*> \brief \b ZLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLANHF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM, TRANSR, UPLO * INTEGER N * .. * .. Array Arguments .. * DOUBLE PRECISION WORK( 0: * ) * COMPLEX*16 A( 0: * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLANHF returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> complex Hermitian matrix A in RFP format. *> \endverbatim *> *> \return ZLANHF *> \verbatim *> *> ZLANHF = ( 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 *> Specifies the value to be returned in ZLANHF as described *> above. *> \endverbatim *> *> \param[in] TRANSR *> \verbatim *> TRANSR is CHARACTER *> Specifies whether the RFP format of A is normal or *> conjugate-transposed format. *> = 'N': RFP format is Normal *> = 'C': RFP format is Conjugate-transposed *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER *> On entry, UPLO specifies whether the RFP matrix A came from *> an upper or lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' RFP A came from an upper triangular *> matrix *> *> UPLO = 'L' or '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, ZLANHF is *> set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); *> On entry, the matrix A in RFP Format. *> RFP Format is described by TRANSR, UPLO and N as follows: *> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; *> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If *> TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A *> as defined when TRANSR = 'N'. The contents of RFP A are *> defined by UPLO as follows: If UPLO = 'U' the RFP A *> contains the ( N*(N+1)/2 ) elements of upper packed A *> either in normal or conjugate-transpose Format. If *> UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements *> of lower packed A either in normal or conjugate-transpose *> Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When *> TRANSR is 'N' the LDA is N+1 when N is even and is N when *> is odd. See the Note below for more details. *> Unchanged on exit. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (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 November 2015 * *> \ingroup complex16OTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> We first consider Standard Packed 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 *> conjugate-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 *> conjugate-transpose of the last three columns of AP lower. *> To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- *> 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 next consider Standard Packed 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 *> conjugate-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 *> conjugate-transpose of the last two columns of AP lower. *> To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- *> 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 ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) * * -- LAPACK computational routine (version 3.6.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2015 * * .. Scalar Arguments .. CHARACTER NORM, TRANSR, UPLO INTEGER N * .. * .. Array Arguments .. DOUBLE PRECISION WORK( 0: * ) COMPLEX*16 A( 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 ZLASSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, SQRT * .. * .. Executable Statements .. * IF( N.EQ.0 ) THEN ZLANHF = ZERO RETURN ELSE IF( N.EQ.1 ) THEN ZLANHF = ABS(DBLE(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='C' or 'c' and 1 otherwise * IFM = 1 IF( LSAME( TRANSR, 'C' ) ) $ 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 & n = k + k - 1 IF( IFM.EQ.1 ) THEN * A is n by k IF( ILU.EQ.1 ) THEN * uplo ='L' J = 0 * -> L(0,0) TEMP = ABS( DBLE( A( J+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = 1, N - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO DO J = 1, K - 1 DO I = 0, J - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = J - 1 * L(k+j,k+j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = J * -> L(j,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = J + 1, N - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO ELSE * uplo = 'U' DO J = 0, K - 2 DO I = 0, K + J - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = K + J - 1 * -> U(i,i) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = I + 1 * =k+j; i -> U(j,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = K + J + 1, N - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO DO I = 0, N - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP * j=k-1 END DO * i=n-1 -> U(n-1,n-1) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END IF ELSE * xpose case; A is k by n IF( ILU.EQ.1 ) THEN * uplo ='L' DO J = 0, K - 2 DO I = 0, J - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = J * L(i,i) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = J + 1 * L(j+k,j+k) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = J + 2, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO J = K - 1 DO I = 0, K - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = K - 1 * -> L(i,i) is at A(i,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO J = K, 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 ELSE * uplo = 'U' DO J = 0, K - 2 DO I = 0, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO J = K - 1 * -> U(j,j) is at A(0,j) TEMP = ABS( DBLE( A( 0+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = 1, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO DO J = K, N - 1 DO I = 0, J - K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = J - K * -> U(i,i) at A(i,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = J - K + 1 * U(j,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = J - K + 2, 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 * n is even & k = n/2 IF( IFM.EQ.1 ) THEN * A is n+1 by k IF( ILU.EQ.1 ) THEN * uplo ='L' J = 0 * -> L(k,k) & j=1 -> L(0,0) TEMP = ABS( DBLE( A( J+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP TEMP = ABS( DBLE( A( J+1+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = 2, N TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO DO J = 1, K - 1 DO I = 0, J - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = J * L(k+j,k+j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = J + 1 * -> L(j,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = J + 2, N TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO ELSE * uplo = 'U' DO J = 0, K - 2 DO I = 0, K + J - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = K + J * -> U(i,i) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = I + 1 * =k+j+1; i -> U(j,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = K + J + 2, N TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO DO I = 0, N - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP * j=k-1 END DO * i=n-1 -> U(n-1,n-1) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = N * -> U(k-1,k-1) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END IF ELSE * xpose case; A is k by n+1 IF( ILU.EQ.1 ) THEN * uplo ='L' J = 0 * -> L(k,k) at A(0,0) TEMP = ABS( DBLE( A( J+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = 1, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO DO J = 1, K - 1 DO I = 0, J - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = J - 1 * L(i,i) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = J * L(j+k,j+k) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = J + 1, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO J = K DO I = 0, K - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = K - 1 * -> L(i,i) is at A(i,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO J = K + 1, 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 ELSE * uplo = 'U' DO J = 0, K - 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 J = K * -> U(j,j) is at A(0,j) TEMP = ABS( DBLE( A( 0+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = 1, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO DO J = K + 1, N - 1 DO I = 0, J - K - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = J - K - 1 * -> U(i,i) at A(i,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP I = J - K * U(j,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP DO I = J - K + 1, K - 1 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO END DO J = N DO I = 0, K - 2 TEMP = ABS( A( I+J*LDA ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END DO I = K - 1 * U(k,k) at A(i,j) TEMP = ABS( DBLE( A( I+J*LDA ) ) ) IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) $ VALUE = TEMP END IF 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 Hermitian). * IF( IFM.EQ.1 ) THEN * A is 'N' K = N / 2 IF( NOE.EQ.1 ) THEN * n is odd & A is n by (n+1)/2 IF( ILU.EQ.0 ) THEN * uplo = 'U' 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( DBLE( 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( DBLE( 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 & uplo = 'L' 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( DBLE( 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( DBLE( 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 & A is n+1 by k = n/2 IF( ILU.EQ.0 ) THEN * uplo = 'U' 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( DBLE( A( I+J*LDA ) ) ) * -> A(j+k,j+k) WORK( J+K ) = S + AA I = I + 1 AA = ABS( DBLE( 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 & uplo = 'L' 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( DBLE( 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( DBLE( 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 & A is (n+1)/2 by n IF( ILU.EQ.0 ) THEN * uplo = 'U' 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( DBLE( 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( DBLE( A( I+J*LDA ) ) ) * A(j-k,j-k) S = S + AA WORK( J-K ) = WORK( J-K ) + S I = I + 1 S = ABS( DBLE( 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 & uplo = 'L' 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( DBLE( 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( DBLE( 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( DBLE( 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 & A is k=n/2 by n+1 IF( ILU.EQ.0 ) THEN * uplo = 'U' 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( DBLE( 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( DBLE( 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( DBLE( 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( DBLE( 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 & uplo = 'L' DO I = K, N - 1 WORK( I ) = ZERO END DO * j=0 is special :process col A(k:n-1,k) S = ABS( DBLE( 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( DBLE( 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( DBLE( 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( DBLE( 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 & A is n by k IF( ILU.EQ.0 ) THEN * A is upper DO J = 0, K - 3 CALL ZLASSQ( 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 ZLASSQ( 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 L = K - 1 * -> U(k,k) at A(k-1,0) DO I = 0, K - 2 AA = DBLE( A( L ) ) * U(k+i,k+i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * U(i,i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO AA = DBLE( A( L ) ) * U(n-1,n-1) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF ELSE * ilu=1 & A is lower DO J = 0, K - 1 CALL ZLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S ) * trap L at A(0,0) END DO DO J = 1, K - 2 CALL ZLASSQ( 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 AA = DBLE( A( 0 ) ) * L(0,0) at A(0,0) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = LDA * -> L(k,k) at A(0,1) DO I = 1, K - 1 AA = DBLE( A( L ) ) * L(k-1+i,k-1+i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * L(i,i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO END IF ELSE * A is xpose & A is k by n IF( ILU.EQ.0 ) THEN * A**H is upper DO J = 1, K - 2 CALL ZLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S ) * U at A(0,k) END DO DO J = 0, K - 2 CALL ZLASSQ( 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 ZLASSQ( 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 L = 0 + K*LDA - LDA * -> U(k-1,k-1) at A(0,k-1) AA = DBLE( A( L ) ) * U(k-1,k-1) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA * -> U(0,0) at A(0,k) DO J = K, N - 1 AA = DBLE( A( L ) ) * -> U(j-k,j-k) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * -> U(j,j) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO ELSE * A**H is lower DO J = 1, K - 1 CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) * U at A(0,0) END DO DO J = K, N - 1 CALL ZLASSQ( 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 ZLASSQ( 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 L = 0 * -> L(0,0) at A(0,0) DO I = 0, K - 2 AA = DBLE( A( L ) ) * L(i,i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * L(k+i,k+i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO * L-> k-1 + (k-1)*lda or L(k-1,k-1) at A(k-1,k-1) AA = DBLE( A( L ) ) * L(k-1,k-1) at A(k-1,k-1) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF 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 ZLASSQ( 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 ZLASSQ( 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 L = K * -> U(k,k) at A(k,0) DO I = 0, K - 1 AA = DBLE( A( L ) ) * U(k+i,k+i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * U(i,i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO ELSE * ilu=1 & A is lower DO J = 0, K - 1 CALL ZLASSQ( 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 ZLASSQ( 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 L = 0 * -> L(k,k) at A(0,0) DO I = 0, K - 1 AA = DBLE( A( L ) ) * L(k-1+i,k-1+i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * L(i,i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO END IF ELSE * A is xpose IF( ILU.EQ.0 ) THEN * A**H is upper DO J = 1, K - 1 CALL ZLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S ) * U at A(0,k+1) END DO DO J = 0, K - 1 CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) * k by k rect. at A(0,0) END DO DO J = 0, K - 2 CALL ZLASSQ( 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 L = 0 + K*LDA * -> U(k,k) at A(0,k) AA = DBLE( A( L ) ) * U(k,k) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA * -> U(0,0) at A(0,k+1) DO J = K + 1, N - 1 AA = DBLE( A( L ) ) * -> U(j-k-1,j-k-1) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * -> U(j,j) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO * L=k-1+n*lda * -> U(k-1,k-1) at A(k-1,n) AA = DBLE( A( L ) ) * U(k,k) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF ELSE * A**H is lower DO J = 1, K - 1 CALL ZLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S ) * U at A(0,1) END DO DO J = K + 1, N CALL ZLASSQ( 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 ZLASSQ( 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 L = 0 * -> L(k,k) at A(0,0) AA = DBLE( A( L ) ) * L(k,k) at A(0,0) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = LDA * -> L(0,0) at A(0,1) DO I = 0, K - 2 AA = DBLE( A( L ) ) * L(i,i) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF AA = DBLE( A( L+1 ) ) * L(k+i+1,k+i+1) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF L = L + LDA + 1 END DO * L-> k - 1 + k*lda or L(k-1,k-1) at A(k-1,k) AA = DBLE( A( L ) ) * L(k-1,k-1) at A(k-1,k) IF( AA.NE.ZERO ) THEN IF( SCALE.LT.AA ) THEN S = ONE + S*( SCALE / AA )**2 SCALE = AA ELSE S = S + ( AA / SCALE )**2 END IF END IF END IF END IF END IF VALUE = SCALE*SQRT( S ) END IF * ZLANHF = VALUE RETURN * * End of ZLANHF * END