SUBROUTINE CHER2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,
$ BETA, C, LDC )
* .. Scalar Arguments ..
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
REAL BETA
COMPLEX ALPHA
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
* Purpose
* =======
*
* CHER2K 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.
*
* Parameters
* ==========
*
* 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 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX 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 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 - REAL .
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* C - COMPLEX 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.
*
*
* 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 REAL( C(J,J) ) when BETA = 1.
* Ed Anderson, Cray Research Inc.
*
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX, REAL
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, L, NROWA
COMPLEX TEMP1, TEMP2
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Executable Statements ..
*
* 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( 'CHER2K', 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.REAL( 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*REAL( C( J, J ) )
40 CONTINUE
END IF
ELSE
IF( BETA.EQ.REAL( 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*REAL( 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.REAL( 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*REAL( C( J, J ) )
ELSE
C( J, J ) = REAL( 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*CONJG( B( J, L ) )
TEMP2 = CONJG( 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 ) = REAL( C( J, J ) ) +
$ REAL( A( J, L )*TEMP1 +
$ B( J, L )*TEMP2 )
END IF
120 CONTINUE
130 CONTINUE
ELSE
DO 180, J = 1, N
IF( BETA.EQ.REAL( 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*REAL( C( J, J ) )
ELSE
C( J, J ) = REAL( 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*CONJG( B( J, L ) )
TEMP2 = CONJG( 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 ) = REAL( C( J, J ) ) +
$ REAL( 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 + CONJG( A( L, I ) )*B( L, J )
TEMP2 = TEMP2 + CONJG( B( L, I ) )*A( L, J )
190 CONTINUE
IF( I.EQ.J )THEN
IF( BETA.EQ.REAL( ZERO ) )THEN
C( J, J ) = REAL( ALPHA *TEMP1 +
$ CONJG( ALPHA )*TEMP2 )
ELSE
C( J, J ) = BETA*REAL( C( J, J ) ) +
$ REAL( ALPHA *TEMP1 +
$ CONJG( ALPHA )*TEMP2 )
END IF
ELSE
IF( BETA.EQ.REAL( ZERO ) )THEN
C( I, J ) = ALPHA*TEMP1 + CONJG( ALPHA )*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) +
$ ALPHA*TEMP1 + CONJG( 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 + CONJG( A( L, I ) )*B( L, J )
TEMP2 = TEMP2 + CONJG( B( L, I ) )*A( L, J )
220 CONTINUE
IF( I.EQ.J )THEN
IF( BETA.EQ.REAL( ZERO ) )THEN
C( J, J ) = REAL( ALPHA *TEMP1 +
$ CONJG( ALPHA )*TEMP2 )
ELSE
C( J, J ) = BETA*REAL( C( J, J ) ) +
$ REAL( ALPHA *TEMP1 +
$ CONJG( ALPHA )*TEMP2 )
END IF
ELSE
IF( BETA.EQ.REAL( ZERO ) )THEN
C( I, J ) = ALPHA*TEMP1 + CONJG( ALPHA )*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) +
$ ALPHA*TEMP1 + CONJG( ALPHA )*TEMP2
END IF
END IF
230 CONTINUE
240 CONTINUE
END IF
END IF
*
RETURN
*
* End of CHER2K.
*
END
