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authorjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
committerjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
commitff981f106bde4ce6a74aa4f4a572c943f5a395b2 (patch)
treea386cad907bcaefd6893535c31d67ec9468e693e /SRC/clanhf.f
parente58b61578b55644f6391f3333262b72c1dc88437 (diff)
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+ REAL FUNCTION CLANHF( NORM, TRANSR, UPLO, N, A, WORK )
+*
+* -- LAPACK routine (version 3.2) --
+*
+* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
+* -- November 2008 --
+*
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*
+* .. Scalar Arguments ..
+ CHARACTER NORM, TRANSR, UPLO
+ INTEGER N
+* ..
+* .. Array Arguments ..
+ REAL WORK( 0: * )
+ COMPLEX A( 0: * )
+* ..
+*
+* Purpose
+* =======
+*
+* CLANHF 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.
+*
+* Description
+* ===========
+*
+* CLANHF returns the value
+*
+* CLANHF = ( 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.
+*
+* Arguments
+* =========
+*
+* NORM (input) CHARACTER
+* Specifies the value to be returned in CLANHF as described
+* above.
+*
+* TRANSR (input) 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
+*
+* UPLO (input) 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
+*
+* N (input) INTEGER
+* The order of the matrix A. N >= 0. When N = 0, CLANHF is
+* set to zero.
+*
+* A (input) 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.
+*
+* WORK (workspace) REAL array, dimension (LWORK),
+* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
+* WORK is not referenced.
+*
+* Note:
+* =====
+*
+* 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
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA
+ REAL SCALE, S, VALUE, AA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ISAMAX
+ EXTERNAL LSAME, ISAMAX
+* ..
+* .. External Subroutines ..
+ EXTERNAL CLASSQ
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, REAL, MAX, SQRT
+* ..
+* .. Executable Statements ..
+*
+ IF( N.EQ.0 ) THEN
+ CLANHF = ZERO
+ 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)
+ VALUE = MAX( VALUE, ABS( REAL( A( J+J*LDA ) ) ) )
+ DO I = 1, N - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ DO J = 1, K - 1
+ DO I = 0, J - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = J - 1
+* L(k+j,k+j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = J
+* -> L(j,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = J + 1, N - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ ELSE
+* uplo = 'U'
+ DO J = 0, K - 2
+ DO I = 0, K + J - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = K + J - 1
+* -> U(i,i)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = I + 1
+* =k+j; i -> U(j,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = K + J + 1, N - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ DO I = 0, N - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+* j=k-1
+ END DO
+* i=n-1 -> U(n-1,n-1)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ 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
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = J
+* L(i,i)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = J + 1
+* L(j+k,j+k)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = J + 2, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ J = K - 1
+ DO I = 0, K - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = K - 1
+* -> L(i,i) is at A(i,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO J = K, N - 1
+ DO I = 0, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ ELSE
+* uplo = 'U'
+ DO J = 0, K - 2
+ DO I = 0, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ J = K - 1
+* -> U(j,j) is at A(0,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( 0+J*LDA ) ) ) )
+ DO I = 1, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ DO J = K, N - 1
+ DO I = 0, J - K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = J - K
+* -> U(i,i) at A(i,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = J - K + 1
+* U(j,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = J - K + 2, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ 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)
+ VALUE = MAX( VALUE, ABS( REAL( A( J+J*LDA ) ) ) )
+ VALUE = MAX( VALUE, ABS( REAL( A( J+1+J*LDA ) ) ) )
+ DO I = 2, N
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ DO J = 1, K - 1
+ DO I = 0, J - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = J
+* L(k+j,k+j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = J + 1
+* -> L(j,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = J + 2, N
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ ELSE
+* uplo = 'U'
+ DO J = 0, K - 2
+ DO I = 0, K + J - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = K + J
+* -> U(i,i)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = I + 1
+* =k+j+1; i -> U(j,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = K + J + 2, N
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ DO I = 0, N - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+* j=k-1
+ END DO
+* i=n-1 -> U(n-1,n-1)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = N
+* -> U(k-1,k-1)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ 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)
+ VALUE = MAX( VALUE, ABS( REAL( A( J+J*LDA ) ) ) )
+ DO I = 1, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ DO J = 1, K - 1
+ DO I = 0, J - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = J - 1
+* L(i,i)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = J
+* L(j+k,j+k)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = J + 1, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ J = K
+ DO I = 0, K - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = K - 1
+* -> L(i,i) is at A(i,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO J = K + 1, N
+ DO I = 0, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ ELSE
+* uplo = 'U'
+ DO J = 0, K - 1
+ DO I = 0, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ J = K
+* -> U(j,j) is at A(0,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( 0+J*LDA ) ) ) )
+ DO I = 1, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ DO J = K + 1, N - 1
+ DO I = 0, J - K - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = J - K - 1
+* -> U(i,i) at A(i,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ I = J - K
+* U(j,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ DO I = J - K + 1, K - 1
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ END DO
+ J = N
+ DO I = 0, K - 2
+ VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ END DO
+ I = K - 1
+* U(k,k) at A(i,j)
+ VALUE = MAX( VALUE, ABS( REAL( A( I+J*LDA ) ) ) )
+ 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( REAL( 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( REAL( 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
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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( REAL( 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( REAL( 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
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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( REAL( A( I+J*LDA ) ) )
+* -> A(j+k,j+k)
+ WORK( J+K ) = S + AA
+ I = I + 1
+ AA = ABS( REAL( 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
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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( REAL( 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( REAL( 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
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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( REAL( 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( REAL( A( I+J*LDA ) ) )
+* A(j-k,j-k)
+ S = S + AA
+ WORK( J-K ) = WORK( J-K ) + S
+ I = I + 1
+ S = ABS( REAL( 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
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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( REAL( 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( REAL( 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( REAL( 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
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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( REAL( 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( REAL( 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( REAL( 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( REAL( A( I+J*LDA ) ) )
+* A(k-1,k-1)
+ S = S + AA
+ WORK( I ) = WORK( I ) + S
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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( REAL( 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( REAL( 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( REAL( 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( REAL( 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
+ I = ISAMAX( N, WORK, 1 )
+ VALUE = WORK( I-1 )
+ 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 CLASSQ( 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 CLASSQ( 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 = REAL( 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 = REAL( 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 = REAL( 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 CLASSQ( 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 CLASSQ( 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 = REAL( 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 = REAL( 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 = REAL( 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' is upper
+ DO J = 1, K - 2
+ CALL CLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S )
+* U at A(0,k)
+ END DO
+ DO J = 0, K - 2
+ CALL CLASSQ( 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 CLASSQ( 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 = REAL( 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 = REAL( 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 = REAL( 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' is lower
+ DO J = 1, K - 1
+ CALL CLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
+* U at A(0,0)
+ END DO
+ DO J = K, N - 1
+ CALL CLASSQ( 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 CLASSQ( 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 = REAL( 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 = REAL( 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 = REAL( 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 CLASSQ( 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 CLASSQ( 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 = REAL( 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 = REAL( 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 CLASSQ( 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 CLASSQ( 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 = REAL( 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 = REAL( 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' is upper
+ DO J = 1, K - 1
+ CALL CLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S )
+* U at A(0,k+1)
+ END DO
+ DO J = 0, K - 1
+ CALL CLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
+* k by k rect. at A(0,0)
+ END DO
+ DO J = 0, K - 2
+ CALL CLASSQ( 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 = REAL( 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 = REAL( 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 = REAL( 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 = REAL( 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' is lower
+ DO J = 1, K - 1
+ CALL CLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S )
+* U at A(0,1)
+ END DO
+ DO J = K + 1, N
+ CALL CLASSQ( 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 CLASSQ( 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 = REAL( 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 = REAL( 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 = REAL( 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 = REAL( 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
+*
+ CLANHF = VALUE
+ RETURN
+*
+* End of CLANHF
+*
+ END