diff options
author | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
commit | ff981f106bde4ce6a74aa4f4a572c943f5a395b2 (patch) | |
tree | a386cad907bcaefd6893535c31d67ec9468e693e /SRC/clanhf.f | |
parent | e58b61578b55644f6391f3333262b72c1dc88437 (diff) |
Diffstat (limited to 'SRC/clanhf.f')
-rw-r--r-- | SRC/clanhf.f | 1358 |
1 files changed, 1358 insertions, 0 deletions
diff --git a/SRC/clanhf.f b/SRC/clanhf.f new file mode 100644 index 00000000..a89474e5 --- /dev/null +++ b/SRC/clanhf.f @@ -0,0 +1,1358 @@ + 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 |