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OpenLibm/slatec/ssyr2k.f
Viral B. Shah c977aa998f Add Makefile.extras to build libopenlibm-extras. 
Replace amos with slatec
2012-12-31 16:37:05 -05:00

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*DECK SSYR2K
SUBROUTINE SSYR2K (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA,
$ C, LDC)
C***BEGIN PROLOGUE SSYR2K
C***PURPOSE Perform symmetric rank 2k update of a real symmetric matrix
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B6
C***TYPE SINGLE PRECISION (SSYR2-S, DSYR2-D, CSYR2-C, SSYR2K-S)
C***KEYWORDS LEVEL 3 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J., (ANL)
C Duff, I., (AERE)
C Du Croz, J., (NAG)
C Hammarling, S. (NAG)
C***DESCRIPTION
C
C SSYR2K performs one of the symmetric rank 2k operations
C
C C := alpha*A*B' + alpha*B*A' + beta*C,
C
C or
C
C C := alpha*A'*B + alpha*B'*A + beta*C,
C
C where alpha and beta are scalars, C is an n by n symmetric matrix
C and A and B are n by k matrices in the first case and k by n
C matrices in the second case.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the upper or lower
C triangular part of the array C is to be referenced as
C follows:
C
C UPLO = 'U' or 'u' Only the upper triangular part of C
C is to be referenced.
C
C UPLO = 'L' or 'l' Only the lower triangular part of C
C is to be referenced.
C
C Unchanged on exit.
C
C TRANS - CHARACTER*1.
C On entry, TRANS specifies the operation to be performed as
C follows:
C
C TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
C beta*C.
C
C TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
C beta*C.
C
C TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A +
C beta*C.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix C. N must be
C at least zero.
C Unchanged on exit.
C
C K - INTEGER.
C On entry with TRANS = 'N' or 'n', K specifies the number
C of columns of the matrices A and B, and on entry with
C TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
C of rows of the matrices A and B. K must be at least zero.
C Unchanged on exit.
C
C ALPHA - REAL .
C On entry, ALPHA specifies the scalar alpha.
C Unchanged on exit.
C
C A - REAL array of DIMENSION ( LDA, ka ), where ka is
C k when TRANS = 'N' or 'n', and is n otherwise.
C Before entry with TRANS = 'N' or 'n', the leading n by k
C part of the array A must contain the matrix A, otherwise
C the leading k by n part of the array A must contain the
C matrix A.
C Unchanged on exit.
C
C LDA - INTEGER.
C On entry, LDA specifies the first dimension of A as declared
C in the calling (sub) program. When TRANS = 'N' or 'n'
C then LDA must be at least max( 1, n ), otherwise LDA must
C be at least max( 1, k ).
C Unchanged on exit.
C
C B - REAL array of DIMENSION ( LDB, kb ), where kb is
C k when TRANS = 'N' or 'n', and is n otherwise.
C Before entry with TRANS = 'N' or 'n', the leading n by k
C part of the array B must contain the matrix B, otherwise
C the leading k by n part of the array B must contain the
C matrix B.
C Unchanged on exit.
C
C LDB - INTEGER.
C On entry, LDB specifies the first dimension of B as declared
C in the calling (sub) program. When TRANS = 'N' or 'n'
C then LDB must be at least max( 1, n ), otherwise LDB must
C be at least max( 1, k ).
C Unchanged on exit.
C
C BETA - REAL .
C On entry, BETA specifies the scalar beta.
C Unchanged on exit.
C
C C - REAL array of DIMENSION ( LDC, n ).
C Before entry with UPLO = 'U' or 'u', the leading n by n
C upper triangular part of the array C must contain the upper
C triangular part of the symmetric matrix and the strictly
C lower triangular part of C is not referenced. On exit, the
C upper triangular part of the array C is overwritten by the
C upper triangular part of the updated matrix.
C Before entry with UPLO = 'L' or 'l', the leading n by n
C lower triangular part of the array C must contain the lower
C triangular part of the symmetric matrix and the strictly
C upper triangular part of C is not referenced. On exit, the
C lower triangular part of the array C is overwritten by the
C lower triangular part of the updated matrix.
C
C LDC - INTEGER.
C On entry, LDC specifies the first dimension of C as declared
C in the calling (sub) program. LDC must be at least
C max( 1, n ).
C Unchanged on exit.
C
C***REFERENCES Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S.
C A set of level 3 basic linear algebra subprograms.
C ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 890208 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE SSYR2K
C .. Scalar Arguments ..
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
REAL ALPHA, BETA
C .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), C( LDC, * )
C
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX
C .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, L, NROWA
REAL TEMP1, TEMP2
C .. Parameters ..
REAL ONE , ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
C***FIRST EXECUTABLE STATEMENT SSYR2K
C
C Test the input parameters.
C
IF( LSAME( TRANS, 'N' ) )THEN
NROWA = N
ELSE
NROWA = K
END IF
UPPER = LSAME( UPLO, 'U' )
C
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( 'SSYR2K', 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
C And when alpha.eq.zero.
C
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
C
C Start the operations.
C
IF( LSAME( TRANS, 'N' ) )THEN
C
C Form C := alpha*A*B' + alpha*B*A' + C.
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
C
C Form C := alpha*A'*B + alpha*B'*A + C.
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
C
RETURN
C
C End of SSYR2K.
C
END
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