1
SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
2
* .. Scalar Arguments ..
4
INTEGER INCX,INCY,K,LDA,N
7
* .. Array Arguments ..
8
COMPLEX A(LDA,*),X(*),Y(*)
14
* CHBMV performs the matrix-vector operation
16
* y := alpha*A*x + beta*y,
18
* where alpha and beta are scalars, x and y are n element vectors and
19
* A is an n by n hermitian band matrix, with k super-diagonals.
25
* On entry, UPLO specifies whether the upper or lower
26
* triangular part of the band matrix A is being supplied as
29
* UPLO = 'U' or 'u' The upper triangular part of A is
32
* UPLO = 'L' or 'l' The lower triangular part of A is
38
* On entry, N specifies the order of the matrix A.
39
* N must be at least zero.
43
* On entry, K specifies the number of super-diagonals of the
44
* matrix A. K must satisfy 0 .le. K.
48
* On entry, ALPHA specifies the scalar alpha.
51
* A - COMPLEX array of DIMENSION ( LDA, n ).
52
* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
53
* by n part of the array A must contain the upper triangular
54
* band part of the hermitian matrix, supplied column by
55
* column, with the leading diagonal of the matrix in row
56
* ( k + 1 ) of the array, the first super-diagonal starting at
57
* position 2 in row k, and so on. The top left k by k triangle
58
* of the array A is not referenced.
59
* The following program segment will transfer the upper
60
* triangular part of a hermitian band matrix from conventional
61
* full matrix storage to band storage:
65
* DO 10, I = MAX( 1, J - K ), J
66
* A( M + I, J ) = matrix( I, J )
70
* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
71
* by n part of the array A must contain the lower triangular
72
* band part of the hermitian matrix, supplied column by
73
* column, with the leading diagonal of the matrix in row 1 of
74
* the array, the first sub-diagonal starting at position 1 in
75
* row 2, and so on. The bottom right k by k triangle of the
76
* array A is not referenced.
77
* The following program segment will transfer the lower
78
* triangular part of a hermitian band matrix from conventional
79
* full matrix storage to band storage:
83
* DO 10, I = J, MIN( N, J + K )
84
* A( M + I, J ) = matrix( I, J )
88
* Note that the imaginary parts of the diagonal elements need
89
* not be set and are assumed to be zero.
93
* On entry, LDA specifies the first dimension of A as declared
94
* in the calling (sub) program. LDA must be at least
98
* X - COMPLEX array of DIMENSION at least
99
* ( 1 + ( n - 1 )*abs( INCX ) ).
100
* Before entry, the incremented array X must contain the
105
* On entry, INCX specifies the increment for the elements of
106
* X. INCX must not be zero.
110
* On entry, BETA specifies the scalar beta.
113
* Y - COMPLEX array of DIMENSION at least
114
* ( 1 + ( n - 1 )*abs( INCY ) ).
115
* Before entry, the incremented array Y must contain the
116
* vector y. On exit, Y is overwritten by the updated vector y.
119
* On entry, INCY specifies the increment for the elements of
120
* Y. INCY must not be zero.
124
* Level 2 Blas routine.
126
* -- Written on 22-October-1986.
127
* Jack Dongarra, Argonne National Lab.
128
* Jeremy Du Croz, Nag Central Office.
129
* Sven Hammarling, Nag Central Office.
130
* Richard Hanson, Sandia National Labs.
135
PARAMETER (ONE= (1.0E+0,0.0E+0))
137
PARAMETER (ZERO= (0.0E+0,0.0E+0))
139
* .. Local Scalars ..
141
INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
143
* .. External Functions ..
147
* .. External Subroutines ..
150
* .. Intrinsic Functions ..
151
INTRINSIC CONJG,MAX,MIN,REAL
154
* Test the input parameters.
157
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
159
ELSE IF (N.LT.0) THEN
161
ELSE IF (K.LT.0) THEN
163
ELSE IF (LDA.LT. (K+1)) THEN
165
ELSE IF (INCX.EQ.0) THEN
167
ELSE IF (INCY.EQ.0) THEN
171
CALL XERBLA('CHBMV ',INFO)
175
* Quick return if possible.
177
IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
179
* Set up the start points in X and Y.
192
* Start the operations. In this version the elements of the array A
193
* are accessed sequentially with one pass through A.
195
* First form y := beta*y.
197
IF (BETA.NE.ONE) THEN
199
IF (BETA.EQ.ZERO) THEN
210
IF (BETA.EQ.ZERO) THEN
223
IF (ALPHA.EQ.ZERO) RETURN
224
IF (LSAME(UPLO,'U')) THEN
226
* Form y when upper triangle of A is stored.
229
IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
234
DO 50 I = MAX(1,J-K),J - 1
235
Y(I) = Y(I) + TEMP1*A(L+I,J)
236
TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I)
238
Y(J) = Y(J) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2
249
DO 70 I = MAX(1,J-K),J - 1
250
Y(IY) = Y(IY) + TEMP1*A(L+I,J)
251
TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX)
255
Y(JY) = Y(JY) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2
266
* Form y when lower triangle of A is stored.
268
IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
272
Y(J) = Y(J) + TEMP1*REAL(A(1,J))
274
DO 90 I = J + 1,MIN(N,J+K)
275
Y(I) = Y(I) + TEMP1*A(L+I,J)
276
TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I)
278
Y(J) = Y(J) + ALPHA*TEMP2
286
Y(JY) = Y(JY) + TEMP1*REAL(A(1,J))
290
DO 110 I = J + 1,MIN(N,J+K)
293
Y(IY) = Y(IY) + TEMP1*A(L+I,J)
294
TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX)
296
Y(JY) = Y(JY) + ALPHA*TEMP2
added
removed
src/blas/f77reference/chbmv.f
