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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZTBMV 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 ZTBMV(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 * COMPLEX*16 A(LDA,*),X(*) 00019 * .. 00020 * 00021 * 00022 *> \par Purpose: 00023 * ============= 00024 *> 00025 *> \verbatim 00026 *> 00027 *> ZTBMV performs one of the matrix-vector operations 00028 *> 00029 *> x := A*x, or x := A**T*x, or x := A**H*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**H*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 COMPLEX*16 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] X 00144 *> \verbatim 00145 *> X is (input/output) COMPLEX*16 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 complex16_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 ZTBMV(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 COMPLEX*16 A(LDA,*),X(*) 00200 * .. 00201 * 00202 * ===================================================================== 00203 * 00204 * .. Parameters .. 00205 COMPLEX*16 ZERO 00206 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 00207 * .. 00208 * .. Local Scalars .. 00209 COMPLEX*16 TEMP 00210 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L 00211 LOGICAL NOCONJ,NOUNIT 00212 * .. 00213 * .. External Functions .. 00214 LOGICAL LSAME 00215 EXTERNAL LSAME 00216 * .. 00217 * .. External Subroutines .. 00218 EXTERNAL XERBLA 00219 * .. 00220 * .. Intrinsic Functions .. 00221 INTRINSIC DCONJG,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('ZTBMV ',INFO) 00245 RETURN 00246 END IF 00247 * 00248 * Quick return if possible. 00249 * 00250 IF (N.EQ.0) RETURN 00251 * 00252 NOCONJ = LSAME(TRANS,'T') 00253 NOUNIT = LSAME(DIAG,'N') 00254 * 00255 * Set up the start point in X if the increment is not unity. This 00256 * will be ( N - 1 )*INCX too small for descending loops. 00257 * 00258 IF (INCX.LE.0) THEN 00259 KX = 1 - (N-1)*INCX 00260 ELSE IF (INCX.NE.1) THEN 00261 KX = 1 00262 END IF 00263 * 00264 * Start the operations. In this version the elements of A are 00265 * accessed sequentially with one pass through A. 00266 * 00267 IF (LSAME(TRANS,'N')) THEN 00268 * 00269 * Form x := A*x. 00270 * 00271 IF (LSAME(UPLO,'U')) THEN 00272 KPLUS1 = K + 1 00273 IF (INCX.EQ.1) THEN 00274 DO 20 J = 1,N 00275 IF (X(J).NE.ZERO) THEN 00276 TEMP = X(J) 00277 L = KPLUS1 - J 00278 DO 10 I = MAX(1,J-K),J - 1 00279 X(I) = X(I) + TEMP*A(L+I,J) 00280 10 CONTINUE 00281 IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) 00282 END IF 00283 20 CONTINUE 00284 ELSE 00285 JX = KX 00286 DO 40 J = 1,N 00287 IF (X(JX).NE.ZERO) THEN 00288 TEMP = X(JX) 00289 IX = KX 00290 L = KPLUS1 - J 00291 DO 30 I = MAX(1,J-K),J - 1 00292 X(IX) = X(IX) + TEMP*A(L+I,J) 00293 IX = IX + INCX 00294 30 CONTINUE 00295 IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) 00296 END IF 00297 JX = JX + INCX 00298 IF (J.GT.K) KX = KX + INCX 00299 40 CONTINUE 00300 END IF 00301 ELSE 00302 IF (INCX.EQ.1) THEN 00303 DO 60 J = N,1,-1 00304 IF (X(J).NE.ZERO) THEN 00305 TEMP = X(J) 00306 L = 1 - J 00307 DO 50 I = MIN(N,J+K),J + 1,-1 00308 X(I) = X(I) + TEMP*A(L+I,J) 00309 50 CONTINUE 00310 IF (NOUNIT) X(J) = X(J)*A(1,J) 00311 END IF 00312 60 CONTINUE 00313 ELSE 00314 KX = KX + (N-1)*INCX 00315 JX = KX 00316 DO 80 J = N,1,-1 00317 IF (X(JX).NE.ZERO) THEN 00318 TEMP = X(JX) 00319 IX = KX 00320 L = 1 - J 00321 DO 70 I = MIN(N,J+K),J + 1,-1 00322 X(IX) = X(IX) + TEMP*A(L+I,J) 00323 IX = IX - INCX 00324 70 CONTINUE 00325 IF (NOUNIT) X(JX) = X(JX)*A(1,J) 00326 END IF 00327 JX = JX - INCX 00328 IF ((N-J).GE.K) KX = KX - INCX 00329 80 CONTINUE 00330 END IF 00331 END IF 00332 ELSE 00333 * 00334 * Form x := A**T*x or x := A**H*x. 00335 * 00336 IF (LSAME(UPLO,'U')) THEN 00337 KPLUS1 = K + 1 00338 IF (INCX.EQ.1) THEN 00339 DO 110 J = N,1,-1 00340 TEMP = X(J) 00341 L = KPLUS1 - J 00342 IF (NOCONJ) THEN 00343 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 00344 DO 90 I = J - 1,MAX(1,J-K),-1 00345 TEMP = TEMP + A(L+I,J)*X(I) 00346 90 CONTINUE 00347 ELSE 00348 IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) 00349 DO 100 I = J - 1,MAX(1,J-K),-1 00350 TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 00351 100 CONTINUE 00352 END IF 00353 X(J) = TEMP 00354 110 CONTINUE 00355 ELSE 00356 KX = KX + (N-1)*INCX 00357 JX = KX 00358 DO 140 J = N,1,-1 00359 TEMP = X(JX) 00360 KX = KX - INCX 00361 IX = KX 00362 L = KPLUS1 - J 00363 IF (NOCONJ) THEN 00364 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 00365 DO 120 I = J - 1,MAX(1,J-K),-1 00366 TEMP = TEMP + A(L+I,J)*X(IX) 00367 IX = IX - INCX 00368 120 CONTINUE 00369 ELSE 00370 IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) 00371 DO 130 I = J - 1,MAX(1,J-K),-1 00372 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) 00373 IX = IX - INCX 00374 130 CONTINUE 00375 END IF 00376 X(JX) = TEMP 00377 JX = JX - INCX 00378 140 CONTINUE 00379 END IF 00380 ELSE 00381 IF (INCX.EQ.1) THEN 00382 DO 170 J = 1,N 00383 TEMP = X(J) 00384 L = 1 - J 00385 IF (NOCONJ) THEN 00386 IF (NOUNIT) TEMP = TEMP*A(1,J) 00387 DO 150 I = J + 1,MIN(N,J+K) 00388 TEMP = TEMP + A(L+I,J)*X(I) 00389 150 CONTINUE 00390 ELSE 00391 IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) 00392 DO 160 I = J + 1,MIN(N,J+K) 00393 TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 00394 160 CONTINUE 00395 END IF 00396 X(J) = TEMP 00397 170 CONTINUE 00398 ELSE 00399 JX = KX 00400 DO 200 J = 1,N 00401 TEMP = X(JX) 00402 KX = KX + INCX 00403 IX = KX 00404 L = 1 - J 00405 IF (NOCONJ) THEN 00406 IF (NOUNIT) TEMP = TEMP*A(1,J) 00407 DO 180 I = J + 1,MIN(N,J+K) 00408 TEMP = TEMP + A(L+I,J)*X(IX) 00409 IX = IX + INCX 00410 180 CONTINUE 00411 ELSE 00412 IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) 00413 DO 190 I = J + 1,MIN(N,J+K) 00414 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) 00415 IX = IX + INCX 00416 190 CONTINUE 00417 END IF 00418 X(JX) = TEMP 00419 JX = JX + INCX 00420 200 CONTINUE 00421 END IF 00422 END IF 00423 END IF 00424 * 00425 RETURN 00426 * 00427 * End of ZTBMV . 00428 * 00429 END