SUBROUTINE DSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, &
BETA, C, LDC )
! .. Scalar Arguments ..
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
DOUBLE PRECISION ALPHA, BETA
! .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
! ..
!
! Purpose
! =======
!
! DSYR2K performs one of the symmetric rank 2k operations
!
! C := alpha*A*B' + alpha*B*A' + beta*C,
!
! or
!
! C := alpha*A'*B + alpha*B'*A + beta*C,
!
! where alpha and beta are scalars, C is an n by n symmetric 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*B' + alpha*B*A' +
! beta*C.
!
! TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
! beta*C.
!
! TRANS = 'C' or 'c' C := alpha*A'*B + alpha*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 = 'T' or 't' or '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 - DOUBLE PRECISION.
! On entry, ALPHA specifies the scalar alpha.
! Unchanged on exit.
!
! A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 symmetric 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 symmetric 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.
!
! 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.
!
!
! .. External Functions ..
! LOGICAL LSAME
! EXTERNAL LSAME
! .. External Subroutines ..
! EXTERNAL XERBLA
! .. Intrinsic Functions ..
INTRINSIC MAX
! .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, L, NROWA
DOUBLE PRECISION TEMP1, TEMP2
! .. 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, 'T' ) ).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( 'DSYR2K', 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
C( I, J ) = BETA*C( I, J )
30 CONTINUE
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
DO 70, I = J, 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*B' + alpha*B*A' + 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
C( I, J ) = BETA*C( I, J )
100 CONTINUE
END IF
DO 120, L = 1, K
IF( ( A( J, L ).NE.ZERO ).OR. &
( B( J, L ).NE.ZERO ) )THEN
TEMP1 = ALPHA*B( J, L )
TEMP2 = ALPHA*A( J, L )
DO 110, I = 1, J
C( I, J ) = C( I, J ) + &
A( I, L )*TEMP1 + B( I, L )*TEMP2
110 CONTINUE
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
DO 150, I = J, N
C( I, J ) = BETA*C( I, J )
150 CONTINUE
END IF
DO 170, L = 1, K
IF( ( A( J, L ).NE.ZERO ).OR. &
( B( J, L ).NE.ZERO ) )THEN
TEMP1 = ALPHA*B( J, L )
TEMP2 = ALPHA*A( J, L )
DO 160, I = J, N
C( I, J ) = C( I, J ) + &
A( I, L )*TEMP1 + B( I, L )*TEMP2
160 CONTINUE
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
!
! Form C := alpha*A'*B + alpha*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 + A( L, I )*B( L, J )
TEMP2 = TEMP2 + B( L, I )*A( L, J )
190 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) + &
ALPHA*TEMP1 + ALPHA*TEMP2
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 + A( L, I )*B( L, J )
TEMP2 = TEMP2 + B( L, I )*A( L, J )
220 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) + &
ALPHA*TEMP1 + ALPHA*TEMP2
END IF
230 CONTINUE
240 CONTINUE
END IF
END IF
!
RETURN
!
! End of DSYR2K.
!
END SUBROUTINE DSYR2K