZERO
00103    10    CONTINUE
00104    20 CONTINUE
00105       DO 30 I = 1, N
00106          A( I, I ) = D( I )
00107    30 CONTINUE
00108 *
00109 *     Generate lower triangle of hermitian matrix
00110 *
00111       DO 40 I = N - 1, 1, -1
00112 *
00113 *        generate random reflection
00114 *
00115          CALL ZLARNV( 3, ISEED, N-I+1, WORK )
00116          WN = DZNRM2( N-I+1, WORK, 1 )
00117          WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
00118          IF( WN.EQ.ZERO ) THEN
00119             TAU = ZERO
00120          ELSE
00121             WB = WORK( 1 ) + WA
00122             CALL ZSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
00123             WORK( 1 ) = ONE
00124             TAU = DBLE( WB / WA )
00125          END IF
00126 *
00127 *        apply random reflection to A(i:n,i:n) from the left
00128 *        and the right
00129 *
00130 *        compute  y := tau * A * u
00131 *
00132          CALL ZHEMV( 'Lower', N-I+1, TAU, A( I, I ), LDA, WORK, 1, ZERO,
00133      $               WORK( N+1 ), 1 )
00134 *
00135 *        compute  v := y - 1/2 * tau * ( y, u ) * u
00136 *
00137          ALPHA = -HALF*TAU*ZDOTC( N-I+1, WORK( N+1 ), 1, WORK, 1 )
00138          CALL ZAXPY( N-I+1, ALPHA, WORK, 1, WORK( N+1 ), 1 )
00139 *
00140 *        apply the transformation as a rank-2 update to A(i:n,i:n)
00141 *
00142          CALL ZHER2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
00143      $               A( I, I ), LDA )
00144    40 CONTINUE
00145 *
00146 *     Reduce number of subdiagonals to K
00147 *
00148       DO 60 I = 1, N - 1 - K
00149 *
00150 *        generate reflection to annihilate A(k+i+1:n,i)
00151 *
00152          WN = DZNRM2( N-K-I+1, A( K+I, I ), 1 )
00153          WA = ( WN / ABS( A( K+I, I ) ) )*A( K+I, I )
00154          IF( WN.EQ.ZERO ) THEN
00155             TAU = ZERO
00156          ELSE
00157             WB = A( K+I, I ) + WA
00158             CALL ZSCAL( N-K-I, ONE / WB, A( K+I+1, I ), 1 )
00159             A( K+I, I ) = ONE
00160             TAU = DBLE( WB / WA )
00161          END IF
00162 *
00163 *        apply reflection to A(k+i:n,i+1:k+i-1) from the left
00164 *
00165          CALL ZGEMV( 'Conjugate transpose', N-K-I+1, K-1, ONE,
00166      $               A( K+I, I+1 ), LDA, A( K+I, I ), 1, ZERO, WORK, 1 )
00167          CALL ZGERC( N-K-I+1, K-1, -TAU, A( K+I, I ), 1, WORK, 1,
00168      $               A( K+I, I+1 ), LDA )
00169 *
00170 *        apply reflection to A(k+i:n,k+i:n) from the left and the right
00171 *
00172 *        compute  y := tau * A * u
00173 *
00174          CALL ZHEMV( 'Lower', N-K-I+1, TAU, A( K+I, K+I ), LDA,
00175      $               A( K+I, I ), 1, ZERO, WORK, 1 )
00176 *
00177 *        compute  v := y - 1/2 * tau * ( y, u ) * u
00178 *
00179          ALPHA = -HALF*TAU*ZDOTC( N-K-I+1, WORK, 1, A( K+I, I ), 1 )
00180          CALL ZAXPY( N-K-I+1, ALPHA, A( K+I, I ), 1, WORK, 1 )
00181 *
00182 *        apply hermitian rank-2 update to A(k+i:n,k+i:n)
00183 *
00184          CALL ZHER2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
00185      $               A( K+I, K+I ), LDA )
00186 *
00187          A( K+I, I ) = -WA
00188          DO 50 J = K + I + 1, N
00189             A( J, I ) = ZERO
00190    50    CONTINUE
00191    60 CONTINUE
00192 *
00193 *     Store full hermitian matrix
00194 *
00195       DO 80 J = 1, N
00196          DO 70 I = J + 1, N
00197             A( J, I ) = DCONJG( A( I, J ) )
00198    70    CONTINUE
00199    80 CONTINUE
00200       RETURN
00201 *
00202 *     End of ZLAGHE
00203 *
00204       END
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