LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
slagge.f
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00001 *> \brief \b SLAGGE
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 SLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER            INFO, KL, KU, LDA, M, N
00015 *       ..
00016 *       .. Array Arguments ..
00017 *       INTEGER            ISEED( 4 )
00018 *       REAL               A( LDA, * ), D( * ), WORK( * )
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> SLAGGE generates a real general m by n matrix A, by pre- and post-
00028 *> multiplying a real diagonal matrix D with random orthogonal matrices:
00029 *> A = U*D*V. The lower and upper bandwidths may then be reduced to
00030 *> kl and ku by additional orthogonal transformations.
00031 *> \endverbatim
00032 *
00033 *  Arguments:
00034 *  ==========
00035 *
00036 *> \param[in] M
00037 *> \verbatim
00038 *>          M is INTEGER
00039 *>          The number of rows of the matrix A.  M >= 0.
00040 *> \endverbatim
00041 *>
00042 *> \param[in] N
00043 *> \verbatim
00044 *>          N is INTEGER
00045 *>          The number of columns of the matrix A.  N >= 0.
00046 *> \endverbatim
00047 *>
00048 *> \param[in] KL
00049 *> \verbatim
00050 *>          KL is INTEGER
00051 *>          The number of nonzero subdiagonals within the band of A.
00052 *>          0 <= KL <= M-1.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] KU
00056 *> \verbatim
00057 *>          KU is INTEGER
00058 *>          The number of nonzero superdiagonals within the band of A.
00059 *>          0 <= KU <= N-1.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] D
00063 *> \verbatim
00064 *>          D is REAL array, dimension (min(M,N))
00065 *>          The diagonal elements of the diagonal matrix D.
00066 *> \endverbatim
00067 *>
00068 *> \param[out] A
00069 *> \verbatim
00070 *>          A is REAL array, dimension (LDA,N)
00071 *>          The generated m by n matrix A.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] LDA
00075 *> \verbatim
00076 *>          LDA is INTEGER
00077 *>          The leading dimension of the array A.  LDA >= M.
00078 *> \endverbatim
00079 *>
00080 *> \param[in,out] ISEED
00081 *> \verbatim
00082 *>          ISEED is INTEGER array, dimension (4)
00083 *>          On entry, the seed of the random number generator; the array
00084 *>          elements must be between 0 and 4095, and ISEED(4) must be
00085 *>          odd.
00086 *>          On exit, the seed is updated.
00087 *> \endverbatim
00088 *>
00089 *> \param[out] WORK
00090 *> \verbatim
00091 *>          WORK is REAL array, dimension (M+N)
00092 *> \endverbatim
00093 *>
00094 *> \param[out] INFO
00095 *> \verbatim
00096 *>          INFO is INTEGER
00097 *>          = 0: successful exit
00098 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00099 *> \endverbatim
00100 *
00101 *  Authors:
00102 *  ========
00103 *
00104 *> \author Univ. of Tennessee 
00105 *> \author Univ. of California Berkeley 
00106 *> \author Univ. of Colorado Denver 
00107 *> \author NAG Ltd. 
00108 *
00109 *> \date November 2011
00110 *
00111 *> \ingroup real_matgen
00112 *
00113 *  =====================================================================
00114       SUBROUTINE SLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
00115 *
00116 *  -- LAPACK auxiliary routine (version 3.4.0) --
00117 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00118 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00119 *     November 2011
00120 *
00121 *     .. Scalar Arguments ..
00122       INTEGER            INFO, KL, KU, LDA, M, N
00123 *     ..
00124 *     .. Array Arguments ..
00125       INTEGER            ISEED( 4 )
00126       REAL               A( LDA, * ), D( * ), WORK( * )
00127 *     ..
00128 *
00129 *  =====================================================================
00130 *
00131 *     .. Parameters ..
00132       REAL               ZERO, ONE
00133       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00134 *     ..
00135 *     .. Local Scalars ..
00136       INTEGER            I, J
00137       REAL               TAU, WA, WB, WN
00138 *     ..
00139 *     .. External Subroutines ..
00140       EXTERNAL           SGEMV, SGER, SLARNV, SSCAL, XERBLA
00141 *     ..
00142 *     .. Intrinsic Functions ..
00143       INTRINSIC          MAX, MIN, SIGN
00144 *     ..
00145 *     .. External Functions ..
00146       REAL               SNRM2
00147       EXTERNAL           SNRM2
00148 *     ..
00149 *     .. Executable Statements ..
00150 *
00151 *     Test the input arguments
00152 *
00153       INFO = 0
00154       IF( M.LT.0 ) THEN
00155          INFO = -1
00156       ELSE IF( N.LT.0 ) THEN
00157          INFO = -2
00158       ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
00159          INFO = -3
00160       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00161          INFO = -4
00162       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00163          INFO = -7
00164       END IF
00165       IF( INFO.LT.0 ) THEN
00166          CALL XERBLA( 'SLAGGE', -INFO )
00167          RETURN
00168       END IF
00169 *
00170 *     initialize A to diagonal matrix
00171 *
00172       DO 20 J = 1, N
00173          DO 10 I = 1, M
00174             A( I, J ) = ZERO
00175    10    CONTINUE
00176    20 CONTINUE
00177       DO 30 I = 1, MIN( M, N )
00178          A( I, I ) = D( I )
00179    30 CONTINUE
00180 *
00181 *     pre- and post-multiply A by random orthogonal matrices
00182 *
00183       DO 40 I = MIN( M, N ), 1, -1
00184          IF( I.LT.M ) THEN
00185 *
00186 *           generate random reflection
00187 *
00188             CALL SLARNV( 3, ISEED, M-I+1, WORK )
00189             WN = SNRM2( M-I+1, WORK, 1 )
00190             WA = SIGN( WN, WORK( 1 ) )
00191             IF( WN.EQ.ZERO ) THEN
00192                TAU = ZERO
00193             ELSE
00194                WB = WORK( 1 ) + WA
00195                CALL SSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
00196                WORK( 1 ) = ONE
00197                TAU = WB / WA
00198             END IF
00199 *
00200 *           multiply A(i:m,i:n) by random reflection from the left
00201 *
00202             CALL SGEMV( 'Transpose', M-I+1, N-I+1, ONE, A( I, I ), LDA,
00203      $                  WORK, 1, ZERO, WORK( M+1 ), 1 )
00204             CALL SGER( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
00205      $                 A( I, I ), LDA )
00206          END IF
00207          IF( I.LT.N ) THEN
00208 *
00209 *           generate random reflection
00210 *
00211             CALL SLARNV( 3, ISEED, N-I+1, WORK )
00212             WN = SNRM2( N-I+1, WORK, 1 )
00213             WA = SIGN( WN, WORK( 1 ) )
00214             IF( WN.EQ.ZERO ) THEN
00215                TAU = ZERO
00216             ELSE
00217                WB = WORK( 1 ) + WA
00218                CALL SSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
00219                WORK( 1 ) = ONE
00220                TAU = WB / WA
00221             END IF
00222 *
00223 *           multiply A(i:m,i:n) by random reflection from the right
00224 *
00225             CALL SGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
00226      $                  LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
00227             CALL SGER( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
00228      $                 A( I, I ), LDA )
00229          END IF
00230    40 CONTINUE
00231 *
00232 *     Reduce number of subdiagonals to KL and number of superdiagonals
00233 *     to KU
00234 *
00235       DO 70 I = 1, MAX( M-1-KL, N-1-KU )
00236          IF( KL.LE.KU ) THEN
00237 *
00238 *           annihilate subdiagonal elements first (necessary if KL = 0)
00239 *
00240             IF( I.LE.MIN( M-1-KL, N ) ) THEN
00241 *
00242 *              generate reflection to annihilate A(kl+i+1:m,i)
00243 *
00244                WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 )
00245                WA = SIGN( WN, A( KL+I, I ) )
00246                IF( WN.EQ.ZERO ) THEN
00247                   TAU = ZERO
00248                ELSE
00249                   WB = A( KL+I, I ) + WA
00250                   CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
00251                   A( KL+I, I ) = ONE
00252                   TAU = WB / WA
00253                END IF
00254 *
00255 *              apply reflection to A(kl+i:m,i+1:n) from the left
00256 *
00257                CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
00258      $                     A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
00259      $                     WORK, 1 )
00260                CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
00261      $                    A( KL+I, I+1 ), LDA )
00262                A( KL+I, I ) = -WA
00263             END IF
00264 *
00265             IF( I.LE.MIN( N-1-KU, M ) ) THEN
00266 *
00267 *              generate reflection to annihilate A(i,ku+i+1:n)
00268 *
00269                WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA )
00270                WA = SIGN( WN, A( I, KU+I ) )
00271                IF( WN.EQ.ZERO ) THEN
00272                   TAU = ZERO
00273                ELSE
00274                   WB = A( I, KU+I ) + WA
00275                   CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
00276                   A( I, KU+I ) = ONE
00277                   TAU = WB / WA
00278                END IF
00279 *
00280 *              apply reflection to A(i+1:m,ku+i:n) from the right
00281 *
00282                CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
00283      $                     A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
00284      $                     WORK, 1 )
00285                CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
00286      $                    LDA, A( I+1, KU+I ), LDA )
00287                A( I, KU+I ) = -WA
00288             END IF
00289          ELSE
00290 *
00291 *           annihilate superdiagonal elements first (necessary if
00292 *           KU = 0)
00293 *
00294             IF( I.LE.MIN( N-1-KU, M ) ) THEN
00295 *
00296 *              generate reflection to annihilate A(i,ku+i+1:n)
00297 *
00298                WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA )
00299                WA = SIGN( WN, A( I, KU+I ) )
00300                IF( WN.EQ.ZERO ) THEN
00301                   TAU = ZERO
00302                ELSE
00303                   WB = A( I, KU+I ) + WA
00304                   CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
00305                   A( I, KU+I ) = ONE
00306                   TAU = WB / WA
00307                END IF
00308 *
00309 *              apply reflection to A(i+1:m,ku+i:n) from the right
00310 *
00311                CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
00312      $                     A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
00313      $                     WORK, 1 )
00314                CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
00315      $                    LDA, A( I+1, KU+I ), LDA )
00316                A( I, KU+I ) = -WA
00317             END IF
00318 *
00319             IF( I.LE.MIN( M-1-KL, N ) ) THEN
00320 *
00321 *              generate reflection to annihilate A(kl+i+1:m,i)
00322 *
00323                WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 )
00324                WA = SIGN( WN, A( KL+I, I ) )
00325                IF( WN.EQ.ZERO ) THEN
00326                   TAU = ZERO
00327                ELSE
00328                   WB = A( KL+I, I ) + WA
00329                   CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
00330                   A( KL+I, I ) = ONE
00331                   TAU = WB / WA
00332                END IF
00333 *
00334 *              apply reflection to A(kl+i:m,i+1:n) from the left
00335 *
00336                CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
00337      $                     A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
00338      $                     WORK, 1 )
00339                CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
00340      $                    A( KL+I, I+1 ), LDA )
00341                A( KL+I, I ) = -WA
00342             END IF
00343          END IF
00344 *
00345          DO 50 J = KL + I + 1, M
00346             A( J, I ) = ZERO
00347    50    CONTINUE
00348 *
00349          DO 60 J = KU + I + 1, N
00350             A( I, J ) = ZERO
00351    60    CONTINUE
00352    70 CONTINUE
00353       RETURN
00354 *
00355 *     End of SLAGGE
00356 *
00357       END
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