1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217
|
SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA)
* .. Scalar Arguments ..
REAL ALPHA
INTEGER INCX,LDA,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
COMPLEX A(LDA,*),X(*)
* ..
*
* Purpose
* =======
*
* CHER performs the hermitian rank 1 operation
*
* A := alpha*x*x**H + A,
*
* where alpha is a real scalar, x is an n element vector and A is an
* n by n hermitian matrix.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the array A is to be referenced as
* follows:
*
* UPLO = 'U' or 'u' Only the upper triangular part of A
* is to be referenced.
*
* UPLO = 'L' or 'l' Only the lower triangular part of A
* is to be referenced.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - REAL .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* A - COMPLEX array of DIMENSION ( LDA, n ).
* Before entry with UPLO = 'U' or 'u', the leading n by n
* upper triangular part of the array A must contain the upper
* triangular part of the hermitian matrix and the strictly
* lower triangular part of A is not referenced. On exit, the
* upper triangular part of the array A is overwritten by the
* upper triangular part of the updated matrix.
* Before entry with UPLO = 'L' or 'l', the leading n by n
* lower triangular part of the array A must contain the lower
* triangular part of the hermitian matrix and the strictly
* upper triangular part of A is not referenced. On exit, the
* lower triangular part of the array A is overwritten by the
* lower triangular part of the updated matrix.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero, and on exit they
* are set to zero.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. LDA must be at least
* max( 1, n ).
* Unchanged on exit.
*
* Further Details
* ===============
*
* Level 2 Blas routine.
*
* -- Written on 22-October-1986.
* Jack Dongarra, Argonne National Lab.
* Jeremy Du Croz, Nag Central Office.
* Sven Hammarling, Nag Central Office.
* Richard Hanson, Sandia National Labs.
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,KX
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLI
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,MAX,REAL
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
INFO = 1
ELSE IF (N.LT.0) THEN
INFO = 2
ELSE IF (INCX.EQ.0) THEN
INFO = 5
ELSE IF (LDA.LT.MAX(1,N)) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLI('CHER ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
*
* Set the start point in X if the increment is not unity.
*
IF (INCX.LE.0) THEN
KX = 1 - (N-1)*INCX
ELSE IF (INCX.NE.1) THEN
KX = 1
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through the triangular part
* of A.
*
IF (LSAME(UPLO,'U')) THEN
*
* Form A when A is stored in upper triangle.
*
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = ALPHA*CONJG(X(J))
DO 10 I = 1,J - 1
A(I,J) = A(I,J) + X(I)*TEMP
10 CONTINUE
A(J,J) = REAL(A(J,J)) + REAL(X(J)*TEMP)
ELSE
A(J,J) = REAL(A(J,J))
END IF
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*CONJG(X(JX))
IX = KX
DO 30 I = 1,J - 1
A(I,J) = A(I,J) + X(IX)*TEMP
IX = IX + INCX
30 CONTINUE
A(J,J) = REAL(A(J,J)) + REAL(X(JX)*TEMP)
ELSE
A(J,J) = REAL(A(J,J))
END IF
JX = JX + INCX
40 CONTINUE
END IF
ELSE
*
* Form A when A is stored in lower triangle.
*
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = ALPHA*CONJG(X(J))
A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(J))
DO 50 I = J + 1,N
A(I,J) = A(I,J) + X(I)*TEMP
50 CONTINUE
ELSE
A(J,J) = REAL(A(J,J))
END IF
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*CONJG(X(JX))
A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(JX))
IX = JX
DO 70 I = J + 1,N
IX = IX + INCX
A(I,J) = A(I,J) + X(IX)*TEMP
70 CONTINUE
ELSE
A(J,J) = REAL(A(J,J))
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of CHER .
*
END
|