SUBROUTINE CHERK ( UPLO, TRANS, N, K, ALPHA, A, LDA,
$ BETA, C, LDC )
* .. Scalar Arguments ..
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDC
REAL ALPHA, BETA
* .. Array Arguments ..
COMPLEX A( LDA, * ), C( LDC, * )
* ..
*
* Purpose
* =======
*
* CHERK performs one of the hermitian rank k operations
*
* C := alpha*A*conjg( A' ) + beta*C,
*
* or
*
* C := alpha*conjg( A' )*A + beta*C,
*
* where alpha and beta are real scalars, C is an n by n hermitian
* matrix and A is an n by k matrix in the first case and a k by n
* matrix 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( A' ) + beta*C.
*
* TRANS = 'C' or 'c' C := alpha*conjg( A' )*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 matrix A, and on entry with
* TRANS = 'C' or 'c', K specifies the number of rows of the
* matrix A. K must be at least zero.
* Unchanged on exit.
*
* ALPHA - REAL .
* 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.
*
* 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 CMPLX, CONJG, MAX, REAL
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, L, NROWA
REAL RTEMP
COMPLEX TEMP
* .. Parameters ..
REAL ONE , ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 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( LDC.LT.MAX( 1, N ) )THEN
INFO = 10
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'CHERK ', 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.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.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( A' ) + beta*C.
*
IF( UPPER )THEN
DO 130, J = 1, N
IF( BETA.EQ.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.CMPLX( ZERO ) )THEN
TEMP = ALPHA*CONJG( A( J, L ) )
DO 110, I = 1, J - 1
C( I, J ) = C( I, J ) + TEMP*A( I, L )
110 CONTINUE
C( J, J ) = REAL( C( J, J ) ) +
$ REAL( TEMP*A( I, L ) )
END IF
120 CONTINUE
130 CONTINUE
ELSE
DO 180, J = 1, N
IF( BETA.EQ.ZERO )THEN
DO 140, I = J, N
C( I, J ) = ZERO
140 CONTINUE
ELSE IF( BETA.NE.ONE )THEN
C( J, J ) = BETA*REAL( C( J, J ) )
DO 150, I = J + 1, N
C( I, J ) = BETA*C( I, J )
150 CONTINUE
ELSE
C( J, J ) = REAL( C( J, J ) )
END IF
DO 170, L = 1, K
IF( A( J, L ).NE.CMPLX( ZERO ) )THEN
TEMP = ALPHA*CONJG( A( J, L ) )
C( J, J ) = REAL( C( J, J ) ) +
$ REAL( TEMP*A( J, L ) )
DO 160, I = J + 1, N
C( I, J ) = C( I, J ) + TEMP*A( I, L )
160 CONTINUE
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
*
* Form C := alpha*conjg( A' )*A + beta*C.
*
IF( UPPER )THEN
DO 220, J = 1, N
DO 200, I = 1, J - 1
TEMP = ZERO
DO 190, L = 1, K
TEMP = TEMP + CONJG( A( L, I ) )*A( L, J )
190 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( I, J ) = ALPHA*TEMP
ELSE
C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
END IF
200 CONTINUE
RTEMP = ZERO
DO 210, L = 1, K
RTEMP = RTEMP + CONJG( A( L, J ) )*A( L, J )
210 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( J, J ) = ALPHA*RTEMP
ELSE
C( J, J ) = ALPHA*RTEMP + BETA*REAL( C( J, J ) )
END IF
220 CONTINUE
ELSE
DO 260, J = 1, N
RTEMP = ZERO
DO 230, L = 1, K
RTEMP = RTEMP + CONJG( A( L, J ) )*A( L, J )
230 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( J, J ) = ALPHA*RTEMP
ELSE
C( J, J ) = ALPHA*RTEMP + BETA*REAL( C( J, J ) )
END IF
DO 250, I = J + 1, N
TEMP = ZERO
DO 240, L = 1, K
TEMP = TEMP + CONJG( A( L, I ) )*A( L, J )
240 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( I, J ) = ALPHA*TEMP
ELSE
C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
END IF
250 CONTINUE
260 CONTINUE
END IF
END IF
*
RETURN
*
* End of CHERK .
*
END
