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- 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
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