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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 ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00002 * .. Scalar Arguments .. 00003 DOUBLE COMPLEX ALPHA,BETA 00004 INTEGER INCX,INCY,K,LDA,N 00005 CHARACTER UPLO 00006 * .. 00007 * .. Array Arguments .. 00008 DOUBLE COMPLEX A(LDA,*),X(*),Y(*) 00009 * .. 00010 * 00011 * Purpose 00012 * ======= 00013 * 00014 * ZHBMV performs the matrix-vector operation 00015 * 00016 * y := alpha*A*x + beta*y, 00017 * 00018 * where alpha and beta are scalars, x and y are n element vectors and 00019 * A is an n by n hermitian band matrix, with k super-diagonals. 00020 * 00021 * Arguments 00022 * ========== 00023 * 00024 * UPLO - CHARACTER*1. 00025 * On entry, UPLO specifies whether the upper or lower 00026 * triangular part of the band matrix A is being supplied as 00027 * follows: 00028 * 00029 * UPLO = 'U' or 'u' The upper triangular part of A is 00030 * being supplied. 00031 * 00032 * UPLO = 'L' or 'l' The lower triangular part of A is 00033 * being supplied. 00034 * 00035 * Unchanged on exit. 00036 * 00037 * N - INTEGER. 00038 * On entry, N specifies the order of the matrix A. 00039 * N must be at least zero. 00040 * Unchanged on exit. 00041 * 00042 * K - INTEGER. 00043 * On entry, K specifies the number of super-diagonals of the 00044 * matrix A. K must satisfy 0 .le. K. 00045 * Unchanged on exit. 00046 * 00047 * ALPHA - COMPLEX*16 . 00048 * On entry, ALPHA specifies the scalar alpha. 00049 * Unchanged on exit. 00050 * 00051 * A - COMPLEX*16 array of DIMENSION ( LDA, n ). 00052 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) 00053 * by n part of the array A must contain the upper triangular 00054 * band part of the hermitian matrix, supplied column by 00055 * column, with the leading diagonal of the matrix in row 00056 * ( k + 1 ) of the array, the first super-diagonal starting at 00057 * position 2 in row k, and so on. The top left k by k triangle 00058 * of the array A is not referenced. 00059 * The following program segment will transfer the upper 00060 * triangular part of a hermitian band matrix from conventional 00061 * full matrix storage to band storage: 00062 * 00063 * DO 20, J = 1, N 00064 * M = K + 1 - J 00065 * DO 10, I = MAX( 1, J - K ), J 00066 * A( M + I, J ) = matrix( I, J ) 00067 * 10 CONTINUE 00068 * 20 CONTINUE 00069 * 00070 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) 00071 * by n part of the array A must contain the lower triangular 00072 * band part of the hermitian matrix, supplied column by 00073 * column, with the leading diagonal of the matrix in row 1 of 00074 * the array, the first sub-diagonal starting at position 1 in 00075 * row 2, and so on. The bottom right k by k triangle of the 00076 * array A is not referenced. 00077 * The following program segment will transfer the lower 00078 * triangular part of a hermitian band matrix from conventional 00079 * full matrix storage to band storage: 00080 * 00081 * DO 20, J = 1, N 00082 * M = 1 - J 00083 * DO 10, I = J, MIN( N, J + K ) 00084 * A( M + I, J ) = matrix( I, J ) 00085 * 10 CONTINUE 00086 * 20 CONTINUE 00087 * 00088 * Note that the imaginary parts of the diagonal elements need 00089 * not be set and are assumed to be zero. 00090 * Unchanged on exit. 00091 * 00092 * LDA - INTEGER. 00093 * On entry, LDA specifies the first dimension of A as declared 00094 * in the calling (sub) program. LDA must be at least 00095 * ( k + 1 ). 00096 * Unchanged on exit. 00097 * 00098 * X - COMPLEX*16 array of DIMENSION at least 00099 * ( 1 + ( n - 1 )*abs( INCX ) ). 00100 * Before entry, the incremented array X must contain the 00101 * vector x. 00102 * Unchanged on exit. 00103 * 00104 * INCX - INTEGER. 00105 * On entry, INCX specifies the increment for the elements of 00106 * X. INCX must not be zero. 00107 * Unchanged on exit. 00108 * 00109 * BETA - COMPLEX*16 . 00110 * On entry, BETA specifies the scalar beta. 00111 * Unchanged on exit. 00112 * 00113 * Y - COMPLEX*16 array of DIMENSION at least 00114 * ( 1 + ( n - 1 )*abs( INCY ) ). 00115 * Before entry, the incremented array Y must contain the 00116 * vector y. On exit, Y is overwritten by the updated vector y. 00117 * 00118 * INCY - INTEGER. 00119 * On entry, INCY specifies the increment for the elements of 00120 * Y. INCY must not be zero. 00121 * Unchanged on exit. 00122 * 00123 * Further Details 00124 * =============== 00125 * 00126 * Level 2 Blas routine. 00127 * The vector and matrix arguments are not referenced when N = 0, or M = 0 00128 * 00129 * -- Written on 22-October-1986. 00130 * Jack Dongarra, Argonne National Lab. 00131 * Jeremy Du Croz, Nag Central Office. 00132 * Sven Hammarling, Nag Central Office. 00133 * Richard Hanson, Sandia National Labs. 00134 * 00135 * ===================================================================== 00136 * 00137 * .. Parameters .. 00138 DOUBLE COMPLEX ONE 00139 PARAMETER (ONE= (1.0D+0,0.0D+0)) 00140 DOUBLE COMPLEX ZERO 00141 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 00142 * .. 00143 * .. Local Scalars .. 00144 DOUBLE COMPLEX TEMP1,TEMP2 00145 INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L 00146 * .. 00147 * .. External Functions .. 00148 LOGICAL LSAME 00149 EXTERNAL LSAME 00150 * .. 00151 * .. External Subroutines .. 00152 EXTERNAL XERBLA 00153 * .. 00154 * .. Intrinsic Functions .. 00155 INTRINSIC DBLE,DCONJG,MAX,MIN 00156 * .. 00157 * 00158 * Test the input parameters. 00159 * 00160 INFO = 0 00161 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00162 INFO = 1 00163 ELSE IF (N.LT.0) THEN 00164 INFO = 2 00165 ELSE IF (K.LT.0) THEN 00166 INFO = 3 00167 ELSE IF (LDA.LT. (K+1)) THEN 00168 INFO = 6 00169 ELSE IF (INCX.EQ.0) THEN 00170 INFO = 8 00171 ELSE IF (INCY.EQ.0) THEN 00172 INFO = 11 00173 END IF 00174 IF (INFO.NE.0) THEN 00175 CALL XERBLA('ZHBMV ',INFO) 00176 RETURN 00177 END IF 00178 * 00179 * Quick return if possible. 00180 * 00181 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 00182 * 00183 * Set up the start points in X and Y. 00184 * 00185 IF (INCX.GT.0) THEN 00186 KX = 1 00187 ELSE 00188 KX = 1 - (N-1)*INCX 00189 END IF 00190 IF (INCY.GT.0) THEN 00191 KY = 1 00192 ELSE 00193 KY = 1 - (N-1)*INCY 00194 END IF 00195 * 00196 * Start the operations. In this version the elements of the array A 00197 * are accessed sequentially with one pass through A. 00198 * 00199 * First form y := beta*y. 00200 * 00201 IF (BETA.NE.ONE) THEN 00202 IF (INCY.EQ.1) THEN 00203 IF (BETA.EQ.ZERO) THEN 00204 DO 10 I = 1,N 00205 Y(I) = ZERO 00206 10 CONTINUE 00207 ELSE 00208 DO 20 I = 1,N 00209 Y(I) = BETA*Y(I) 00210 20 CONTINUE 00211 END IF 00212 ELSE 00213 IY = KY 00214 IF (BETA.EQ.ZERO) THEN 00215 DO 30 I = 1,N 00216 Y(IY) = ZERO 00217 IY = IY + INCY 00218 30 CONTINUE 00219 ELSE 00220 DO 40 I = 1,N 00221 Y(IY) = BETA*Y(IY) 00222 IY = IY + INCY 00223 40 CONTINUE 00224 END IF 00225 END IF 00226 END IF 00227 IF (ALPHA.EQ.ZERO) RETURN 00228 IF (LSAME(UPLO,'U')) THEN 00229 * 00230 * Form y when upper triangle of A is stored. 00231 * 00232 KPLUS1 = K + 1 00233 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00234 DO 60 J = 1,N 00235 TEMP1 = ALPHA*X(J) 00236 TEMP2 = ZERO 00237 L = KPLUS1 - J 00238 DO 50 I = MAX(1,J-K),J - 1 00239 Y(I) = Y(I) + TEMP1*A(L+I,J) 00240 TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I) 00241 50 CONTINUE 00242 Y(J) = Y(J) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2 00243 60 CONTINUE 00244 ELSE 00245 JX = KX 00246 JY = KY 00247 DO 80 J = 1,N 00248 TEMP1 = ALPHA*X(JX) 00249 TEMP2 = ZERO 00250 IX = KX 00251 IY = KY 00252 L = KPLUS1 - J 00253 DO 70 I = MAX(1,J-K),J - 1 00254 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 00255 TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX) 00256 IX = IX + INCX 00257 IY = IY + INCY 00258 70 CONTINUE 00259 Y(JY) = Y(JY) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2 00260 JX = JX + INCX 00261 JY = JY + INCY 00262 IF (J.GT.K) THEN 00263 KX = KX + INCX 00264 KY = KY + INCY 00265 END IF 00266 80 CONTINUE 00267 END IF 00268 ELSE 00269 * 00270 * Form y when lower triangle of A is stored. 00271 * 00272 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00273 DO 100 J = 1,N 00274 TEMP1 = ALPHA*X(J) 00275 TEMP2 = ZERO 00276 Y(J) = Y(J) + TEMP1*DBLE(A(1,J)) 00277 L = 1 - J 00278 DO 90 I = J + 1,MIN(N,J+K) 00279 Y(I) = Y(I) + TEMP1*A(L+I,J) 00280 TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I) 00281 90 CONTINUE 00282 Y(J) = Y(J) + ALPHA*TEMP2 00283 100 CONTINUE 00284 ELSE 00285 JX = KX 00286 JY = KY 00287 DO 120 J = 1,N 00288 TEMP1 = ALPHA*X(JX) 00289 TEMP2 = ZERO 00290 Y(JY) = Y(JY) + TEMP1*DBLE(A(1,J)) 00291 L = 1 - J 00292 IX = JX 00293 IY = JY 00294 DO 110 I = J + 1,MIN(N,J+K) 00295 IX = IX + INCX 00296 IY = IY + INCY 00297 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 00298 TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX) 00299 110 CONTINUE 00300 Y(JY) = Y(JY) + ALPHA*TEMP2 00301 JX = JX + INCX 00302 JY = JY + INCY 00303 120 CONTINUE 00304 END IF 00305 END IF 00306 * 00307 RETURN 00308 * 00309 * End of ZHBMV . 00310 * 00311 END
1.7.3 
