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