*> \brief \b DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix in RFP format. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLANSF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM, TRANSR, UPLO * INTEGER N * .. * .. Array Arguments .. * DOUBLE PRECISION A( 0: * ), WORK( 0: * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLANSF returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> real symmetric matrix A in RFP format. *> \endverbatim *> *> \return DLANSF *> \verbatim *> *> DLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm' *> ( *> ( norm1(A), NORM = '1', 'O' or 'o' *> ( *> ( normI(A), NORM = 'I' or 'i' *> ( *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' *> *> where norm1 denotes the one norm of a matrix (maximum column sum), *> normI denotes the infinity norm of a matrix (maximum row sum) and *> normF denotes the Frobenius norm of a matrix (square root of sum of *> squares). Note that max(abs(A(i,j))) is not a matrix norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies the value to be returned in DLANSF as described *> above. *> \endverbatim *> *> \param[in] TRANSR *> \verbatim *> TRANSR is CHARACTER*1 *> Specifies whether the RFP format of A is normal or *> transposed format. *> = 'N': RFP format is Normal; *> = 'T': RFP format is Transpose. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the RFP matrix A came from *> an upper or lower triangular matrix as follows: *> = 'U': RFP A came from an upper triangular matrix; *> = 'L': RFP A came from a lower triangular matrix. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, DLANSF is *> set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); *> On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') *> part of the symmetric matrix A stored in RFP format. See the *> "Notes" below for more details. *> Unchanged on exit. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, *> WORK is not referenced. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> We first consider Rectangular Full Packed (RFP) Format when N is *> even. We give an example where N = 6. *> *> AP is Upper AP is Lower *> *> 00 01 02 03 04 05 00 *> 11 12 13 14 15 10 11 *> 22 23 24 25 20 21 22 *> 33 34 35 30 31 32 33 *> 44 45 40 41 42 43 44 *> 55 50 51 52 53 54 55 *> *> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of *> the transpose of the first three columns of AP upper. *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of *> the transpose of the last three columns of AP lower. *> This covers the case N even and TRANSR = 'N'. *> *> RFP A RFP A *> *> 03 04 05 33 43 53 *> 13 14 15 00 44 54 *> 23 24 25 10 11 55 *> 33 34 35 20 21 22 *> 00 44 45 30 31 32 *> 01 11 55 40 41 42 *> 02 12 22 50 51 52 *> *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the *> transpose of RFP A above. One therefore gets: *> *> *> RFP A RFP A *> *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 *> *> *> We then consider Rectangular Full Packed (RFP) Format when N is *> odd. We give an example where N = 5. *> *> AP is Upper AP is Lower *> *> 00 01 02 03 04 00 *> 11 12 13 14 10 11 *> 22 23 24 20 21 22 *> 33 34 30 31 32 33 *> 44 40 41 42 43 44 *> *> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of *> the transpose of the first two columns of AP upper. *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of *> the transpose of the last two columns of AP lower. *> This covers the case N odd and TRANSR = 'N'. *> *> RFP A RFP A *> *> 02 03 04 00 33 43 *> 12 13 14 10 11 44 *> 22 23 24 20 21 22 *> 00 33 34 30 31 32 *> 01 11 44 40 41 42 *> *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the *> transpose of RFP A above. One therefore gets: *> *> RFP A RFP A *> *> 02 12 22 00 01 00 10 20 30 40 50 *> 03 13 23 33 11 33 11 21 31 41 51 *> 04 14 24 34 44 43 44 22 32 42 52 *> \endverbatim * * ===================================================================== DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER NORM, TRANSR, UPLO INTEGER N * .. * .. Array Arguments .. DOUBLE PRECISION A( 0: * ), WORK( 0: * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA DOUBLE PRECISION SCALE, S, VALUE, AA, TEMP * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL DLASSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * IF( N.EQ.0 ) THEN DLANSF = ZERO RETURN ELSE IF( N.EQ.1 ) THEN DLANSF = ABS( A(0) ) RETURN END IF * * set noe = 1 if n is odd. if n is even set noe=0 * NOE = 1 IF( MOD( N, 2 ).EQ.0 ) \$ NOE = 0 * * set ifm = 0 when form='T or 't' and 1 otherwise * IFM = 1 IF( LSAME( TRANSR, 'T' ) ) \$ IFM = 0 * * set ilu = 0 when uplo='U or 'u' and 1 otherwise * ILU = 1 IF( LSAME( UPLO, 'U' ) ) \$ ILU = 0 * * set lda = (n+1)/2 when ifm = 0 * set lda = n when ifm = 1 and noe = 1 * set lda = n+1 when ifm = 1 and noe = 0 * IF( IFM.EQ.1 ) THEN IF( NOE.EQ.1 ) THEN LDA = N ELSE * noe=0 LDA = N + 1 END IF ELSE * ifm=0 LDA = ( N+1 ) / 2 END IF * IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * K = ( N+1 ) / 2 VALUE = ZERO IF( NOE.EQ.1 ) THEN * n is odd IF( IFM.EQ.1 ) THEN * A is n by k DO J = 0, K - 1 DO I = 0, N - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END DO ELSE * xpose case; A is k by n DO J = 0, N - 1 DO I = 0, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END DO END IF ELSE * n is even IF( IFM.EQ.1 ) THEN * A is n+1 by k DO J = 0, K - 1 DO I = 0, N TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END DO ELSE * xpose case; A is k by n+1 DO J = 0, N DO I = 0, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END DO END IF END IF ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. \$ ( NORM.EQ.'1' ) ) THEN * * Find normI(A) ( = norm1(A), since A is symmetric). * IF( IFM.EQ.1 ) THEN K = N / 2 IF( NOE.EQ.1 ) THEN * n is odd IF( ILU.EQ.0 ) THEN DO I = 0, K - 1 WORK( I ) = ZERO END DO DO J = 0, K S = ZERO DO I = 0, K + J - 1 AA = ABS( A( I+J*LDA ) ) * -> A(i,j+k) S = S + AA WORK( I ) = WORK( I ) + AA END DO AA = ABS( A( I+J*LDA ) ) * -> A(j+k,j+k) WORK( J+K ) = S + AA IF( I.EQ.K+K ) \$ GO TO 10 I = I + 1 AA = ABS( A( I+J*LDA ) ) * -> A(j,j) WORK( J ) = WORK( J ) + AA S = ZERO DO L = J + 1, K - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * -> A(l,j) S = S + AA WORK( L ) = WORK( L ) + AA END DO WORK( J ) = WORK( J ) + S END DO 10 CONTINUE VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO ELSE * ilu = 1 K = K + 1 * k=(n+1)/2 for n odd and ilu=1 DO I = K, N - 1 WORK( I ) = ZERO END DO DO J = K - 1, 0, -1 S = ZERO DO I = 0, J - 2 AA = ABS( A( I+J*LDA ) ) * -> A(j+k,i+k) S = S + AA WORK( I+K ) = WORK( I+K ) + AA END DO IF( J.GT.0 ) THEN AA = ABS( A( I+J*LDA ) ) * -> A(j+k,j+k) S = S + AA WORK( I+K ) = WORK( I+K ) + S * i=j I = I + 1 END IF AA = ABS( A( I+J*LDA ) ) * -> A(j,j) WORK( J ) = AA S = ZERO DO L = J + 1, N - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * -> A(l,j) S = S + AA WORK( L ) = WORK( L ) + AA END DO WORK( J ) = WORK( J ) + S END DO VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END IF ELSE * n is even IF( ILU.EQ.0 ) THEN DO I = 0, K - 1 WORK( I ) = ZERO END DO DO J = 0, K - 1 S = ZERO DO I = 0, K + J - 1 AA = ABS( A( I+J*LDA ) ) * -> A(i,j+k) S = S + AA WORK( I ) = WORK( I ) + AA END DO AA = ABS( A( I+J*LDA ) ) * -> A(j+k,j+k) WORK( J+K ) = S + AA I = I + 1 AA = ABS( A( I+J*LDA ) ) * -> A(j,j) WORK( J ) = WORK( J ) + AA S = ZERO DO L = J + 1, K - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * -> A(l,j) S = S + AA WORK( L ) = WORK( L ) + AA END DO WORK( J ) = WORK( J ) + S END DO VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO ELSE * ilu = 1 DO I = K, N - 1 WORK( I ) = ZERO END DO DO J = K - 1, 0, -1 S = ZERO DO I = 0, J - 1 AA = ABS( A( I+J*LDA ) ) * -> A(j+k,i+k) S = S + AA WORK( I+K ) = WORK( I+K ) + AA END DO AA = ABS( A( I+J*LDA ) ) * -> A(j+k,j+k) S = S + AA WORK( I+K ) = WORK( I+K ) + S * i=j I = I + 1 AA = ABS( A( I+J*LDA ) ) * -> A(j,j) WORK( J ) = AA S = ZERO DO L = J + 1, N - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * -> A(l,j) S = S + AA WORK( L ) = WORK( L ) + AA END DO WORK( J ) = WORK( J ) + S END DO VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END IF END IF ELSE * ifm=0 K = N / 2 IF( NOE.EQ.1 ) THEN * n is odd IF( ILU.EQ.0 ) THEN N1 = K * n/2 K = K + 1 * k is the row size and lda DO I = N1, N - 1 WORK( I ) = ZERO END DO DO J = 0, N1 - 1 S = ZERO DO I = 0, K - 1 AA = ABS( A( I+J*LDA ) ) * A(j,n1+i) WORK( I+N1 ) = WORK( I+N1 ) + AA S = S + AA END DO WORK( J ) = S END DO * j=n1=k-1 is special S = ABS( A( 0+J*LDA ) ) * A(k-1,k-1) DO I = 1, K - 1 AA = ABS( A( I+J*LDA ) ) * A(k-1,i+n1) WORK( I+N1 ) = WORK( I+N1 ) + AA S = S + AA END DO WORK( J ) = WORK( J ) + S DO J = K, N - 1 S = ZERO DO I = 0, J - K - 1 AA = ABS( A( I+J*LDA ) ) * A(i,j-k) WORK( I ) = WORK( I ) + AA S = S + AA END DO * i=j-k AA = ABS( A( I+J*LDA ) ) * A(j-k,j-k) S = S + AA WORK( J-K ) = WORK( J-K ) + S I = I + 1 S = ABS( A( I+J*LDA ) ) * A(j,j) DO L = J + 1, N - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * A(j,l) WORK( L ) = WORK( L ) + AA S = S + AA END DO WORK( J ) = WORK( J ) + S END DO VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO ELSE * ilu=1 K = K + 1 * k=(n+1)/2 for n odd and ilu=1 DO I = K, N - 1 WORK( I ) = ZERO END DO DO J = 0, K - 2 * process S = ZERO DO I = 0, J - 1 AA = ABS( A( I+J*LDA ) ) * A(j,i) WORK( I ) = WORK( I ) + AA S = S + AA END DO AA = ABS( A( I+J*LDA ) ) * i=j so process of A(j,j) S = S + AA WORK( J ) = S * is initialised here I = I + 1 * i=j process A(j+k,j+k) AA = ABS( A( I+J*LDA ) ) S = AA DO L = K + J + 1, N - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * A(l,k+j) S = S + AA WORK( L ) = WORK( L ) + AA END DO WORK( K+J ) = WORK( K+J ) + S END DO * j=k-1 is special :process col A(k-1,0:k-1) S = ZERO DO I = 0, K - 2 AA = ABS( A( I+J*LDA ) ) * A(k,i) WORK( I ) = WORK( I ) + AA S = S + AA END DO * i=k-1 AA = ABS( A( I+J*LDA ) ) * A(k-1,k-1) S = S + AA WORK( I ) = S * done with col j=k+1 DO J = K, N - 1 * process col j of A = A(j,0:k-1) S = ZERO DO I = 0, K - 1 AA = ABS( A( I+J*LDA ) ) * A(j,i) WORK( I ) = WORK( I ) + AA S = S + AA END DO WORK( J ) = WORK( J ) + S END DO VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END IF ELSE * n is even IF( ILU.EQ.0 ) THEN DO I = K, N - 1 WORK( I ) = ZERO END DO DO J = 0, K - 1 S = ZERO DO I = 0, K - 1 AA = ABS( A( I+J*LDA ) ) * A(j,i+k) WORK( I+K ) = WORK( I+K ) + AA S = S + AA END DO WORK( J ) = S END DO * j=k AA = ABS( A( 0+J*LDA ) ) * A(k,k) S = AA DO I = 1, K - 1 AA = ABS( A( I+J*LDA ) ) * A(k,k+i) WORK( I+K ) = WORK( I+K ) + AA S = S + AA END DO WORK( J ) = WORK( J ) + S DO J = K + 1, N - 1 S = ZERO DO I = 0, J - 2 - K AA = ABS( A( I+J*LDA ) ) * A(i,j-k-1) WORK( I ) = WORK( I ) + AA S = S + AA END DO * i=j-1-k AA = ABS( A( I+J*LDA ) ) * A(j-k-1,j-k-1) S = S + AA WORK( J-K-1 ) = WORK( J-K-1 ) + S I = I + 1 AA = ABS( A( I+J*LDA ) ) * A(j,j) S = AA DO L = J + 1, N - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * A(j,l) WORK( L ) = WORK( L ) + AA S = S + AA END DO WORK( J ) = WORK( J ) + S END DO * j=n S = ZERO DO I = 0, K - 2 AA = ABS( A( I+J*LDA ) ) * A(i,k-1) WORK( I ) = WORK( I ) + AA S = S + AA END DO * i=k-1 AA = ABS( A( I+J*LDA ) ) * A(k-1,k-1) S = S + AA WORK( I ) = WORK( I ) + S VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO ELSE * ilu=1 DO I = K, N - 1 WORK( I ) = ZERO END DO * j=0 is special :process col A(k:n-1,k) S = ABS( A( 0 ) ) * A(k,k) DO I = 1, K - 1 AA = ABS( A( I ) ) * A(k+i,k) WORK( I+K ) = WORK( I+K ) + AA S = S + AA END DO WORK( K ) = WORK( K ) + S DO J = 1, K - 1 * process S = ZERO DO I = 0, J - 2 AA = ABS( A( I+J*LDA ) ) * A(j-1,i) WORK( I ) = WORK( I ) + AA S = S + AA END DO AA = ABS( A( I+J*LDA ) ) * i=j-1 so process of A(j-1,j-1) S = S + AA WORK( J-1 ) = S * is initialised here I = I + 1 * i=j process A(j+k,j+k) AA = ABS( A( I+J*LDA ) ) S = AA DO L = K + J + 1, N - 1 I = I + 1 AA = ABS( A( I+J*LDA ) ) * A(l,k+j) S = S + AA WORK( L ) = WORK( L ) + AA END DO WORK( K+J ) = WORK( K+J ) + S END DO * j=k is special :process col A(k,0:k-1) S = ZERO DO I = 0, K - 2 AA = ABS( A( I+J*LDA ) ) * A(k,i) WORK( I ) = WORK( I ) + AA S = S + AA END DO * i=k-1 AA = ABS( A( I+J*LDA ) ) * A(k-1,k-1) S = S + AA WORK( I ) = S * done with col j=k+1 DO J = K + 1, N * process col j-1 of A = A(j-1,0:k-1) S = ZERO DO I = 0, K - 1 AA = ABS( A( I+J*LDA ) ) * A(j-1,i) WORK( I ) = WORK( I ) + AA S = S + AA END DO WORK( J-1 ) = WORK( J-1 ) + S END DO VALUE = WORK( 0 ) DO I = 1, N-1 TEMP = WORK( I ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) \$ VALUE = TEMP END DO END IF END IF END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * K = ( N+1 ) / 2 SCALE = ZERO S = ONE IF( NOE.EQ.1 ) THEN * n is odd IF( IFM.EQ.1 ) THEN * A is normal IF( ILU.EQ.0 ) THEN * A is upper DO J = 0, K - 3 CALL DLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S ) * L at A(k,0) END DO DO J = 0, K - 1 CALL DLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S ) * trap U at A(0,0) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K-1, A( K ), LDA+1, SCALE, S ) * tri L at A(k,0) CALL DLASSQ( K, A( K-1 ), LDA+1, SCALE, S ) * tri U at A(k-1,0) ELSE * ilu=1 & A is lower DO J = 0, K - 1 CALL DLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S ) * trap L at A(0,0) END DO DO J = 0, K - 2 CALL DLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S ) * U at A(0,1) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) * tri L at A(0,0) CALL DLASSQ( K-1, A( 0+LDA ), LDA+1, SCALE, S ) * tri U at A(0,1) END IF ELSE * A is xpose IF( ILU.EQ.0 ) THEN * A**T is upper DO J = 1, K - 2 CALL DLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S ) * U at A(0,k) END DO DO J = 0, K - 2 CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) * k by k-1 rect. at A(0,0) END DO DO J = 0, K - 2 CALL DLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1, \$ SCALE, S ) * L at A(0,k-1) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K-1, A( 0+K*LDA ), LDA+1, SCALE, S ) * tri U at A(0,k) CALL DLASSQ( K, A( 0+( K-1 )*LDA ), LDA+1, SCALE, S ) * tri L at A(0,k-1) ELSE * A**T is lower DO J = 1, K - 1 CALL DLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) * U at A(0,0) END DO DO J = K, N - 1 CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) * k by k-1 rect. at A(0,k) END DO DO J = 0, K - 3 CALL DLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S ) * L at A(1,0) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) * tri U at A(0,0) CALL DLASSQ( K-1, A( 1 ), LDA+1, SCALE, S ) * tri L at A(1,0) END IF END IF ELSE * n is even IF( IFM.EQ.1 ) THEN * A is normal IF( ILU.EQ.0 ) THEN * A is upper DO J = 0, K - 2 CALL DLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S ) * L at A(k+1,0) END DO DO J = 0, K - 1 CALL DLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S ) * trap U at A(0,0) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K, A( K+1 ), LDA+1, SCALE, S ) * tri L at A(k+1,0) CALL DLASSQ( K, A( K ), LDA+1, SCALE, S ) * tri U at A(k,0) ELSE * ilu=1 & A is lower DO J = 0, K - 1 CALL DLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S ) * trap L at A(1,0) END DO DO J = 1, K - 1 CALL DLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) * U at A(0,0) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K, A( 1 ), LDA+1, SCALE, S ) * tri L at A(1,0) CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) * tri U at A(0,0) END IF ELSE * A is xpose IF( ILU.EQ.0 ) THEN * A**T is upper DO J = 1, K - 1 CALL DLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S ) * U at A(0,k+1) END DO DO J = 0, K - 1 CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) * k by k rect. at A(0,0) END DO DO J = 0, K - 2 CALL DLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE, \$ S ) * L at A(0,k) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K, A( 0+( K+1 )*LDA ), LDA+1, SCALE, S ) * tri U at A(0,k+1) CALL DLASSQ( K, A( 0+K*LDA ), LDA+1, SCALE, S ) * tri L at A(0,k) ELSE * A**T is lower DO J = 1, K - 1 CALL DLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S ) * U at A(0,1) END DO DO J = K + 1, N CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) * k by k rect. at A(0,k+1) END DO DO J = 0, K - 2 CALL DLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S ) * L at A(0,0) END DO S = S + S * double s for the off diagonal elements CALL DLASSQ( K, A( LDA ), LDA+1, SCALE, S ) * tri L at A(0,1) CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) * tri U at A(0,0) END IF END IF END IF VALUE = SCALE*SQRT( S ) END IF * DLANSF = VALUE RETURN * * End of DLANSF * END