1*> \brief \b STBMV 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) 12* 13* .. Scalar Arguments .. 14* INTEGER INCX,K,LDA,N 15* CHARACTER DIAG,TRANS,UPLO 16* .. 17* .. Array Arguments .. 18* REAL A(LDA,*),X(*) 19* .. 20* 21* 22*> \par Purpose: 23* ============= 24*> 25*> \verbatim 26*> 27*> STBMV performs one of the matrix-vector operations 28*> 29*> x := A*x, or x := A**T*x, 30*> 31*> where x is an n element vector and A is an n by n unit, or non-unit, 32*> upper or lower triangular band matrix, with ( k + 1 ) diagonals. 33*> \endverbatim 34* 35* Arguments: 36* ========== 37* 38*> \param[in] UPLO 39*> \verbatim 40*> UPLO is CHARACTER*1 41*> On entry, UPLO specifies whether the matrix is an upper or 42*> lower triangular matrix as follows: 43*> 44*> UPLO = 'U' or 'u' A is an upper triangular matrix. 45*> 46*> UPLO = 'L' or 'l' A is a lower triangular matrix. 47*> \endverbatim 48*> 49*> \param[in] TRANS 50*> \verbatim 51*> TRANS is CHARACTER*1 52*> On entry, TRANS specifies the operation to be performed as 53*> follows: 54*> 55*> TRANS = 'N' or 'n' x := A*x. 56*> 57*> TRANS = 'T' or 't' x := A**T*x. 58*> 59*> TRANS = 'C' or 'c' x := A**T*x. 60*> \endverbatim 61*> 62*> \param[in] DIAG 63*> \verbatim 64*> DIAG is CHARACTER*1 65*> On entry, DIAG specifies whether or not A is unit 66*> triangular as follows: 67*> 68*> DIAG = 'U' or 'u' A is assumed to be unit triangular. 69*> 70*> DIAG = 'N' or 'n' A is not assumed to be unit 71*> triangular. 72*> \endverbatim 73*> 74*> \param[in] N 75*> \verbatim 76*> N is INTEGER 77*> On entry, N specifies the order of the matrix A. 78*> N must be at least zero. 79*> \endverbatim 80*> 81*> \param[in] K 82*> \verbatim 83*> K is INTEGER 84*> On entry with UPLO = 'U' or 'u', K specifies the number of 85*> super-diagonals of the matrix A. 86*> On entry with UPLO = 'L' or 'l', K specifies the number of 87*> sub-diagonals of the matrix A. 88*> K must satisfy 0 .le. K. 89*> \endverbatim 90*> 91*> \param[in] A 92*> \verbatim 93*> A is REAL array, dimension ( LDA, N ) 94*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) 95*> by n part of the array A must contain the upper triangular 96*> band part of the matrix of coefficients, supplied column by 97*> column, with the leading diagonal of the matrix in row 98*> ( k + 1 ) of the array, the first super-diagonal starting at 99*> position 2 in row k, and so on. The top left k by k triangle 100*> of the array A is not referenced. 101*> The following program segment will transfer an upper 102*> triangular band matrix from conventional full matrix storage 103*> to band storage: 104*> 105*> DO 20, J = 1, N 106*> M = K + 1 - J 107*> DO 10, I = MAX( 1, J - K ), J 108*> A( M + I, J ) = matrix( I, J ) 109*> 10 CONTINUE 110*> 20 CONTINUE 111*> 112*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) 113*> by n part of the array A must contain the lower triangular 114*> band part of the matrix of coefficients, supplied column by 115*> column, with the leading diagonal of the matrix in row 1 of 116*> the array, the first sub-diagonal starting at position 1 in 117*> row 2, and so on. The bottom right k by k triangle of the 118*> array A is not referenced. 119*> The following program segment will transfer a lower 120*> triangular band matrix from conventional full matrix storage 121*> to band storage: 122*> 123*> DO 20, J = 1, N 124*> M = 1 - J 125*> DO 10, I = J, MIN( N, J + K ) 126*> A( M + I, J ) = matrix( I, J ) 127*> 10 CONTINUE 128*> 20 CONTINUE 129*> 130*> Note that when DIAG = 'U' or 'u' the elements of the array A 131*> corresponding to the diagonal elements of the matrix are not 132*> referenced, but are assumed to be unity. 133*> \endverbatim 134*> 135*> \param[in] LDA 136*> \verbatim 137*> LDA is INTEGER 138*> On entry, LDA specifies the first dimension of A as declared 139*> in the calling (sub) program. LDA must be at least 140*> ( k + 1 ). 141*> \endverbatim 142*> 143*> \param[in,out] X 144*> \verbatim 145*> X is REAL array, dimension at least 146*> ( 1 + ( n - 1 )*abs( INCX ) ). 147*> Before entry, the incremented array X must contain the n 148*> element vector x. On exit, X is overwritten with the 149*> transformed vector x. 150*> \endverbatim 151*> 152*> \param[in] INCX 153*> \verbatim 154*> INCX is INTEGER 155*> On entry, INCX specifies the increment for the elements of 156*> X. INCX must not be zero. 157*> \endverbatim 158* 159* Authors: 160* ======== 161* 162*> \author Univ. of Tennessee 163*> \author Univ. of California Berkeley 164*> \author Univ. of Colorado Denver 165*> \author NAG Ltd. 166* 167*> \ingroup single_blas_level2 168* 169*> \par Further Details: 170* ===================== 171*> 172*> \verbatim 173*> 174*> Level 2 Blas routine. 175*> The vector and matrix arguments are not referenced when N = 0, or M = 0 176*> 177*> -- Written on 22-October-1986. 178*> Jack Dongarra, Argonne National Lab. 179*> Jeremy Du Croz, Nag Central Office. 180*> Sven Hammarling, Nag Central Office. 181*> Richard Hanson, Sandia National Labs. 182*> \endverbatim 183*> 184* ===================================================================== 185 SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) 186* 187* -- Reference BLAS level2 routine -- 188* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 189* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 190* 191* .. Scalar Arguments .. 192 INTEGER INCX,K,LDA,N 193 CHARACTER DIAG,TRANS,UPLO 194* .. 195* .. Array Arguments .. 196 REAL A(LDA,*),X(*) 197* .. 198* 199* ===================================================================== 200* 201* .. Parameters .. 202 REAL ZERO 203 PARAMETER (ZERO=0.0E+0) 204* .. 205* .. Local Scalars .. 206 REAL TEMP 207 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L 208 LOGICAL NOUNIT 209* .. 210* .. External Functions .. 211 LOGICAL LSAME 212 EXTERNAL LSAME 213* .. 214* .. External Subroutines .. 215 EXTERNAL XERBLA 216* .. 217* .. Intrinsic Functions .. 218 INTRINSIC MAX,MIN 219* .. 220* 221* Test the input parameters. 222* 223 INFO = 0 224 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 225 INFO = 1 226 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 227 + .NOT.LSAME(TRANS,'C')) THEN 228 INFO = 2 229 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 230 INFO = 3 231 ELSE IF (N.LT.0) THEN 232 INFO = 4 233 ELSE IF (K.LT.0) THEN 234 INFO = 5 235 ELSE IF (LDA.LT. (K+1)) THEN 236 INFO = 7 237 ELSE IF (INCX.EQ.0) THEN 238 INFO = 9 239 END IF 240 IF (INFO.NE.0) THEN 241 CALL XERBLA('STBMV ',INFO) 242 RETURN 243 END IF 244* 245* Quick return if possible. 246* 247 IF (N.EQ.0) RETURN 248* 249 NOUNIT = LSAME(DIAG,'N') 250* 251* Set up the start point in X if the increment is not unity. This 252* will be ( N - 1 )*INCX too small for descending loops. 253* 254 IF (INCX.LE.0) THEN 255 KX = 1 - (N-1)*INCX 256 ELSE IF (INCX.NE.1) THEN 257 KX = 1 258 END IF 259* 260* Start the operations. In this version the elements of A are 261* accessed sequentially with one pass through A. 262* 263 IF (LSAME(TRANS,'N')) THEN 264* 265* Form x := A*x. 266* 267 IF (LSAME(UPLO,'U')) THEN 268 KPLUS1 = K + 1 269 IF (INCX.EQ.1) THEN 270 DO 20 J = 1,N 271 IF (X(J).NE.ZERO) THEN 272 TEMP = X(J) 273 L = KPLUS1 - J 274 DO 10 I = MAX(1,J-K),J - 1 275 X(I) = X(I) + TEMP*A(L+I,J) 276 10 CONTINUE 277 IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) 278 END IF 279 20 CONTINUE 280 ELSE 281 JX = KX 282 DO 40 J = 1,N 283 IF (X(JX).NE.ZERO) THEN 284 TEMP = X(JX) 285 IX = KX 286 L = KPLUS1 - J 287 DO 30 I = MAX(1,J-K),J - 1 288 X(IX) = X(IX) + TEMP*A(L+I,J) 289 IX = IX + INCX 290 30 CONTINUE 291 IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) 292 END IF 293 JX = JX + INCX 294 IF (J.GT.K) KX = KX + INCX 295 40 CONTINUE 296 END IF 297 ELSE 298 IF (INCX.EQ.1) THEN 299 DO 60 J = N,1,-1 300 IF (X(J).NE.ZERO) THEN 301 TEMP = X(J) 302 L = 1 - J 303 DO 50 I = MIN(N,J+K),J + 1,-1 304 X(I) = X(I) + TEMP*A(L+I,J) 305 50 CONTINUE 306 IF (NOUNIT) X(J) = X(J)*A(1,J) 307 END IF 308 60 CONTINUE 309 ELSE 310 KX = KX + (N-1)*INCX 311 JX = KX 312 DO 80 J = N,1,-1 313 IF (X(JX).NE.ZERO) THEN 314 TEMP = X(JX) 315 IX = KX 316 L = 1 - J 317 DO 70 I = MIN(N,J+K),J + 1,-1 318 X(IX) = X(IX) + TEMP*A(L+I,J) 319 IX = IX - INCX 320 70 CONTINUE 321 IF (NOUNIT) X(JX) = X(JX)*A(1,J) 322 END IF 323 JX = JX - INCX 324 IF ((N-J).GE.K) KX = KX - INCX 325 80 CONTINUE 326 END IF 327 END IF 328 ELSE 329* 330* Form x := A**T*x. 331* 332 IF (LSAME(UPLO,'U')) THEN 333 KPLUS1 = K + 1 334 IF (INCX.EQ.1) THEN 335 DO 100 J = N,1,-1 336 TEMP = X(J) 337 L = KPLUS1 - J 338 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 339 DO 90 I = J - 1,MAX(1,J-K),-1 340 TEMP = TEMP + A(L+I,J)*X(I) 341 90 CONTINUE 342 X(J) = TEMP 343 100 CONTINUE 344 ELSE 345 KX = KX + (N-1)*INCX 346 JX = KX 347 DO 120 J = N,1,-1 348 TEMP = X(JX) 349 KX = KX - INCX 350 IX = KX 351 L = KPLUS1 - J 352 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 353 DO 110 I = J - 1,MAX(1,J-K),-1 354 TEMP = TEMP + A(L+I,J)*X(IX) 355 IX = IX - INCX 356 110 CONTINUE 357 X(JX) = TEMP 358 JX = JX - INCX 359 120 CONTINUE 360 END IF 361 ELSE 362 IF (INCX.EQ.1) THEN 363 DO 140 J = 1,N 364 TEMP = X(J) 365 L = 1 - J 366 IF (NOUNIT) TEMP = TEMP*A(1,J) 367 DO 130 I = J + 1,MIN(N,J+K) 368 TEMP = TEMP + A(L+I,J)*X(I) 369 130 CONTINUE 370 X(J) = TEMP 371 140 CONTINUE 372 ELSE 373 JX = KX 374 DO 160 J = 1,N 375 TEMP = X(JX) 376 KX = KX + INCX 377 IX = KX 378 L = 1 - J 379 IF (NOUNIT) TEMP = TEMP*A(1,J) 380 DO 150 I = J + 1,MIN(N,J+K) 381 TEMP = TEMP + A(L+I,J)*X(IX) 382 IX = IX + INCX 383 150 CONTINUE 384 X(JX) = TEMP 385 JX = JX + INCX 386 160 CONTINUE 387 END IF 388 END IF 389 END IF 390* 391 RETURN 392* 393* End of STBMV 394* 395 END 396