LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
stbmv.f
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00001 *> \brief \b STBMV
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 STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER INCX,K,LDA,N
00015 *       CHARACTER DIAG,TRANS,UPLO
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       REAL A(LDA,*),X(*)
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> STBMV  performs one of the matrix-vector operations
00028 *>
00029 *>    x := A*x,   or   x := A**T*x,
00030 *>
00031 *> where x is an n element vector and  A is an n by n unit, or non-unit,
00032 *> upper or lower triangular band matrix, with ( k + 1 ) diagonals.
00033 *> \endverbatim
00034 *
00035 *  Arguments:
00036 *  ==========
00037 *
00038 *> \param[in] UPLO
00039 *> \verbatim
00040 *>          UPLO is CHARACTER*1
00041 *>           On entry, UPLO specifies whether the matrix is an upper or
00042 *>           lower triangular matrix as follows:
00043 *>
00044 *>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
00045 *>
00046 *>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
00047 *> \endverbatim
00048 *>
00049 *> \param[in] TRANS
00050 *> \verbatim
00051 *>          TRANS is CHARACTER*1
00052 *>           On entry, TRANS specifies the operation to be performed as
00053 *>           follows:
00054 *>
00055 *>              TRANS = 'N' or 'n'   x := A*x.
00056 *>
00057 *>              TRANS = 'T' or 't'   x := A**T*x.
00058 *>
00059 *>              TRANS = 'C' or 'c'   x := A**T*x.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] DIAG
00063 *> \verbatim
00064 *>          DIAG is CHARACTER*1
00065 *>           On entry, DIAG specifies whether or not A is unit
00066 *>           triangular as follows:
00067 *>
00068 *>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
00069 *>
00070 *>              DIAG = 'N' or 'n'   A is not assumed to be unit
00071 *>                                  triangular.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] N
00075 *> \verbatim
00076 *>          N is INTEGER
00077 *>           On entry, N specifies the order of the matrix A.
00078 *>           N must be at least zero.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] K
00082 *> \verbatim
00083 *>          K is INTEGER
00084 *>           On entry with UPLO = 'U' or 'u', K specifies the number of
00085 *>           super-diagonals of the matrix A.
00086 *>           On entry with UPLO = 'L' or 'l', K specifies the number of
00087 *>           sub-diagonals of the matrix A.
00088 *>           K must satisfy  0 .le. K.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] A
00092 *> \verbatim
00093 *>          A is REAL array of DIMENSION ( LDA, n ).
00094 *>           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
00095 *>           by n part of the array A must contain the upper triangular
00096 *>           band part of the matrix of coefficients, supplied column by
00097 *>           column, with the leading diagonal of the matrix in row
00098 *>           ( k + 1 ) of the array, the first super-diagonal starting at
00099 *>           position 2 in row k, and so on. The top left k by k triangle
00100 *>           of the array A is not referenced.
00101 *>           The following program segment will transfer an upper
00102 *>           triangular band matrix from conventional full matrix storage
00103 *>           to band storage:
00104 *>
00105 *>                 DO 20, J = 1, N
00106 *>                    M = K + 1 - J
00107 *>                    DO 10, I = MAX( 1, J - K ), J
00108 *>                       A( M + I, J ) = matrix( I, J )
00109 *>              10    CONTINUE
00110 *>              20 CONTINUE
00111 *>
00112 *>           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
00113 *>           by n part of the array A must contain the lower triangular
00114 *>           band part of the matrix of coefficients, supplied column by
00115 *>           column, with the leading diagonal of the matrix in row 1 of
00116 *>           the array, the first sub-diagonal starting at position 1 in
00117 *>           row 2, and so on. The bottom right k by k triangle of the
00118 *>           array A is not referenced.
00119 *>           The following program segment will transfer a lower
00120 *>           triangular band matrix from conventional full matrix storage
00121 *>           to band storage:
00122 *>
00123 *>                 DO 20, J = 1, N
00124 *>                    M = 1 - J
00125 *>                    DO 10, I = J, MIN( N, J + K )
00126 *>                       A( M + I, J ) = matrix( I, J )
00127 *>              10    CONTINUE
00128 *>              20 CONTINUE
00129 *>
00130 *>           Note that when DIAG = 'U' or 'u' the elements of the array A
00131 *>           corresponding to the diagonal elements of the matrix are not
00132 *>           referenced, but are assumed to be unity.
00133 *> \endverbatim
00134 *>
00135 *> \param[in] LDA
00136 *> \verbatim
00137 *>          LDA is INTEGER
00138 *>           On entry, LDA specifies the first dimension of A as declared
00139 *>           in the calling (sub) program. LDA must be at least
00140 *>           ( k + 1 ).
00141 *> \endverbatim
00142 *>
00143 *> \param[in,out] X
00144 *> \verbatim
00145 *>          X is REAL array of dimension at least
00146 *>           ( 1 + ( n - 1 )*abs( INCX ) ).
00147 *>           Before entry, the incremented array X must contain the n
00148 *>           element vector x. On exit, X is overwritten with the
00149 *>           tranformed vector x.
00150 *> \endverbatim
00151 *>
00152 *> \param[in] INCX
00153 *> \verbatim
00154 *>          INCX is INTEGER
00155 *>           On entry, INCX specifies the increment for the elements of
00156 *>           X. INCX must not be zero.
00157 *> \endverbatim
00158 *
00159 *  Authors:
00160 *  ========
00161 *
00162 *> \author Univ. of Tennessee 
00163 *> \author Univ. of California Berkeley 
00164 *> \author Univ. of Colorado Denver 
00165 *> \author NAG Ltd. 
00166 *
00167 *> \date November 2011
00168 *
00169 *> \ingroup single_blas_level2
00170 *
00171 *> \par Further Details:
00172 *  =====================
00173 *>
00174 *> \verbatim
00175 *>
00176 *>  Level 2 Blas routine.
00177 *>  The vector and matrix arguments are not referenced when N = 0, or M = 0
00178 *>
00179 *>  -- Written on 22-October-1986.
00180 *>     Jack Dongarra, Argonne National Lab.
00181 *>     Jeremy Du Croz, Nag Central Office.
00182 *>     Sven Hammarling, Nag Central Office.
00183 *>     Richard Hanson, Sandia National Labs.
00184 *> \endverbatim
00185 *>
00186 *  =====================================================================
00187       SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
00188 *
00189 *  -- Reference BLAS level2 routine (version 3.4.0) --
00190 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00191 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00192 *     November 2011
00193 *
00194 *     .. Scalar Arguments ..
00195       INTEGER INCX,K,LDA,N
00196       CHARACTER DIAG,TRANS,UPLO
00197 *     ..
00198 *     .. Array Arguments ..
00199       REAL A(LDA,*),X(*)
00200 *     ..
00201 *
00202 *  =====================================================================
00203 *
00204 *     .. Parameters ..
00205       REAL ZERO
00206       PARAMETER (ZERO=0.0E+0)
00207 *     ..
00208 *     .. Local Scalars ..
00209       REAL TEMP
00210       INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
00211       LOGICAL NOUNIT
00212 *     ..
00213 *     .. External Functions ..
00214       LOGICAL LSAME
00215       EXTERNAL LSAME
00216 *     ..
00217 *     .. External Subroutines ..
00218       EXTERNAL XERBLA
00219 *     ..
00220 *     .. Intrinsic Functions ..
00221       INTRINSIC MAX,MIN
00222 *     ..
00223 *
00224 *     Test the input parameters.
00225 *
00226       INFO = 0
00227       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00228           INFO = 1
00229       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00230      +         .NOT.LSAME(TRANS,'C')) THEN
00231           INFO = 2
00232       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00233           INFO = 3
00234       ELSE IF (N.LT.0) THEN
00235           INFO = 4
00236       ELSE IF (K.LT.0) THEN
00237           INFO = 5
00238       ELSE IF (LDA.LT. (K+1)) THEN
00239           INFO = 7
00240       ELSE IF (INCX.EQ.0) THEN
00241           INFO = 9
00242       END IF
00243       IF (INFO.NE.0) THEN
00244           CALL XERBLA('STBMV ',INFO)
00245           RETURN
00246       END IF
00247 *
00248 *     Quick return if possible.
00249 *
00250       IF (N.EQ.0) RETURN
00251 *
00252       NOUNIT = LSAME(DIAG,'N')
00253 *
00254 *     Set up the start point in X if the increment is not unity. This
00255 *     will be  ( N - 1 )*INCX   too small for descending loops.
00256 *
00257       IF (INCX.LE.0) THEN
00258           KX = 1 - (N-1)*INCX
00259       ELSE IF (INCX.NE.1) THEN
00260           KX = 1
00261       END IF
00262 *
00263 *     Start the operations. In this version the elements of A are
00264 *     accessed sequentially with one pass through A.
00265 *
00266       IF (LSAME(TRANS,'N')) THEN
00267 *
00268 *         Form  x := A*x.
00269 *
00270           IF (LSAME(UPLO,'U')) THEN
00271               KPLUS1 = K + 1
00272               IF (INCX.EQ.1) THEN
00273                   DO 20 J = 1,N
00274                       IF (X(J).NE.ZERO) THEN
00275                           TEMP = X(J)
00276                           L = KPLUS1 - J
00277                           DO 10 I = MAX(1,J-K),J - 1
00278                               X(I) = X(I) + TEMP*A(L+I,J)
00279    10                     CONTINUE
00280                           IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
00281                       END IF
00282    20             CONTINUE
00283               ELSE
00284                   JX = KX
00285                   DO 40 J = 1,N
00286                       IF (X(JX).NE.ZERO) THEN
00287                           TEMP = X(JX)
00288                           IX = KX
00289                           L = KPLUS1 - J
00290                           DO 30 I = MAX(1,J-K),J - 1
00291                               X(IX) = X(IX) + TEMP*A(L+I,J)
00292                               IX = IX + INCX
00293    30                     CONTINUE
00294                           IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
00295                       END IF
00296                       JX = JX + INCX
00297                       IF (J.GT.K) KX = KX + INCX
00298    40             CONTINUE
00299               END IF
00300           ELSE
00301               IF (INCX.EQ.1) THEN
00302                   DO 60 J = N,1,-1
00303                       IF (X(J).NE.ZERO) THEN
00304                           TEMP = X(J)
00305                           L = 1 - J
00306                           DO 50 I = MIN(N,J+K),J + 1,-1
00307                               X(I) = X(I) + TEMP*A(L+I,J)
00308    50                     CONTINUE
00309                           IF (NOUNIT) X(J) = X(J)*A(1,J)
00310                       END IF
00311    60             CONTINUE
00312               ELSE
00313                   KX = KX + (N-1)*INCX
00314                   JX = KX
00315                   DO 80 J = N,1,-1
00316                       IF (X(JX).NE.ZERO) THEN
00317                           TEMP = X(JX)
00318                           IX = KX
00319                           L = 1 - J
00320                           DO 70 I = MIN(N,J+K),J + 1,-1
00321                               X(IX) = X(IX) + TEMP*A(L+I,J)
00322                               IX = IX - INCX
00323    70                     CONTINUE
00324                           IF (NOUNIT) X(JX) = X(JX)*A(1,J)
00325                       END IF
00326                       JX = JX - INCX
00327                       IF ((N-J).GE.K) KX = KX - INCX
00328    80             CONTINUE
00329               END IF
00330           END IF
00331       ELSE
00332 *
00333 *        Form  x := A**T*x.
00334 *
00335           IF (LSAME(UPLO,'U')) THEN
00336               KPLUS1 = K + 1
00337               IF (INCX.EQ.1) THEN
00338                   DO 100 J = N,1,-1
00339                       TEMP = X(J)
00340                       L = KPLUS1 - J
00341                       IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
00342                       DO 90 I = J - 1,MAX(1,J-K),-1
00343                           TEMP = TEMP + A(L+I,J)*X(I)
00344    90                 CONTINUE
00345                       X(J) = TEMP
00346   100             CONTINUE
00347               ELSE
00348                   KX = KX + (N-1)*INCX
00349                   JX = KX
00350                   DO 120 J = N,1,-1
00351                       TEMP = X(JX)
00352                       KX = KX - INCX
00353                       IX = KX
00354                       L = KPLUS1 - J
00355                       IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
00356                       DO 110 I = J - 1,MAX(1,J-K),-1
00357                           TEMP = TEMP + A(L+I,J)*X(IX)
00358                           IX = IX - INCX
00359   110                 CONTINUE
00360                       X(JX) = TEMP
00361                       JX = JX - INCX
00362   120             CONTINUE
00363               END IF
00364           ELSE
00365               IF (INCX.EQ.1) THEN
00366                   DO 140 J = 1,N
00367                       TEMP = X(J)
00368                       L = 1 - J
00369                       IF (NOUNIT) TEMP = TEMP*A(1,J)
00370                       DO 130 I = J + 1,MIN(N,J+K)
00371                           TEMP = TEMP + A(L+I,J)*X(I)
00372   130                 CONTINUE
00373                       X(J) = TEMP
00374   140             CONTINUE
00375               ELSE
00376                   JX = KX
00377                   DO 160 J = 1,N
00378                       TEMP = X(JX)
00379                       KX = KX + INCX
00380                       IX = KX
00381                       L = 1 - J
00382                       IF (NOUNIT) TEMP = TEMP*A(1,J)
00383                       DO 150 I = J + 1,MIN(N,J+K)
00384                           TEMP = TEMP + A(L+I,J)*X(IX)
00385                           IX = IX + INCX
00386   150                 CONTINUE
00387                       X(JX) = TEMP
00388                       JX = JX + INCX
00389   160             CONTINUE
00390               END IF
00391           END IF
00392       END IF
00393 *
00394       RETURN
00395 *
00396 *     End of STBMV .
00397 *
00398       END
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