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SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
* .. Scalar Arguments .. COMPLEX ALPHA REAL BETA INTEGER K,LDA,LDB,LDC,N CHARACTER TRANS,UPLO * .. * .. Array Arguments .. COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) * .. * * Purpose * ======= * * CHER2K performs one of the hermitian rank 2k operations * * C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, * * or * * C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, * * where alpha and beta are scalars with beta real, C is an n by n * hermitian matrix and A and B are n by k matrices in the first case * and k by n matrices in the second case. * * Arguments * ========== * * 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**H + * conjg( alpha )*B*A**H + * beta*C. * * TRANS = 'C' or 'c' C := alpha*A**H*B + * conjg( alpha )*B**H*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 = '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 - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX 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 - COMPLEX 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 - COMPLEX 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 hermitian 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 hermitian 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. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * 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. * * Further Details * =============== * * 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. * * -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. * Ed Anderson, Cray Research Inc. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG,MAX,REAL * .. * .. Local Scalars .. COMPLEX TEMP1,TEMP2 INTEGER I,INFO,J,L,NROWA LOGICAL UPPER * .. * .. Parameters .. REAL ONE PARAMETER (ONE=1.0E+0) COMPLEX ZERO PARAMETER (ZERO= (0.0E+0,0.0E+0)) * .. * * 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,'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('CHER2K',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.REAL(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 - 1 C(I,J) = BETA*C(I,J) 30 CONTINUE C(J,J) = BETA*REAL(C(J,J)) 40 CONTINUE END IF ELSE IF (BETA.EQ.REAL(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 C(J,J) = BETA*REAL(C(J,J)) DO 70 I = J + 1,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**H + conjg( alpha )*B*A**H + * C. * IF (UPPER) THEN DO 130 J = 1,N IF (BETA.EQ.REAL(ZERO)) THEN DO 90 I = 1,J C(I,J) = ZERO 90 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 100 I = 1,J - 1 C(I,J) = BETA*C(I,J) 100 CONTINUE C(J,J) = BETA*REAL(C(J,J)) ELSE C(J,J) = REAL(C(J,J)) END IF DO 120 L = 1,K IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN TEMP1 = ALPHA*CONJG(B(J,L)) TEMP2 = CONJG(ALPHA*A(J,L)) DO 110 I = 1,J - 1 C(I,J) = C(I,J) + A(I,L)*TEMP1 + + B(I,L)*TEMP2 110 CONTINUE C(J,J) = REAL(C(J,J)) + + REAL(A(J,L)*TEMP1+B(J,L)*TEMP2) END IF 120 CONTINUE 130 CONTINUE ELSE DO 180 J = 1,N IF (BETA.EQ.REAL(ZERO)) THEN DO 140 I = J,N C(I,J) = ZERO 140 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 150 I = J + 1,N C(I,J) = BETA*C(I,J) 150 CONTINUE C(J,J) = BETA*REAL(C(J,J)) ELSE C(J,J) = REAL(C(J,J)) END IF DO 170 L = 1,K IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN TEMP1 = ALPHA*CONJG(B(J,L)) TEMP2 = CONJG(ALPHA*A(J,L)) DO 160 I = J + 1,N C(I,J) = C(I,J) + A(I,L)*TEMP1 + + B(I,L)*TEMP2 160 CONTINUE C(J,J) = REAL(C(J,J)) + + REAL(A(J,L)*TEMP1+B(J,L)*TEMP2) END IF 170 CONTINUE 180 CONTINUE END IF ELSE * * Form C := alpha*A**H*B + conjg( alpha )*B**H*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 + CONJG(A(L,I))*B(L,J) TEMP2 = TEMP2 + CONJG(B(L,I))*A(L,J) 190 CONTINUE IF (I.EQ.J) THEN IF (BETA.EQ.REAL(ZERO)) THEN C(J,J) = REAL(ALPHA*TEMP1+ + CONJG(ALPHA)*TEMP2) ELSE C(J,J) = BETA*REAL(C(J,J)) + + REAL(ALPHA*TEMP1+ + CONJG(ALPHA)*TEMP2) END IF ELSE IF (BETA.EQ.REAL(ZERO)) THEN C(I,J) = ALPHA*TEMP1 + CONJG(ALPHA)*TEMP2 ELSE C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + + CONJG(ALPHA)*TEMP2 END IF 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 + CONJG(A(L,I))*B(L,J) TEMP2 = TEMP2 + CONJG(B(L,I))*A(L,J) 220 CONTINUE IF (I.EQ.J) THEN IF (BETA.EQ.REAL(ZERO)) THEN C(J,J) = REAL(ALPHA*TEMP1+ + CONJG(ALPHA)*TEMP2) ELSE C(J,J) = BETA*REAL(C(J,J)) + + REAL(ALPHA*TEMP1+ + CONJG(ALPHA)*TEMP2) END IF ELSE IF (BETA.EQ.REAL(ZERO)) THEN C(I,J) = ALPHA*TEMP1 + CONJG(ALPHA)*TEMP2 ELSE C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + + CONJG(ALPHA)*TEMP2 END IF END IF 230 CONTINUE 240 CONTINUE END IF END IF * RETURN * * End of CHER2K. * END |