--- rpl/lapack/lapack/zlanhf.f 2010/08/13 21:04:09 1.3 +++ rpl/lapack/lapack/zlanhf.f 2023/08/07 08:39:29 1.18 @@ -1,10 +1,250 @@ - DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) +*> \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: +* =========== * -* -- LAPACK routine (version 3.2.1) -- +* DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) * -* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- -* -- April 2009 -- +* .. 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. +* +*> \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 -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * @@ -17,184 +257,6 @@ COMPLEX*16 A( 0: * ) * .. * -* Purpose -* ======= -* -* 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. -* -* Description -* =========== -* -* ZLANHF returns the value -* -* 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. -* -* Arguments -* ========= -* -* NORM (input) CHARACTER -* Specifies the value to be returned in ZLANHF 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, ZLANHF 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) DOUBLE PRECISION array, dimension (LWORK), -* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, -* WORK is not referenced. -* -* Further Details -* =============== -* -* 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 .. @@ -203,43 +265,45 @@ * .. * .. Local Scalars .. INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA - DOUBLE PRECISION SCALE, S, VALUE, AA + DOUBLE PRECISION SCALE, S, VALUE, AA, TEMP * .. * .. External Functions .. - LOGICAL LSAME - INTEGER IDAMAX - EXTERNAL LSAME, IDAMAX + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ * .. * .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, MAX, SQRT + 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 + $ NOE = 0 * * set ifm = 0 when form='C' or 'c' and 1 otherwise * IFM = 1 IF( LSAME( TRANSR, 'C' ) ) - + IFM = 0 + $ IFM = 0 * * set ilu = 0 when uplo='U or 'u' and 1 otherwise * ILU = 1 IF( LSAME( UPLO, 'U' ) ) - + ILU = 0 + $ ILU = 0 * * set lda = (n+1)/2 when ifm = 0 * set lda = n when ifm = 1 and noe = 1 @@ -271,46 +335,70 @@ * uplo ='L' J = 0 * -> L(0,0) - VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( J+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = 1, N - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP I = J * -> L(j,j) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = J + 1, N - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO I = K + J - 1 * -> U(i,i) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = K + J + 1, N - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO END DO DO I = 0, N - 2 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + 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 @@ -318,55 +406,83 @@ * uplo ='L' DO J = 0, K - 2 DO I = 0, J - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO I = J * L(i,i) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP I = J + 1 * L(j+k,j+k) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = J + 2, K - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( 0+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = 1, K - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP I = J - K + 1 * U(j,j) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = J - K + 2, K - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO END DO END IF @@ -379,50 +495,78 @@ * uplo ='L' J = 0 * -> L(k,k) & j=1 -> L(0,0) - VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) ) - VALUE = MAX( VALUE, ABS( DBLE( A( J+1+J*LDA ) ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO I = J * L(k+j,k+j) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP I = J + 1 * -> L(j,j) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = J + 2, N - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO I = K + J * -> U(i,i) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = K + J + 2, N - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO END DO DO I = 0, N - 2 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP I = N * -> U(k-1,k-1) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + 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 @@ -430,75 +574,111 @@ * uplo ='L' J = 0 * -> L(k,k) at A(0,0) - VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( J+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = 1, K - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + TEMP = ABS( A( I+J*LDA ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP END DO I = J - 1 * L(i,i) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP I = J * L(j+k,j+k) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = J + 1, K - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( 0+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = 1, K - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP I = J - K * U(j,j) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + TEMP = ABS( DBLE( A( I+J*LDA ) ) ) + IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) ) + $ VALUE = TEMP DO I = J - K + 1, K - 1 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) + 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) - VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) + 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 + $ ( NORM.EQ.'1' ) ) THEN * * Find normI(A) ( = norm1(A), since A is Hermitian). * @@ -524,7 +704,7 @@ * -> A(j+k,j+k) WORK( J+K ) = S + AA IF( I.EQ.K+K ) - + GO TO 10 + $ GO TO 10 I = I + 1 AA = ABS( DBLE( A( I+J*LDA ) ) ) * -> A(j,j) @@ -540,8 +720,12 @@ WORK( J ) = WORK( J ) + S END DO 10 CONTINUE - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -578,8 +762,12 @@ END DO WORK( J ) = WORK( J ) + S END DO - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -613,8 +801,12 @@ END DO WORK( J ) = WORK( J ) + S END DO - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -647,8 +839,12 @@ END DO WORK( J ) = WORK( J ) + S END DO - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -710,8 +906,12 @@ END DO WORK( J ) = WORK( J ) + S END DO - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -771,8 +971,12 @@ END DO WORK( J ) = WORK( J ) + S END DO - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -841,8 +1045,12 @@ * A(k-1,k-1) S = S + AA WORK( I ) = WORK( I ) + S - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -912,8 +1120,12 @@ END DO WORK( J-1 ) = WORK( J-1 ) + S END DO - I = IDAMAX( N, WORK, 1 ) - VALUE = WORK( I-1 ) + 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 @@ -1026,7 +1238,7 @@ ELSE * A is xpose & A is k by n IF( ILU.EQ.0 ) THEN -* A' is upper +* 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) @@ -1037,7 +1249,7 @@ END DO DO J = 0, K - 2 CALL ZLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1, - + SCALE, S ) + $ SCALE, S ) * L at A(0,k-1) END DO S = S + S @@ -1080,7 +1292,7 @@ L = L + LDA + 1 END DO ELSE -* A' is lower +* A**H is lower DO J = 1, K - 1 CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) * U at A(0,0) @@ -1215,7 +1427,7 @@ ELSE * A is xpose IF( ILU.EQ.0 ) THEN -* A' is upper +* 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) @@ -1226,7 +1438,7 @@ END DO DO J = 0, K - 2 CALL ZLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE, - + S ) + $ S ) * L at A(0,k) END DO S = S + S @@ -1281,7 +1493,7 @@ END IF END IF ELSE -* A' is lower +* 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)