328 lines
10 KiB
FortranFixed
328 lines
10 KiB
FortranFixed
SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
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* .. Scalar Arguments ..
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REAL ALPHA,BETA
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INTEGER K,LDA,LDC,N
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CHARACTER TRANS,UPLO
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* ..
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* .. Array Arguments ..
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COMPLEX A(LDA,*),C(LDC,*)
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* ..
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*
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* Purpose
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* =======
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*
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* CHERK performs one of the hermitian rank k operations
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*
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* C := alpha*A*conjg( A' ) + beta*C,
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*
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* or
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*
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* C := alpha*conjg( A' )*A + beta*C,
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*
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* where alpha and beta are real scalars, C is an n by n hermitian
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* matrix and A is an n by k matrix in the first case and a k by n
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* matrix in the second case.
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*
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* Arguments
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the upper or lower
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* triangular part of the array C is to be referenced as
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* follows:
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*
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* UPLO = 'U' or 'u' Only the upper triangular part of C
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* is to be referenced.
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*
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* UPLO = 'L' or 'l' Only the lower triangular part of C
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* is to be referenced.
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*
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* Unchanged on exit.
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*
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* TRANS - CHARACTER*1.
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* On entry, TRANS specifies the operation to be performed as
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* follows:
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*
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* TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C.
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*
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* TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix C. N must be
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* at least zero.
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* Unchanged on exit.
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*
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* K - INTEGER.
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* On entry with TRANS = 'N' or 'n', K specifies the number
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* of columns of the matrix A, and on entry with
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* TRANS = 'C' or 'c', K specifies the number of rows of the
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* matrix A. K must be at least zero.
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* Unchanged on exit.
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*
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* ALPHA - REAL .
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* On entry, ALPHA specifies the scalar alpha.
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* Unchanged on exit.
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*
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* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
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* k when TRANS = 'N' or 'n', and is n otherwise.
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* Before entry with TRANS = 'N' or 'n', the leading n by k
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* part of the array A must contain the matrix A, otherwise
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* the leading k by n part of the array A must contain the
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* matrix A.
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* Unchanged on exit.
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*
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* LDA - INTEGER.
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* On entry, LDA specifies the first dimension of A as declared
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* in the calling (sub) program. When TRANS = 'N' or 'n'
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* then LDA must be at least max( 1, n ), otherwise LDA must
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* be at least max( 1, k ).
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* Unchanged on exit.
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*
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* BETA - REAL .
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* On entry, BETA specifies the scalar beta.
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* Unchanged on exit.
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*
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* C - COMPLEX array of DIMENSION ( LDC, n ).
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* Before entry with UPLO = 'U' or 'u', the leading n by n
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* upper triangular part of the array C must contain the upper
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* triangular part of the hermitian matrix and the strictly
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* lower triangular part of C is not referenced. On exit, the
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* upper triangular part of the array C is overwritten by the
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* upper triangular part of the updated matrix.
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* Before entry with UPLO = 'L' or 'l', the leading n by n
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* lower triangular part of the array C must contain the lower
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* triangular part of the hermitian matrix and the strictly
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* upper triangular part of C is not referenced. On exit, the
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* lower triangular part of the array C is overwritten by the
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* lower triangular part of the updated matrix.
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* Note that the imaginary parts of the diagonal elements need
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* not be set, they are assumed to be zero, and on exit they
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* are set to zero.
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*
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* LDC - INTEGER.
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* On entry, LDC specifies the first dimension of C as declared
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* in the calling (sub) program. LDC must be at least
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* max( 1, n ).
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* Unchanged on exit.
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*
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*
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* Level 3 Blas routine.
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*
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* -- Written on 8-February-1989.
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* Jack Dongarra, Argonne National Laboratory.
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* Iain Duff, AERE Harwell.
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* Jeremy Du Croz, Numerical Algorithms Group Ltd.
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* Sven Hammarling, Numerical Algorithms Group Ltd.
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*
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* -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
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* Ed Anderson, Cray Research Inc.
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*
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*
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CMPLX,CONJG,MAX,REAL
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* ..
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* .. Local Scalars ..
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COMPLEX TEMP
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REAL RTEMP
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INTEGER I,INFO,J,L,NROWA
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LOGICAL UPPER
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* ..
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* .. Parameters ..
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REAL ONE,ZERO
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PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
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* ..
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*
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* Test the input parameters.
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*
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IF (LSAME(TRANS,'N')) THEN
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NROWA = N
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ELSE
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NROWA = K
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END IF
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UPPER = LSAME(UPLO,'U')
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*
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INFO = 0
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IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
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INFO = 1
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ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
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+ (.NOT.LSAME(TRANS,'C'))) THEN
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INFO = 2
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ELSE IF (N.LT.0) THEN
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INFO = 3
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ELSE IF (K.LT.0) THEN
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INFO = 4
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
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INFO = 7
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ELSE IF (LDC.LT.MAX(1,N)) THEN
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INFO = 10
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('CHERK ',INFO)
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
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+ (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
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*
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* And when alpha.eq.zero.
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*
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IF (ALPHA.EQ.ZERO) THEN
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IF (UPPER) THEN
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IF (BETA.EQ.ZERO) THEN
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DO 20 J = 1,N
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DO 10 I = 1,J
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C(I,J) = ZERO
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10 CONTINUE
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20 CONTINUE
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ELSE
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DO 40 J = 1,N
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DO 30 I = 1,J - 1
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C(I,J) = BETA*C(I,J)
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30 CONTINUE
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C(J,J) = BETA*REAL(C(J,J))
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40 CONTINUE
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END IF
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ELSE
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IF (BETA.EQ.ZERO) THEN
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DO 60 J = 1,N
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DO 50 I = J,N
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C(I,J) = ZERO
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50 CONTINUE
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60 CONTINUE
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ELSE
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DO 80 J = 1,N
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C(J,J) = BETA*REAL(C(J,J))
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DO 70 I = J + 1,N
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C(I,J) = BETA*C(I,J)
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70 CONTINUE
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80 CONTINUE
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END IF
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END IF
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RETURN
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END IF
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*
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* Start the operations.
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*
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IF (LSAME(TRANS,'N')) THEN
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*
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* Form C := alpha*A*conjg( A' ) + beta*C.
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*
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IF (UPPER) THEN
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DO 130 J = 1,N
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IF (BETA.EQ.ZERO) THEN
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DO 90 I = 1,J
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C(I,J) = ZERO
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90 CONTINUE
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ELSE IF (BETA.NE.ONE) THEN
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DO 100 I = 1,J - 1
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C(I,J) = BETA*C(I,J)
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100 CONTINUE
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C(J,J) = BETA*REAL(C(J,J))
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ELSE
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C(J,J) = REAL(C(J,J))
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END IF
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DO 120 L = 1,K
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IF (A(J,L).NE.CMPLX(ZERO)) THEN
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TEMP = ALPHA*CONJG(A(J,L))
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DO 110 I = 1,J - 1
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C(I,J) = C(I,J) + TEMP*A(I,L)
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110 CONTINUE
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C(J,J) = REAL(C(J,J)) + REAL(TEMP*A(I,L))
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END IF
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120 CONTINUE
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130 CONTINUE
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ELSE
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DO 180 J = 1,N
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IF (BETA.EQ.ZERO) THEN
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DO 140 I = J,N
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C(I,J) = ZERO
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140 CONTINUE
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ELSE IF (BETA.NE.ONE) THEN
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C(J,J) = BETA*REAL(C(J,J))
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DO 150 I = J + 1,N
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C(I,J) = BETA*C(I,J)
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150 CONTINUE
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ELSE
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C(J,J) = REAL(C(J,J))
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END IF
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DO 170 L = 1,K
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IF (A(J,L).NE.CMPLX(ZERO)) THEN
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TEMP = ALPHA*CONJG(A(J,L))
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C(J,J) = REAL(C(J,J)) + REAL(TEMP*A(J,L))
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DO 160 I = J + 1,N
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C(I,J) = C(I,J) + TEMP*A(I,L)
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160 CONTINUE
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END IF
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170 CONTINUE
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180 CONTINUE
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END IF
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ELSE
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*
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* Form C := alpha*conjg( A' )*A + beta*C.
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*
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IF (UPPER) THEN
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DO 220 J = 1,N
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DO 200 I = 1,J - 1
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TEMP = ZERO
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DO 190 L = 1,K
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TEMP = TEMP + CONJG(A(L,I))*A(L,J)
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190 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = ALPHA*TEMP
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ELSE
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C(I,J) = ALPHA*TEMP + BETA*C(I,J)
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END IF
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200 CONTINUE
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RTEMP = ZERO
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DO 210 L = 1,K
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RTEMP = RTEMP + CONJG(A(L,J))*A(L,J)
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210 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(J,J) = ALPHA*RTEMP
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ELSE
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C(J,J) = ALPHA*RTEMP + BETA*REAL(C(J,J))
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END IF
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220 CONTINUE
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ELSE
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DO 260 J = 1,N
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RTEMP = ZERO
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DO 230 L = 1,K
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RTEMP = RTEMP + CONJG(A(L,J))*A(L,J)
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230 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(J,J) = ALPHA*RTEMP
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ELSE
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C(J,J) = ALPHA*RTEMP + BETA*REAL(C(J,J))
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END IF
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DO 250 I = J + 1,N
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TEMP = ZERO
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DO 240 L = 1,K
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TEMP = TEMP + CONJG(A(L,I))*A(L,J)
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240 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = ALPHA*TEMP
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ELSE
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C(I,J) = ALPHA*TEMP + BETA*C(I,J)
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END IF
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250 CONTINUE
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260 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of CHERK .
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*
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END
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