LAPACK 3.3.1 Linear Algebra PACKage

# dlagge.f

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```00001       SUBROUTINE DLAGGE( 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   A( LDA, * ), D( * ), WORK( * )
00013 *     ..
00014 *
00015 *  Purpose
00016 *  =======
00017 *
00018 *  DLAGGE generates a real general m by n matrix A, by pre- and post-
00019 *  multiplying a real diagonal matrix D with random orthogonal matrices:
00020 *  A = U*D*V. The lower and upper bandwidths may then be reduced to
00021 *  kl and ku by additional orthogonal transformations.
00022 *
00023 *  Arguments
00024 *  =========
00025 *
00026 *  M       (input) INTEGER
00027 *          The number of rows of the matrix A.  M >= 0.
00028 *
00029 *  N       (input) INTEGER
00030 *          The number of columns of the matrix A.  N >= 0.
00031 *
00032 *  KL      (input) INTEGER
00033 *          The number of nonzero subdiagonals within the band of A.
00034 *          0 <= KL <= M-1.
00035 *
00036 *  KU      (input) INTEGER
00037 *          The number of nonzero superdiagonals within the band of A.
00038 *          0 <= KU <= N-1.
00039 *
00040 *  D       (input) DOUBLE PRECISION array, dimension (min(M,N))
00041 *          The diagonal elements of the diagonal matrix D.
00042 *
00043 *  A       (output) DOUBLE PRECISION array, dimension (LDA,N)
00044 *          The generated m by n matrix A.
00045 *
00046 *  LDA     (input) INTEGER
00047 *          The leading dimension of the array A.  LDA >= M.
00048 *
00049 *  ISEED   (input/output) INTEGER array, dimension (4)
00050 *          On entry, the seed of the random number generator; the array
00051 *          elements must be between 0 and 4095, and ISEED(4) must be
00052 *          odd.
00053 *          On exit, the seed is updated.
00054 *
00055 *  WORK    (workspace) DOUBLE PRECISION array, dimension (M+N)
00056 *
00057 *  INFO    (output) INTEGER
00058 *          = 0: successful exit
00059 *          < 0: if INFO = -i, the i-th argument had an illegal value
00060 *
00061 *  =====================================================================
00062 *
00063 *     .. Parameters ..
00064       DOUBLE PRECISION   ZERO, ONE
00065       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00066 *     ..
00067 *     .. Local Scalars ..
00068       INTEGER            I, J
00069       DOUBLE PRECISION   TAU, WA, WB, WN
00070 *     ..
00071 *     .. External Subroutines ..
00072       EXTERNAL           DGEMV, DGER, DLARNV, DSCAL, XERBLA
00073 *     ..
00074 *     .. Intrinsic Functions ..
00075       INTRINSIC          MAX, MIN, SIGN
00076 *     ..
00077 *     .. External Functions ..
00078       DOUBLE PRECISION   DNRM2
00079       EXTERNAL           DNRM2
00080 *     ..
00081 *     .. Executable Statements ..
00082 *
00083 *     Test the input arguments
00084 *
00085       INFO = 0
00086       IF( M.LT.0 ) THEN
00087          INFO = -1
00088       ELSE IF( N.LT.0 ) THEN
00089          INFO = -2
00090       ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
00091          INFO = -3
00092       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00093          INFO = -4
00094       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00095          INFO = -7
00096       END IF
00097       IF( INFO.LT.0 ) THEN
00098          CALL XERBLA( 'DLAGGE', -INFO )
00099          RETURN
00100       END IF
00101 *
00102 *     initialize A to diagonal matrix
00103 *
00104       DO 20 J = 1, N
00105          DO 10 I = 1, M
00106             A( I, J ) = ZERO
00107    10    CONTINUE
00108    20 CONTINUE
00109       DO 30 I = 1, MIN( M, N )
00110          A( I, I ) = D( I )
00111    30 CONTINUE
00112 *
00113 *     pre- and post-multiply A by random orthogonal matrices
00114 *
00115       DO 40 I = MIN( M, N ), 1, -1
00116          IF( I.LT.M ) THEN
00117 *
00118 *           generate random reflection
00119 *
00120             CALL DLARNV( 3, ISEED, M-I+1, WORK )
00121             WN = DNRM2( M-I+1, WORK, 1 )
00122             WA = SIGN( WN, WORK( 1 ) )
00123             IF( WN.EQ.ZERO ) THEN
00124                TAU = ZERO
00125             ELSE
00126                WB = WORK( 1 ) + WA
00127                CALL DSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
00128                WORK( 1 ) = ONE
00129                TAU = WB / WA
00130             END IF
00131 *
00132 *           multiply A(i:m,i:n) by random reflection from the left
00133 *
00134             CALL DGEMV( 'Transpose', M-I+1, N-I+1, ONE, A( I, I ), LDA,
00135      \$                  WORK, 1, ZERO, WORK( M+1 ), 1 )
00136             CALL DGER( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
00137      \$                 A( I, I ), LDA )
00138          END IF
00139          IF( I.LT.N ) THEN
00140 *
00141 *           generate random reflection
00142 *
00143             CALL DLARNV( 3, ISEED, N-I+1, WORK )
00144             WN = DNRM2( N-I+1, WORK, 1 )
00145             WA = SIGN( WN, WORK( 1 ) )
00146             IF( WN.EQ.ZERO ) THEN
00147                TAU = ZERO
00148             ELSE
00149                WB = WORK( 1 ) + WA
00150                CALL DSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
00151                WORK( 1 ) = ONE
00152                TAU = WB / WA
00153             END IF
00154 *
00155 *           multiply A(i:m,i:n) by random reflection from the right
00156 *
00157             CALL DGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
00158      \$                  LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
00159             CALL DGER( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
00160      \$                 A( I, I ), LDA )
00161          END IF
00162    40 CONTINUE
00163 *
00164 *     Reduce number of subdiagonals to KL and number of superdiagonals
00165 *     to KU
00166 *
00167       DO 70 I = 1, MAX( M-1-KL, N-1-KU )
00168          IF( KL.LE.KU ) THEN
00169 *
00170 *           annihilate subdiagonal elements first (necessary if KL = 0)
00171 *
00172             IF( I.LE.MIN( M-1-KL, N ) ) THEN
00173 *
00174 *              generate reflection to annihilate A(kl+i+1:m,i)
00175 *
00176                WN = DNRM2( M-KL-I+1, A( KL+I, I ), 1 )
00177                WA = SIGN( WN, A( KL+I, I ) )
00178                IF( WN.EQ.ZERO ) THEN
00179                   TAU = ZERO
00180                ELSE
00181                   WB = A( KL+I, I ) + WA
00182                   CALL DSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
00183                   A( KL+I, I ) = ONE
00184                   TAU = WB / WA
00185                END IF
00186 *
00187 *              apply reflection to A(kl+i:m,i+1:n) from the left
00188 *
00189                CALL DGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
00190      \$                     A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
00191      \$                     WORK, 1 )
00192                CALL DGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
00193      \$                    A( KL+I, I+1 ), LDA )
00194                A( KL+I, I ) = -WA
00195             END IF
00196 *
00197             IF( I.LE.MIN( N-1-KU, M ) ) THEN
00198 *
00199 *              generate reflection to annihilate A(i,ku+i+1:n)
00200 *
00201                WN = DNRM2( N-KU-I+1, A( I, KU+I ), LDA )
00202                WA = SIGN( WN, A( I, KU+I ) )
00203                IF( WN.EQ.ZERO ) THEN
00204                   TAU = ZERO
00205                ELSE
00206                   WB = A( I, KU+I ) + WA
00207                   CALL DSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
00208                   A( I, KU+I ) = ONE
00209                   TAU = WB / WA
00210                END IF
00211 *
00212 *              apply reflection to A(i+1:m,ku+i:n) from the right
00213 *
00214                CALL DGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
00215      \$                     A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
00216      \$                     WORK, 1 )
00217                CALL DGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
00218      \$                    LDA, A( I+1, KU+I ), LDA )
00219                A( I, KU+I ) = -WA
00220             END IF
00221          ELSE
00222 *
00223 *           annihilate superdiagonal elements first (necessary if
00224 *           KU = 0)
00225 *
00226             IF( I.LE.MIN( N-1-KU, M ) ) THEN
00227 *
00228 *              generate reflection to annihilate A(i,ku+i+1:n)
00229 *
00230                WN = DNRM2( N-KU-I+1, A( I, KU+I ), LDA )
00231                WA = SIGN( WN, A( I, KU+I ) )
00232                IF( WN.EQ.ZERO ) THEN
00233                   TAU = ZERO
00234                ELSE
00235                   WB = A( I, KU+I ) + WA
00236                   CALL DSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
00237                   A( I, KU+I ) = ONE
00238                   TAU = WB / WA
00239                END IF
00240 *
00241 *              apply reflection to A(i+1:m,ku+i:n) from the right
00242 *
00243                CALL DGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
00244      \$                     A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
00245      \$                     WORK, 1 )
00246                CALL DGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
00247      \$                    LDA, A( I+1, KU+I ), LDA )
00248                A( I, KU+I ) = -WA
00249             END IF
00250 *
00251             IF( I.LE.MIN( M-1-KL, N ) ) THEN
00252 *
00253 *              generate reflection to annihilate A(kl+i+1:m,i)
00254 *
00255                WN = DNRM2( M-KL-I+1, A( KL+I, I ), 1 )
00256                WA = SIGN( WN, A( KL+I, I ) )
00257                IF( WN.EQ.ZERO ) THEN
00258                   TAU = ZERO
00259                ELSE
00260                   WB = A( KL+I, I ) + WA
00261                   CALL DSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
00262                   A( KL+I, I ) = ONE
00263                   TAU = WB / WA
00264                END IF
00265 *
00266 *              apply reflection to A(kl+i:m,i+1:n) from the left
00267 *
00268                CALL DGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
00269      \$                     A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
00270      \$                     WORK, 1 )
00271                CALL DGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
00272      \$                    A( KL+I, I+1 ), LDA )
00273                A( KL+I, I ) = -WA
00274             END IF
00275          END IF
00276 *
00277          DO 50 J = KL + I + 1, M
00278             A( J, I ) = ZERO
00279    50    CONTINUE
00280 *
00281          DO 60 J = KU + I + 1, N
00282             A( I, J ) = ZERO
00283    60    CONTINUE
00284    70 CONTINUE
00285       RETURN
00286 *
00287 *     End of DLAGGE
00288 *
00289       END
```