SUBROUTINE SSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, $ BETA, C, LDC ) **************************************************************************** * * * DATA PARALLEL BLAS based on MPL * * * * Version 1.0 1/9-92 , * * For MasPar MP-1 computers * * * * para//ab, University of Bergen, NORWAY * * * * These programs must be called using F90 style array syntax. * * Note that the F77 style calling sequence has been retained * * in this version for compatibility reasons, be aware that * * parameters related to the array dimensions and shape therefore may * * be redundant and without any influence. * * The calling sequence may be changed in a future version. * * Please report any BUGs, ideas for improvement or other * * comments to * * adm@parallab.uib.no * * * * Future versions may then reflect your suggestions. * * The most current version of this software is available * * from netlib@nac.no , send the message `send index from maspar' * * * * REVISIONS: * * * **************************************************************************** implicit none * .. Scalar Arguments .. CHARACTER*1 UPLO, TRANS INTEGER N, K, LDA, LDB, LDC REAL ALPHA, BETA * .. Array Arguments .. REAL, array(:,:) :: a,b,c intent(in) :: a, b intent(inout) :: c * .. * * Purpose * ======= * * SSYR2K 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 -REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A -REAL 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 -REAL 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 -REAL . * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * C -REAL 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. * * * .. Local Arrays .. integer, array (n,n) :: maskc REAL, array (n,n) :: cloc REAL, array (n,n) :: cltmp * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA EXTERNAL SGEMM * .. Intrinsic Functions .. INTRINSIC MAX INTRINSIC matmul INTRINSIC merge INTRINSIC transpose * .. Local Scalars .. LOGICAL UPPER INTEGER I, INFO, J, L, NROWA REAL TEMP1, TEMP2 * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * cmpf ondpu a,b,c,cloc,cltmp * 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( 'SSYR2K', 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 * * Start the operations. * forall (i = 1:n, j = 1:n) maskc(i,j) = j-i * * And when alpha.eq.zero. * IF( ALPHA.EQ.ZERO )THEN if (upper) then where (maskc.ge.0) cloc = c(1:n,1:n) * beta else where (maskc.le.0) cloc = c(1:n,1:n) * beta endif c ELSE c c now symmetrize it c if (upper) then cloc = merge (c(1:n,1:n),transpose(c(1:n,1:n)),maskc.ge.0) else cloc = merge (c(1:n,1:n),transpose(c(1:n,1:n)),maskc.le.0) endif c c do the matrix multiply c cltmp(1:n,1:n) = 0 IF( LSAME( TRANS, 'N' ) )THEN * * Form C := alpha*A*B' + alpha*B*A' + C. * cts CALL SGEMM('N','T',n,n,k,alpha,a(1:n,1:k),n,b(1:n,1:k) cts $ ,n,ZERO,cltmp(1:n,1:n),n) CALL SGEMM('N','T',n,n,k,alpha,a,n,b $ ,n,ZERO,cltmp,n) cloc = beta * cloc + cltmp + transpose(cltmp(1:n,1:n)) * cloc = beta * cloc + * & alpha * ( matmul(a(1:n,1:k),transpose(b(1:n,1:k))) * & + matmul(b(1:n,1:k),transpose(a(1:n,1:k))) ) ELSE * * Form C := alpha*A'*B + alpha*B'*A + C. * cts CALL SGEMM('T','N',n,n,k,alpha,a(1:k,1:n),k,b(1:k,1:n) cts $ ,k,ZERO,cltmp(1:n,1:n),n) CALL SGEMM('T','N',n,n,k,alpha,a,k,b $ ,k,ZERO,cltmp,n) cloc = beta * cloc + cltmp + transpose(cltmp(1:n,1:n)) * cloc = beta * cloc + * & alpha * ( matmul(transpose(a(1:k,1:n)),b(1:k,1:n)) * & + matmul(transpose(b(1:k,1:n)),a(1:k,1:n)) ) ENDIF ENDIF c c put c back c if (upper) then where (maskc.ge.0) c(1:n,1:n) = cloc else where (maskc.le.0) c(1:n,1:n) = cloc endif * RETURN * * End of SSYR2K. * END