SUBROUTINE MB01YD( UPLO, TRANS, N, K, L, ALPHA, BETA, A, LDA, C,
$ LDC, INFO )
C
C PURPOSE
C
C To perform the symmetric rank k operations
C
C C := alpha*op( A )*op( A )' + beta*C,
C
C where alpha and beta are scalars, C is an n-by-n symmetric matrix,
C op( A ) is an n-by-k matrix, and op( A ) is one of
C
C op( A ) = A or op( A ) = A'.
C
C The matrix A has l nonzero codiagonals, either upper or lower.
C
C ARGUMENTS
C
C Mode Parameters
C
C UPLO CHARACTER*1
C Specifies which triangle of the symmetric matrix C
C is given and computed, as follows:
C = 'U': the upper triangular part is given/computed;
C = 'L': the lower triangular part is given/computed.
C UPLO also defines the pattern of the matrix A (see below).
C
C TRANS CHARACTER*1
C Specifies the form of op( A ) to be used, as follows:
C = 'N': op( A ) = A;
C = 'T': op( A ) = A';
C = 'C': op( A ) = A'.
C
C Input/Output Parameters
C
C N (input) INTEGER
C The order of the matrix C. N >= 0.
C
C K (input) INTEGER
C The number of columns of the matrix op( A ). K >= 0.
C
C L (input) INTEGER
C If UPLO = 'U', matrix A has L nonzero subdiagonals.
C If UPLO = 'L', matrix A has L nonzero superdiagonals.
C MAX(0,NR-1) >= L >= 0, if UPLO = 'U',
C MAX(0,NC-1) >= L >= 0, if UPLO = 'L',
C where NR and NC are the numbers of rows and columns of the
C matrix A, respectively.
C
C ALPHA (input) DOUBLE PRECISION
C The scalar alpha. When alpha is zero then the array A is
C not referenced.
C
C BETA (input) DOUBLE PRECISION
C The scalar beta. When beta is zero then the array C need
C not be set before entry.
C
C A (input) DOUBLE PRECISION array, dimension (LDA,NC), where
C NC is K when TRANS = 'N', and is N otherwise.
C If TRANS = 'N', the leading N-by-K part of this array must
C contain the matrix A, otherwise the leading K-by-N part of
C this array must contain the matrix A.
C If UPLO = 'U', only the upper triangular part and the
C first L subdiagonals are referenced, and the remaining
C subdiagonals are assumed to be zero.
C If UPLO = 'L', only the lower triangular part and the
C first L superdiagonals are referenced, and the remaining
C superdiagonals are assumed to be zero.
C
C LDA INTEGER
C The leading dimension of array A. LDA >= max(1,NR),
C where NR = N, if TRANS = 'N', and NR = K, otherwise.
C
C C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
C On entry with UPLO = 'U', the leading N-by-N upper
C triangular part of this array must contain the upper
C triangular part of the symmetric matrix C.
C On entry with UPLO = 'L', the leading N-by-N lower
C triangular part of this array must contain the lower
C triangular part of the symmetric matrix C.
C On exit, the leading N-by-N upper triangular part (if
C UPLO = 'U'), or lower triangular part (if UPLO = 'L'), of
C this array contains the corresponding triangular part of
C the updated matrix C.
C
C LDC INTEGER
C The leading dimension of array C. LDC >= MAX(1,N).
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C METHOD
C
C The calculations are efficiently performed taking the symmetry
C and structure into account.
C
C FURTHER COMMENTS
C
C The matrix A may have the following patterns, when n = 7, k = 5,
C and l = 2 are used for illustration:
C
C UPLO = 'U', TRANS = 'N' UPLO = 'L', TRANS = 'N'
C
C [ x x x x x ] [ x x x 0 0 ]
C [ x x x x x ] [ x x x x 0 ]
C [ x x x x x ] [ x x x x x ]
C A = [ 0 x x x x ], A = [ x x x x x ],
C [ 0 0 x x x ] [ x x x x x ]
C [ 0 0 0 x x ] [ x x x x x ]
C [ 0 0 0 0 x ] [ x x x x x ]
C
C UPLO = 'U', TRANS = 'T' UPLO = 'L', TRANS = 'T'
C
C [ x x x x x x x ] [ x x x 0 0 0 0 ]
C [ x x x x x x x ] [ x x x x 0 0 0 ]
C A = [ x x x x x x x ], A = [ x x x x x 0 0 ].
C [ 0 x x x x x x ] [ x x x x x x 0 ]
C [ 0 0 x x x x x ] [ x x x x x x x ]
C
C If N = K, the matrix A is upper or lower triangular, for L = 0,
C and upper or lower Hessenberg, for L = 1.
C
C This routine is a specialization of the BLAS 3 routine DSYRK.
C BLAS 1 calls are used when appropriate, instead of in-line code,
C in order to increase the efficiency. If the matrix A is full, or
C its zero triangle has small order, an optimized DSYRK code could
C be faster than MB01YD.
C
C CONTRIBUTOR
C
C V. Sima, Research Institute for Informatics, Bucharest, Nov. 2000.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Elementary matrix operations, matrix operations.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
C ..
C .. Scalar Arguments ..
CHARACTER TRANS, UPLO
INTEGER INFO, LDA, LDC, K, L, N
DOUBLE PRECISION ALPHA, BETA
C ..
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), C( LDC, * )
C ..
C .. Local Scalars ..
LOGICAL TRANSP, UPPER
INTEGER I, J, M, NCOLA, NROWA
DOUBLE PRECISION TEMP
C ..
C .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DDOT
EXTERNAL DDOT, LSAME
C ..
C .. External Subroutines ..
EXTERNAL DAXPY, DLASCL, DLASET, DSCAL, XERBLA
C ..
C .. Intrinsic Functions ..
INTRINSIC MAX, MIN
C ..
C .. Executable Statements ..
C
C Test the input scalar arguments.
C
INFO = 0
UPPER = LSAME( UPLO, 'U' )
TRANSP = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' )
C
IF( TRANSP )THEN
NROWA = K
NCOLA = N
ELSE
NROWA = N
NCOLA = K
END IF
C
IF( UPPER )THEN
M = NROWA
ELSE
M = NCOLA
END IF
C
IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( TRANSP .OR. LSAME( TRANS, 'N' ) ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( K.LT.0 ) THEN
INFO = -4
ELSE IF( L.LT.0 .OR. L.GT.MAX( 0, M-1 ) ) THEN
INFO = -5
ELSE IF( LDA.LT.MAX( 1, NROWA ) ) THEN
INFO = -9
ELSE IF( LDC.LT.MAX( 1, N ) ) THEN
INFO = -11
END IF
C
IF( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'MB01YD', -INFO )
RETURN
END IF
C
C Quick return, if possible.
C
IF( ( N.EQ.0 ).OR.
$ ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
C
IF ( ALPHA.EQ.ZERO ) THEN
IF ( BETA.EQ.ZERO ) THEN
C
C Special case when both alpha = 0 and beta = 0.
C
CALL DLASET( UPLO, N, N, ZERO, ZERO, C, LDC )
ELSE
C
C Special case alpha = 0.
C
CALL DLASCL( UPLO, 0, 0, ONE, BETA, N, N, C, LDC, INFO )
END IF
RETURN
END IF
C
C General case: alpha <> 0.
C
IF ( .NOT.TRANSP ) THEN
C
C Form C := alpha*A*A' + beta*C.
C
IF ( UPPER ) THEN
C
DO 30 J = 1, N
IF ( BETA.EQ.ZERO ) THEN
C
DO 10 I = 1, J
C( I, J ) = ZERO
10 CONTINUE
C
ELSE IF ( BETA.NE.ONE ) THEN
CALL DSCAL ( J, BETA, C( 1, J ), 1 )
END IF
C
DO 20 M = MAX( 1, J-L ), K
CALL DAXPY ( MIN( J, L+M ), ALPHA*A( J, M ),
$ A( 1, M ), 1, C( 1, J ), 1 )
20 CONTINUE
C
30 CONTINUE
C
ELSE
C
DO 60 J = 1, N
IF ( BETA.EQ.ZERO ) THEN
C
DO 40 I = J, N
C( I, J ) = ZERO
40 CONTINUE
C
ELSE IF ( BETA.NE.ONE ) THEN
CALL DSCAL ( N-J+1, BETA, C( J, J ), 1 )
END IF
C
DO 50 M = 1, MIN( J+L, K )
CALL DAXPY ( N-J+1, ALPHA*A( J, M ), A( J, M ), 1,
$ C( J, J ), 1 )
50 CONTINUE
C
60 CONTINUE
C
END IF
C
ELSE
C
C Form C := alpha*A'*A + beta*C.
C
IF ( UPPER ) THEN
C
DO 80 J = 1, N
C
DO 70 I = 1, J
TEMP = ALPHA*DDOT ( MIN( J+L, K ), A( 1, I ), 1,
$ A( 1, J ), 1 )
IF ( BETA.EQ.ZERO ) THEN
C( I, J ) = TEMP
ELSE
C( I, J ) = TEMP + BETA*C( I, J )
END IF
70 CONTINUE
C
80 CONTINUE
C
ELSE
C
DO 100 J = 1, N
C
DO 90 I = J, N
M = MAX( 1, I-L )
TEMP = ALPHA*DDOT ( K-M+1, A( M, I ), 1, A( M, J ),
$ 1 )
IF ( BETA.EQ.ZERO ) THEN
C( I, J ) = TEMP
ELSE
C( I, J ) = TEMP + BETA*C( I, J )
END IF
90 CONTINUE
C
100 CONTINUE
C
END IF
C
END IF
C
RETURN
C
C *** Last line of MB01YD ***
END