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- SUBROUTINE ZHERK( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )
-* .. Scalar Arguments ..
- CHARACTER TRANS, UPLO
- INTEGER K, LDA, LDC, N
- DOUBLE PRECISION ALPHA, BETA
-* ..
-* .. Array Arguments ..
- COMPLEX*16 A( LDA, * ), C( LDC, * )
-* ..
-*
-* Purpose
-* =======
-*
-* ZHERK 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 - DOUBLE PRECISION .
-* 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.
-*
-* 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.
-*
-*
-* 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, DCMPLX, DCONJG, MAX
-* ..
-* .. Local Scalars ..
- LOGICAL UPPER
- INTEGER I, INFO, J, L, NROWA
- DOUBLE PRECISION RTEMP
- COMPLEX*16 TEMP
-* ..
-* .. Parameters ..
- DOUBLE PRECISION ONE, ZERO
- PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+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( 'ZHERK ', 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*DBLE( 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*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( 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*DBLE( C( J, J ) )
- ELSE
- C( J, J ) = DBLE( C( J, J ) )
- END IF
- DO 120 L = 1, K
- IF( A( J, L ).NE.DCMPLX( ZERO ) ) THEN
- TEMP = ALPHA*DCONJG( A( J, L ) )
- DO 110 I = 1, J - 1
- C( I, J ) = C( I, J ) + TEMP*A( I, L )
- 110 CONTINUE
- C( J, J ) = DBLE( C( J, J ) ) +
- $ DBLE( 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*DBLE( C( J, J ) )
- DO 150 I = J + 1, N
- C( I, J ) = BETA*C( I, J )
- 150 CONTINUE
- ELSE
- C( J, J ) = DBLE( C( J, J ) )
- END IF
- DO 170 L = 1, K
- IF( A( J, L ).NE.DCMPLX( ZERO ) ) THEN
- TEMP = ALPHA*DCONJG( A( J, L ) )
- C( J, J ) = DBLE( C( J, J ) ) +
- $ DBLE( 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 + DCONJG( 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 + DCONJG( 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*DBLE( C( J, J ) )
- END IF
- 220 CONTINUE
- ELSE
- DO 260 J = 1, N
- RTEMP = ZERO
- DO 230 L = 1, K
- RTEMP = RTEMP + DCONJG( 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*DBLE( C( J, J ) )
- END IF
- DO 250 I = J + 1, N
- TEMP = ZERO
- DO 240 L = 1, K
- TEMP = TEMP + DCONJG( 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 ZHERK .
-*
- END
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