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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 ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) 00002 * .. Scalar Arguments .. 00003 DOUBLE COMPLEX ALPHA,BETA 00004 INTEGER INCX,INCY,N 00005 CHARACTER UPLO 00006 * .. 00007 * .. Array Arguments .. 00008 DOUBLE COMPLEX AP(*),X(*),Y(*) 00009 * .. 00010 * 00011 * Purpose 00012 * ======= 00013 * 00014 * ZHPMV 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 matrix, supplied in packed form. 00020 * 00021 * Arguments 00022 * ========== 00023 * 00024 * UPLO - CHARACTER*1. 00025 * On entry, UPLO specifies whether the upper or lower 00026 * triangular part of the matrix A is supplied in the packed 00027 * array AP as follows: 00028 * 00029 * UPLO = 'U' or 'u' The upper triangular part of A is 00030 * supplied in AP. 00031 * 00032 * UPLO = 'L' or 'l' The lower triangular part of A is 00033 * supplied in AP. 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 * ALPHA - COMPLEX*16 . 00043 * On entry, ALPHA specifies the scalar alpha. 00044 * Unchanged on exit. 00045 * 00046 * AP - COMPLEX*16 array of DIMENSION at least 00047 * ( ( n*( n + 1 ) )/2 ). 00048 * Before entry with UPLO = 'U' or 'u', the array AP must 00049 * contain the upper triangular part of the hermitian matrix 00050 * packed sequentially, column by column, so that AP( 1 ) 00051 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) 00052 * and a( 2, 2 ) respectively, and so on. 00053 * Before entry with UPLO = 'L' or 'l', the array AP must 00054 * contain the lower triangular part of the hermitian matrix 00055 * packed sequentially, column by column, so that AP( 1 ) 00056 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) 00057 * and a( 3, 1 ) respectively, and so on. 00058 * Note that the imaginary parts of the diagonal elements need 00059 * not be set and are assumed to be zero. 00060 * Unchanged on exit. 00061 * 00062 * X - COMPLEX*16 array of dimension at least 00063 * ( 1 + ( n - 1 )*abs( INCX ) ). 00064 * Before entry, the incremented array X must contain the n 00065 * element vector x. 00066 * Unchanged on exit. 00067 * 00068 * INCX - INTEGER. 00069 * On entry, INCX specifies the increment for the elements of 00070 * X. INCX must not be zero. 00071 * Unchanged on exit. 00072 * 00073 * BETA - COMPLEX*16 . 00074 * On entry, BETA specifies the scalar beta. When BETA is 00075 * supplied as zero then Y need not be set on input. 00076 * Unchanged on exit. 00077 * 00078 * Y - COMPLEX*16 array of dimension at least 00079 * ( 1 + ( n - 1 )*abs( INCY ) ). 00080 * Before entry, the incremented array Y must contain the n 00081 * element vector y. On exit, Y is overwritten by the updated 00082 * vector y. 00083 * 00084 * INCY - INTEGER. 00085 * On entry, INCY specifies the increment for the elements of 00086 * Y. INCY must not be zero. 00087 * Unchanged on exit. 00088 * 00089 * Further Details 00090 * =============== 00091 * 00092 * Level 2 Blas routine. 00093 * The vector and matrix arguments are not referenced when N = 0, or M = 0 00094 * 00095 * -- Written on 22-October-1986. 00096 * Jack Dongarra, Argonne National Lab. 00097 * Jeremy Du Croz, Nag Central Office. 00098 * Sven Hammarling, Nag Central Office. 00099 * Richard Hanson, Sandia National Labs. 00100 * 00101 * ===================================================================== 00102 * 00103 * .. Parameters .. 00104 DOUBLE COMPLEX ONE 00105 PARAMETER (ONE= (1.0D+0,0.0D+0)) 00106 DOUBLE COMPLEX ZERO 00107 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 00108 * .. 00109 * .. Local Scalars .. 00110 DOUBLE COMPLEX TEMP1,TEMP2 00111 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 EXTERNAL LSAME 00116 * .. 00117 * .. External Subroutines .. 00118 EXTERNAL XERBLA 00119 * .. 00120 * .. Intrinsic Functions .. 00121 INTRINSIC DBLE,DCONJG 00122 * .. 00123 * 00124 * Test the input parameters. 00125 * 00126 INFO = 0 00127 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00128 INFO = 1 00129 ELSE IF (N.LT.0) THEN 00130 INFO = 2 00131 ELSE IF (INCX.EQ.0) THEN 00132 INFO = 6 00133 ELSE IF (INCY.EQ.0) THEN 00134 INFO = 9 00135 END IF 00136 IF (INFO.NE.0) THEN 00137 CALL XERBLA('ZHPMV ',INFO) 00138 RETURN 00139 END IF 00140 * 00141 * Quick return if possible. 00142 * 00143 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 00144 * 00145 * Set up the start points in X and Y. 00146 * 00147 IF (INCX.GT.0) THEN 00148 KX = 1 00149 ELSE 00150 KX = 1 - (N-1)*INCX 00151 END IF 00152 IF (INCY.GT.0) THEN 00153 KY = 1 00154 ELSE 00155 KY = 1 - (N-1)*INCY 00156 END IF 00157 * 00158 * Start the operations. In this version the elements of the array AP 00159 * are accessed sequentially with one pass through AP. 00160 * 00161 * First form y := beta*y. 00162 * 00163 IF (BETA.NE.ONE) THEN 00164 IF (INCY.EQ.1) THEN 00165 IF (BETA.EQ.ZERO) THEN 00166 DO 10 I = 1,N 00167 Y(I) = ZERO 00168 10 CONTINUE 00169 ELSE 00170 DO 20 I = 1,N 00171 Y(I) = BETA*Y(I) 00172 20 CONTINUE 00173 END IF 00174 ELSE 00175 IY = KY 00176 IF (BETA.EQ.ZERO) THEN 00177 DO 30 I = 1,N 00178 Y(IY) = ZERO 00179 IY = IY + INCY 00180 30 CONTINUE 00181 ELSE 00182 DO 40 I = 1,N 00183 Y(IY) = BETA*Y(IY) 00184 IY = IY + INCY 00185 40 CONTINUE 00186 END IF 00187 END IF 00188 END IF 00189 IF (ALPHA.EQ.ZERO) RETURN 00190 KK = 1 00191 IF (LSAME(UPLO,'U')) THEN 00192 * 00193 * Form y when AP contains the upper triangle. 00194 * 00195 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00196 DO 60 J = 1,N 00197 TEMP1 = ALPHA*X(J) 00198 TEMP2 = ZERO 00199 K = KK 00200 DO 50 I = 1,J - 1 00201 Y(I) = Y(I) + TEMP1*AP(K) 00202 TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) 00203 K = K + 1 00204 50 CONTINUE 00205 Y(J) = Y(J) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 00206 KK = KK + J 00207 60 CONTINUE 00208 ELSE 00209 JX = KX 00210 JY = KY 00211 DO 80 J = 1,N 00212 TEMP1 = ALPHA*X(JX) 00213 TEMP2 = ZERO 00214 IX = KX 00215 IY = KY 00216 DO 70 K = KK,KK + J - 2 00217 Y(IY) = Y(IY) + TEMP1*AP(K) 00218 TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) 00219 IX = IX + INCX 00220 IY = IY + INCY 00221 70 CONTINUE 00222 Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 00223 JX = JX + INCX 00224 JY = JY + INCY 00225 KK = KK + J 00226 80 CONTINUE 00227 END IF 00228 ELSE 00229 * 00230 * Form y when AP contains the lower triangle. 00231 * 00232 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00233 DO 100 J = 1,N 00234 TEMP1 = ALPHA*X(J) 00235 TEMP2 = ZERO 00236 Y(J) = Y(J) + TEMP1*DBLE(AP(KK)) 00237 K = KK + 1 00238 DO 90 I = J + 1,N 00239 Y(I) = Y(I) + TEMP1*AP(K) 00240 TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) 00241 K = K + 1 00242 90 CONTINUE 00243 Y(J) = Y(J) + ALPHA*TEMP2 00244 KK = KK + (N-J+1) 00245 100 CONTINUE 00246 ELSE 00247 JX = KX 00248 JY = KY 00249 DO 120 J = 1,N 00250 TEMP1 = ALPHA*X(JX) 00251 TEMP2 = ZERO 00252 Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK)) 00253 IX = JX 00254 IY = JY 00255 DO 110 K = KK + 1,KK + N - J 00256 IX = IX + INCX 00257 IY = IY + INCY 00258 Y(IY) = Y(IY) + TEMP1*AP(K) 00259 TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) 00260 110 CONTINUE 00261 Y(JY) = Y(JY) + ALPHA*TEMP2 00262 JX = JX + INCX 00263 JY = JY + INCY 00264 KK = KK + (N-J+1) 00265 120 CONTINUE 00266 END IF 00267 END IF 00268 * 00269 RETURN 00270 * 00271 * End of ZHPMV . 00272 * 00273 END
1.7.3 
