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SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
DOUBLE PRECISION BETA
INTEGER K,LDA,LDB,LDC,N
CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* Purpose
* =======
*
* ZHER2K performs one of the hermitian rank 2k operations
*
* C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
*
* or
*
* C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
*
* where alpha and beta are scalars with beta real, C is an n by n
* hermitian matrix and A and B are n by k matrices in the first case
* and k by n matrices in the second case.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the array C is to be referenced as
* follows:
*
* UPLO = 'U' or 'u' Only the upper triangular part of C
* is to be referenced.
*
* UPLO = 'L' or 'l' Only the lower triangular part of C
* is to be referenced.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) +
* conjg( alpha )*B*conjg( A' ) +
* beta*C.
*
* TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
* conjg( alpha )*conjg( B' )*A +
* beta*C.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix C. N must be
* at least zero.
* Unchanged on exit.
*
* K - INTEGER.
* On entry with TRANS = 'N' or 'n', K specifies the number
* of columns of the matrices A and B, and on entry with
* TRANS = 'C' or 'c', K specifies the number of rows of the
* matrices A and B. K must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
* k when TRANS = 'N' or 'n', and is n otherwise.
* Before entry with TRANS = 'N' or 'n', the leading n by k
* part of the array A must contain the matrix A, otherwise
* the leading k by n part of the array A must contain the
* matrix A.
* Unchanged on exit.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. When TRANS = 'N' or 'n'
* then LDA must be at least max( 1, n ), otherwise LDA must
* be at least max( 1, k ).
* Unchanged on exit.
*
* B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
* k when TRANS = 'N' or 'n', and is n otherwise.
* Before entry with TRANS = 'N' or 'n', the leading n by k
* part of the array B must contain the matrix B, otherwise
* the leading k by n part of the array B must contain the
* matrix B.
* Unchanged on exit.
*
* LDB - INTEGER.
* On entry, LDB specifies the first dimension of B as declared
* in the calling (sub) program. When TRANS = 'N' or 'n'
* then LDB must be at least max( 1, n ), otherwise LDB must
* be at least max( 1, k ).
* Unchanged on exit.
*
* BETA - DOUBLE PRECISION .
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* C - COMPLEX*16 array of DIMENSION ( LDC, n ).
* Before entry with UPLO = 'U' or 'u', the leading n by n
* upper triangular part of the array C must contain the upper
* triangular part of the hermitian matrix and the strictly
* lower triangular part of C is not referenced. On exit, the
* upper triangular part of the array C 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 C must contain the lower
* triangular part of the hermitian matrix and the strictly
* upper triangular part of C is not referenced. On exit, the
* lower triangular part of the array C 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.
*
* LDC - INTEGER.
* On entry, LDC specifies the first dimension of C as declared
* in the calling (sub) program. LDC must be at least
* max( 1, n ).
* Unchanged on exit.
*
* Further Details
* ===============
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
* -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
* Ed Anderson, Cray Research Inc.
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE,DCONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP1,TEMP2
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER (ONE=1.0D+0)
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* Test the input parameters.
*
IF (LSAME(TRANS,'N')) THEN
NROWA = N
ELSE
NROWA = K
END IF
UPPER = LSAME(UPLO,'U')
*
INFO = 0
IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
INFO = 1
ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
+ (.NOT.LSAME(TRANS,'C'))) THEN
INFO = 2
ELSE IF (N.LT.0) THEN
INFO = 3
ELSE IF (K.LT.0) THEN
INFO = 4
ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
INFO = 7
ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
INFO = 9
ELSE IF (LDC.LT.MAX(1,N)) THEN
INFO = 12
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('ZHER2K',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
+ (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
*
* And when alpha.eq.zero.
*
IF (ALPHA.EQ.ZERO) THEN
IF (UPPER) THEN
IF (BETA.EQ.DBLE(ZERO)) THEN
DO 20 J = 1,N
DO 10 I = 1,J
C(I,J) = ZERO
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1,N
DO 30 I = 1,J - 1
C(I,J) = BETA*C(I,J)
30 CONTINUE
C(J,J) = BETA*DBLE(C(J,J))
40 CONTINUE
END IF
ELSE
IF (BETA.EQ.DBLE(ZERO)) THEN
DO 60 J = 1,N
DO 50 I = J,N
C(I,J) = ZERO
50 CONTINUE
60 CONTINUE
ELSE
DO 80 J = 1,N
C(J,J) = BETA*DBLE(C(J,J))
DO 70 I = J + 1,N
C(I,J) = BETA*C(I,J)
70 CONTINUE
80 CONTINUE
END IF
END IF
RETURN
END IF
*
* Start the operations.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) +
* C.
*
IF (UPPER) THEN
DO 130 J = 1,N
IF (BETA.EQ.DBLE(ZERO)) THEN
DO 90 I = 1,J
C(I,J) = ZERO
90 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 100 I = 1,J - 1
C(I,J) = BETA*C(I,J)
100 CONTINUE
C(J,J) = BETA*DBLE(C(J,J))
ELSE
C(J,J) = DBLE(C(J,J))
END IF
DO 120 L = 1,K
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
TEMP1 = ALPHA*DCONJG(B(J,L))
TEMP2 = DCONJG(ALPHA*A(J,L))
DO 110 I = 1,J - 1
C(I,J) = C(I,J) + A(I,L)*TEMP1 +
+ B(I,L)*TEMP2
110 CONTINUE
C(J,J) = DBLE(C(J,J)) +
+ DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
END IF
120 CONTINUE
130 CONTINUE
ELSE
DO 180 J = 1,N
IF (BETA.EQ.DBLE(ZERO)) THEN
DO 140 I = J,N
C(I,J) = ZERO
140 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 150 I = J + 1,N
C(I,J) = BETA*C(I,J)
150 CONTINUE
C(J,J) = BETA*DBLE(C(J,J))
ELSE
C(J,J) = DBLE(C(J,J))
END IF
DO 170 L = 1,K
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
TEMP1 = ALPHA*DCONJG(B(J,L))
TEMP2 = DCONJG(ALPHA*A(J,L))
DO 160 I = J + 1,N
C(I,J) = C(I,J) + A(I,L)*TEMP1 +
+ B(I,L)*TEMP2
160 CONTINUE
C(J,J) = DBLE(C(J,J)) +
+ DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
*
* Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
* C.
*
IF (UPPER) THEN
DO 210 J = 1,N
DO 200 I = 1,J
TEMP1 = ZERO
TEMP2 = ZERO
DO 190 L = 1,K
TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
190 CONTINUE
IF (I.EQ.J) THEN
IF (BETA.EQ.DBLE(ZERO)) THEN
C(J,J) = DBLE(ALPHA*TEMP1+
+ DCONJG(ALPHA)*TEMP2)
ELSE
C(J,J) = BETA*DBLE(C(J,J)) +
+ DBLE(ALPHA*TEMP1+
+ DCONJG(ALPHA)*TEMP2)
END IF
ELSE
IF (BETA.EQ.DBLE(ZERO)) THEN
C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
ELSE
C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
+ DCONJG(ALPHA)*TEMP2
END IF
END IF
200 CONTINUE
210 CONTINUE
ELSE
DO 240 J = 1,N
DO 230 I = J,N
TEMP1 = ZERO
TEMP2 = ZERO
DO 220 L = 1,K
TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
220 CONTINUE
IF (I.EQ.J) THEN
IF (BETA.EQ.DBLE(ZERO)) THEN
C(J,J) = DBLE(ALPHA*TEMP1+
+ DCONJG(ALPHA)*TEMP2)
ELSE
C(J,J) = BETA*DBLE(C(J,J)) +
+ DBLE(ALPHA*TEMP1+
+ DCONJG(ALPHA)*TEMP2)
END IF
ELSE
IF (BETA.EQ.DBLE(ZERO)) THEN
C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
ELSE
C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
+ DCONJG(ALPHA)*TEMP2
END IF
END IF
230 CONTINUE
240 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZHER2K.
*
END
|
