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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) 00002 * .. Scalar Arguments .. 00003 INTEGER INCX,K,LDA,N 00004 CHARACTER DIAG,TRANS,UPLO 00005 * .. 00006 * .. Array Arguments .. 00007 COMPLEX A(LDA,*),X(*) 00008 * .. 00009 * 00010 * Purpose 00011 * ======= 00012 * 00013 * CTBMV performs one of the matrix-vector operations 00014 * 00015 * x := A*x, or x := A**T*x, or x := A**H*x, 00016 * 00017 * where x is an n element vector and A is an n by n unit, or non-unit, 00018 * upper or lower triangular band matrix, with ( k + 1 ) diagonals. 00019 * 00020 * Arguments 00021 * ========== 00022 * 00023 * UPLO - CHARACTER*1. 00024 * On entry, UPLO specifies whether the matrix is an upper or 00025 * lower triangular matrix as follows: 00026 * 00027 * UPLO = 'U' or 'u' A is an upper triangular matrix. 00028 * 00029 * UPLO = 'L' or 'l' A is a lower triangular matrix. 00030 * 00031 * Unchanged on exit. 00032 * 00033 * TRANS - CHARACTER*1. 00034 * On entry, TRANS specifies the operation to be performed as 00035 * follows: 00036 * 00037 * TRANS = 'N' or 'n' x := A*x. 00038 * 00039 * TRANS = 'T' or 't' x := A**T*x. 00040 * 00041 * TRANS = 'C' or 'c' x := A**H*x. 00042 * 00043 * Unchanged on exit. 00044 * 00045 * DIAG - CHARACTER*1. 00046 * On entry, DIAG specifies whether or not A is unit 00047 * triangular as follows: 00048 * 00049 * DIAG = 'U' or 'u' A is assumed to be unit triangular. 00050 * 00051 * DIAG = 'N' or 'n' A is not assumed to be unit 00052 * triangular. 00053 * 00054 * Unchanged on exit. 00055 * 00056 * N - INTEGER. 00057 * On entry, N specifies the order of the matrix A. 00058 * N must be at least zero. 00059 * Unchanged on exit. 00060 * 00061 * K - INTEGER. 00062 * On entry with UPLO = 'U' or 'u', K specifies the number of 00063 * super-diagonals of the matrix A. 00064 * On entry with UPLO = 'L' or 'l', K specifies the number of 00065 * sub-diagonals of the matrix A. 00066 * K must satisfy 0 .le. K. 00067 * Unchanged on exit. 00068 * 00069 * A - COMPLEX array of DIMENSION ( LDA, n ). 00070 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) 00071 * by n part of the array A must contain the upper triangular 00072 * band part of the matrix of coefficients, supplied column by 00073 * column, with the leading diagonal of the matrix in row 00074 * ( k + 1 ) of the array, the first super-diagonal starting at 00075 * position 2 in row k, and so on. The top left k by k triangle 00076 * of the array A is not referenced. 00077 * The following program segment will transfer an upper 00078 * triangular band matrix from conventional full matrix storage 00079 * to band storage: 00080 * 00081 * DO 20, J = 1, N 00082 * M = K + 1 - J 00083 * DO 10, I = MAX( 1, J - K ), J 00084 * A( M + I, J ) = matrix( I, J ) 00085 * 10 CONTINUE 00086 * 20 CONTINUE 00087 * 00088 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) 00089 * by n part of the array A must contain the lower triangular 00090 * band part of the matrix of coefficients, supplied column by 00091 * column, with the leading diagonal of the matrix in row 1 of 00092 * the array, the first sub-diagonal starting at position 1 in 00093 * row 2, and so on. The bottom right k by k triangle of the 00094 * array A is not referenced. 00095 * The following program segment will transfer a lower 00096 * triangular band matrix from conventional full matrix storage 00097 * to band storage: 00098 * 00099 * DO 20, J = 1, N 00100 * M = 1 - J 00101 * DO 10, I = J, MIN( N, J + K ) 00102 * A( M + I, J ) = matrix( I, J ) 00103 * 10 CONTINUE 00104 * 20 CONTINUE 00105 * 00106 * Note that when DIAG = 'U' or 'u' the elements of the array A 00107 * corresponding to the diagonal elements of the matrix are not 00108 * referenced, but are assumed to be unity. 00109 * Unchanged on exit. 00110 * 00111 * LDA - INTEGER. 00112 * On entry, LDA specifies the first dimension of A as declared 00113 * in the calling (sub) program. LDA must be at least 00114 * ( k + 1 ). 00115 * Unchanged on exit. 00116 * 00117 * X - COMPLEX array of dimension at least 00118 * ( 1 + ( n - 1 )*abs( INCX ) ). 00119 * Before entry, the incremented array X must contain the n 00120 * element vector x. On exit, X is overwritten with the 00121 * tranformed vector x. 00122 * 00123 * INCX - INTEGER. 00124 * On entry, INCX specifies the increment for the elements of 00125 * X. INCX must not be zero. 00126 * Unchanged on exit. 00127 * 00128 * Further Details 00129 * =============== 00130 * 00131 * Level 2 Blas routine. 00132 * The vector and matrix arguments are not referenced when N = 0, or M = 0 00133 * 00134 * -- Written on 22-October-1986. 00135 * Jack Dongarra, Argonne National Lab. 00136 * Jeremy Du Croz, Nag Central Office. 00137 * Sven Hammarling, Nag Central Office. 00138 * Richard Hanson, Sandia National Labs. 00139 * 00140 * ===================================================================== 00141 * 00142 * .. Parameters .. 00143 COMPLEX ZERO 00144 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00145 * .. 00146 * .. Local Scalars .. 00147 COMPLEX TEMP 00148 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L 00149 LOGICAL NOCONJ,NOUNIT 00150 * .. 00151 * .. External Functions .. 00152 LOGICAL LSAME 00153 EXTERNAL LSAME 00154 * .. 00155 * .. External Subroutines .. 00156 EXTERNAL XERBLA 00157 * .. 00158 * .. Intrinsic Functions .. 00159 INTRINSIC CONJG,MAX,MIN 00160 * .. 00161 * 00162 * Test the input parameters. 00163 * 00164 INFO = 0 00165 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00166 INFO = 1 00167 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00168 + .NOT.LSAME(TRANS,'C')) THEN 00169 INFO = 2 00170 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00171 INFO = 3 00172 ELSE IF (N.LT.0) THEN 00173 INFO = 4 00174 ELSE IF (K.LT.0) THEN 00175 INFO = 5 00176 ELSE IF (LDA.LT. (K+1)) THEN 00177 INFO = 7 00178 ELSE IF (INCX.EQ.0) THEN 00179 INFO = 9 00180 END IF 00181 IF (INFO.NE.0) THEN 00182 CALL XERBLA('CTBMV ',INFO) 00183 RETURN 00184 END IF 00185 * 00186 * Quick return if possible. 00187 * 00188 IF (N.EQ.0) RETURN 00189 * 00190 NOCONJ = LSAME(TRANS,'T') 00191 NOUNIT = LSAME(DIAG,'N') 00192 * 00193 * Set up the start point in X if the increment is not unity. This 00194 * will be ( N - 1 )*INCX too small for descending loops. 00195 * 00196 IF (INCX.LE.0) THEN 00197 KX = 1 - (N-1)*INCX 00198 ELSE IF (INCX.NE.1) THEN 00199 KX = 1 00200 END IF 00201 * 00202 * Start the operations. In this version the elements of A are 00203 * accessed sequentially with one pass through A. 00204 * 00205 IF (LSAME(TRANS,'N')) THEN 00206 * 00207 * Form x := A*x. 00208 * 00209 IF (LSAME(UPLO,'U')) THEN 00210 KPLUS1 = K + 1 00211 IF (INCX.EQ.1) THEN 00212 DO 20 J = 1,N 00213 IF (X(J).NE.ZERO) THEN 00214 TEMP = X(J) 00215 L = KPLUS1 - J 00216 DO 10 I = MAX(1,J-K),J - 1 00217 X(I) = X(I) + TEMP*A(L+I,J) 00218 10 CONTINUE 00219 IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) 00220 END IF 00221 20 CONTINUE 00222 ELSE 00223 JX = KX 00224 DO 40 J = 1,N 00225 IF (X(JX).NE.ZERO) THEN 00226 TEMP = X(JX) 00227 IX = KX 00228 L = KPLUS1 - J 00229 DO 30 I = MAX(1,J-K),J - 1 00230 X(IX) = X(IX) + TEMP*A(L+I,J) 00231 IX = IX + INCX 00232 30 CONTINUE 00233 IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) 00234 END IF 00235 JX = JX + INCX 00236 IF (J.GT.K) KX = KX + INCX 00237 40 CONTINUE 00238 END IF 00239 ELSE 00240 IF (INCX.EQ.1) THEN 00241 DO 60 J = N,1,-1 00242 IF (X(J).NE.ZERO) THEN 00243 TEMP = X(J) 00244 L = 1 - J 00245 DO 50 I = MIN(N,J+K),J + 1,-1 00246 X(I) = X(I) + TEMP*A(L+I,J) 00247 50 CONTINUE 00248 IF (NOUNIT) X(J) = X(J)*A(1,J) 00249 END IF 00250 60 CONTINUE 00251 ELSE 00252 KX = KX + (N-1)*INCX 00253 JX = KX 00254 DO 80 J = N,1,-1 00255 IF (X(JX).NE.ZERO) THEN 00256 TEMP = X(JX) 00257 IX = KX 00258 L = 1 - J 00259 DO 70 I = MIN(N,J+K),J + 1,-1 00260 X(IX) = X(IX) + TEMP*A(L+I,J) 00261 IX = IX - INCX 00262 70 CONTINUE 00263 IF (NOUNIT) X(JX) = X(JX)*A(1,J) 00264 END IF 00265 JX = JX - INCX 00266 IF ((N-J).GE.K) KX = KX - INCX 00267 80 CONTINUE 00268 END IF 00269 END IF 00270 ELSE 00271 * 00272 * Form x := A**T*x or x := A**H*x. 00273 * 00274 IF (LSAME(UPLO,'U')) THEN 00275 KPLUS1 = K + 1 00276 IF (INCX.EQ.1) THEN 00277 DO 110 J = N,1,-1 00278 TEMP = X(J) 00279 L = KPLUS1 - J 00280 IF (NOCONJ) THEN 00281 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 00282 DO 90 I = J - 1,MAX(1,J-K),-1 00283 TEMP = TEMP + A(L+I,J)*X(I) 00284 90 CONTINUE 00285 ELSE 00286 IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J)) 00287 DO 100 I = J - 1,MAX(1,J-K),-1 00288 TEMP = TEMP + CONJG(A(L+I,J))*X(I) 00289 100 CONTINUE 00290 END IF 00291 X(J) = TEMP 00292 110 CONTINUE 00293 ELSE 00294 KX = KX + (N-1)*INCX 00295 JX = KX 00296 DO 140 J = N,1,-1 00297 TEMP = X(JX) 00298 KX = KX - INCX 00299 IX = KX 00300 L = KPLUS1 - J 00301 IF (NOCONJ) THEN 00302 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 00303 DO 120 I = J - 1,MAX(1,J-K),-1 00304 TEMP = TEMP + A(L+I,J)*X(IX) 00305 IX = IX - INCX 00306 120 CONTINUE 00307 ELSE 00308 IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J)) 00309 DO 130 I = J - 1,MAX(1,J-K),-1 00310 TEMP = TEMP + CONJG(A(L+I,J))*X(IX) 00311 IX = IX - INCX 00312 130 CONTINUE 00313 END IF 00314 X(JX) = TEMP 00315 JX = JX - INCX 00316 140 CONTINUE 00317 END IF 00318 ELSE 00319 IF (INCX.EQ.1) THEN 00320 DO 170 J = 1,N 00321 TEMP = X(J) 00322 L = 1 - J 00323 IF (NOCONJ) THEN 00324 IF (NOUNIT) TEMP = TEMP*A(1,J) 00325 DO 150 I = J + 1,MIN(N,J+K) 00326 TEMP = TEMP + A(L+I,J)*X(I) 00327 150 CONTINUE 00328 ELSE 00329 IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J)) 00330 DO 160 I = J + 1,MIN(N,J+K) 00331 TEMP = TEMP + CONJG(A(L+I,J))*X(I) 00332 160 CONTINUE 00333 END IF 00334 X(J) = TEMP 00335 170 CONTINUE 00336 ELSE 00337 JX = KX 00338 DO 200 J = 1,N 00339 TEMP = X(JX) 00340 KX = KX + INCX 00341 IX = KX 00342 L = 1 - J 00343 IF (NOCONJ) THEN 00344 IF (NOUNIT) TEMP = TEMP*A(1,J) 00345 DO 180 I = J + 1,MIN(N,J+K) 00346 TEMP = TEMP + A(L+I,J)*X(IX) 00347 IX = IX + INCX 00348 180 CONTINUE 00349 ELSE 00350 IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J)) 00351 DO 190 I = J + 1,MIN(N,J+K) 00352 TEMP = TEMP + CONJG(A(L+I,J))*X(IX) 00353 IX = IX + INCX 00354 190 CONTINUE 00355 END IF 00356 X(JX) = TEMP 00357 JX = JX + INCX 00358 200 CONTINUE 00359 END IF 00360 END IF 00361 END IF 00362 * 00363 RETURN 00364 * 00365 * End of CTBMV . 00366 * 00367 END
1.7.3 
