--- rpl/lapack/lapack/dlansf.f 2010/08/13 21:03:49 1.3 +++ rpl/lapack/lapack/dlansf.f 2017/06/17 10:53:54 1.15 @@ -1,12 +1,218 @@ - DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK ) +*> \brief \b DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix in RFP format. +* +* =========== DOCUMENTATION =========== * -* -- LAPACK routine (version 3.2.2) -- +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- -* -- June 2010 -- +*> \htmlonly +*> Download DLANSF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== * +* DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER NORM, TRANSR, UPLO +* INTEGER N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( 0: * ), WORK( 0: * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANSF returns the value of the one norm, or the Frobenius norm, or +*> the infinity norm, or the element of largest absolute value of a +*> real symmetric matrix A in RFP format. +*> \endverbatim +*> +*> \return DLANSF +*> \verbatim +*> +*> DLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm' +*> ( +*> ( norm1(A), NORM = '1', 'O' or 'o' +*> ( +*> ( normI(A), NORM = 'I' or 'i' +*> ( +*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' +*> +*> where norm1 denotes the one norm of a matrix (maximum column sum), +*> normI denotes the infinity norm of a matrix (maximum row sum) and +*> normF denotes the Frobenius norm of a matrix (square root of sum of +*> squares). Note that max(abs(A(i,j))) is not a matrix norm. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] NORM +*> \verbatim +*> NORM is CHARACTER*1 +*> Specifies the value to be returned in DLANSF as described +*> above. +*> \endverbatim +*> +*> \param[in] TRANSR +*> \verbatim +*> TRANSR is CHARACTER*1 +*> Specifies whether the RFP format of A is normal or +*> transposed format. +*> = 'N': RFP format is Normal; +*> = 'T': RFP format is Transpose. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the RFP matrix A came from +*> an upper or lower triangular matrix as follows: +*> = 'U': RFP A came from an upper triangular matrix; +*> = 'L': RFP A came from a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. When N = 0, DLANSF is +*> set to zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); +*> On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') +*> part of the symmetric matrix A stored in RFP format. See the +*> "Notes" below for more details. +*> Unchanged on exit. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), +*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, +*> WORK is not referenced. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date December 2016 +* +*> \ingroup doubleOTHERcomputational +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> We first consider Rectangular Full Packed (RFP) Format when N is +*> even. We give an example where N = 6. +*> +*> AP is Upper AP is Lower +*> +*> 00 01 02 03 04 05 00 +*> 11 12 13 14 15 10 11 +*> 22 23 24 25 20 21 22 +*> 33 34 35 30 31 32 33 +*> 44 45 40 41 42 43 44 +*> 55 50 51 52 53 54 55 +*> +*> +*> Let TRANSR = 'N'. RFP holds AP as follows: +*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last +*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of +*> the transpose of the first three columns of AP upper. +*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first +*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of +*> the transpose of the last three columns of AP lower. +*> This covers the case N even and TRANSR = 'N'. +*> +*> RFP A RFP A +*> +*> 03 04 05 33 43 53 +*> 13 14 15 00 44 54 +*> 23 24 25 10 11 55 +*> 33 34 35 20 21 22 +*> 00 44 45 30 31 32 +*> 01 11 55 40 41 42 +*> 02 12 22 50 51 52 +*> +*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the +*> transpose of RFP A above. One therefore gets: +*> +*> +*> RFP A RFP A +*> +*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 +*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 +*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 +*> +*> +*> We then consider Rectangular Full Packed (RFP) Format when N is +*> odd. We give an example where N = 5. +*> +*> AP is Upper AP is Lower +*> +*> 00 01 02 03 04 00 +*> 11 12 13 14 10 11 +*> 22 23 24 20 21 22 +*> 33 34 30 31 32 33 +*> 44 40 41 42 43 44 +*> +*> +*> Let TRANSR = 'N'. RFP holds AP as follows: +*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last +*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of +*> the transpose of the first two columns of AP upper. +*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first +*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of +*> the transpose of the last two columns of AP lower. +*> This covers the case N odd and TRANSR = 'N'. +*> +*> RFP A RFP A +*> +*> 02 03 04 00 33 43 +*> 12 13 14 10 11 44 +*> 22 23 24 20 21 22 +*> 00 33 34 30 31 32 +*> 01 11 44 40 41 42 +*> +*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the +*> transpose of RFP A above. One therefore gets: +*> +*> RFP A RFP A +*> +*> 02 12 22 00 01 00 10 20 30 40 50 +*> 03 13 23 33 11 33 11 21 31 41 51 +*> 04 14 24 34 44 43 44 22 32 42 52 +*> \endverbatim +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK ) +* +* -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* December 2016 * * .. Scalar Arguments .. CHARACTER NORM, TRANSR, UPLO @@ -16,151 +222,6 @@ DOUBLE PRECISION A( 0: * ), WORK( 0: * ) * .. * -* Purpose -* ======= -* -* DLANSF returns the value of the one norm, or the Frobenius norm, or -* the infinity norm, or the element of largest absolute value of a -* real symmetric matrix A in RFP format. -* -* Description -* =========== -* -* DLANSF returns the value -* -* DLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm' -* ( -* ( norm1(A), NORM = '1', 'O' or 'o' -* ( -* ( normI(A), NORM = 'I' or 'i' -* ( -* ( normF(A), NORM = 'F', 'f', 'E' or 'e' -* -* where norm1 denotes the one norm of a matrix (maximum column sum), -* normI denotes the infinity norm of a matrix (maximum row sum) and -* normF denotes the Frobenius norm of a matrix (square root of sum of -* squares). Note that max(abs(A(i,j))) is not a matrix norm. -* -* Arguments -* ========= -* -* NORM (input) CHARACTER -* Specifies the value to be returned in DLANSF as described -* above. -* -* TRANSR (input) CHARACTER -* Specifies whether the RFP format of A is normal or -* transposed format. -* = 'N': RFP format is Normal; -* = 'T': RFP format is Transpose. -* -* UPLO (input) CHARACTER -* On entry, UPLO specifies whether the RFP matrix A came from -* an upper or lower triangular matrix as follows: -* = 'U': RFP A came from an upper triangular matrix; -* = 'L': RFP A came from a lower triangular matrix. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. When N = 0, DLANSF is -* set to zero. -* -* A (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); -* On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') -* part of the symmetric matrix A stored in RFP format. See the -* "Notes" below for more details. -* Unchanged on exit. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, -* WORK is not referenced. -* -* Further Details -* =============== -* -* We first consider Rectangular Full Packed (RFP) Format when N is -* even. We give an example where N = 6. -* -* AP is Upper AP is Lower -* -* 00 01 02 03 04 05 00 -* 11 12 13 14 15 10 11 -* 22 23 24 25 20 21 22 -* 33 34 35 30 31 32 33 -* 44 45 40 41 42 43 44 -* 55 50 51 52 53 54 55 -* -* -* Let TRANSR = 'N'. RFP holds AP as follows: -* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last -* three columns of AP upper. The lower triangle A(4:6,0:2) consists of -* the transpose of the first three columns of AP upper. -* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first -* three columns of AP lower. The upper triangle A(0:2,0:2) consists of -* the transpose of the last three columns of AP lower. -* This covers the case N even and TRANSR = 'N'. -* -* RFP A RFP A -* -* 03 04 05 33 43 53 -* 13 14 15 00 44 54 -* 23 24 25 10 11 55 -* 33 34 35 20 21 22 -* 00 44 45 30 31 32 -* 01 11 55 40 41 42 -* 02 12 22 50 51 52 -* -* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the -* transpose of RFP A above. One therefore gets: -* -* -* RFP A RFP A -* -* 03 13 23 33 00 01 02 33 00 10 20 30 40 50 -* 04 14 24 34 44 11 12 43 44 11 21 31 41 51 -* 05 15 25 35 45 55 22 53 54 55 22 32 42 52 -* -* -* We then consider Rectangular Full Packed (RFP) Format when N is -* odd. We give an example where N = 5. -* -* AP is Upper AP is Lower -* -* 00 01 02 03 04 00 -* 11 12 13 14 10 11 -* 22 23 24 20 21 22 -* 33 34 30 31 32 33 -* 44 40 41 42 43 44 -* -* -* Let TRANSR = 'N'. RFP holds AP as follows: -* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last -* three columns of AP upper. The lower triangle A(3:4,0:1) consists of -* the transpose of the first two columns of AP upper. -* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first -* three columns of AP lower. The upper triangle A(0:1,1:2) consists of -* the transpose of the last two columns of AP lower. -* This covers the case N odd and TRANSR = 'N'. -* -* RFP A RFP A -* -* 02 03 04 00 33 43 -* 12 13 14 10 11 44 -* 22 23 24 20 21 22 -* 00 33 34 30 31 32 -* 01 11 44 40 41 42 -* -* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the -* transpose of RFP A above. One therefore gets: -* -* RFP A RFP A -* -* 02 12 22 00 01 00 10 20 30 40 50 -* 03 13 23 33 11 33 11 21 31 41 51 -* 04 14 24 34 44 43 44 22 32 42 52 -* -* Reference -* ========= -* * ===================================================================== * * .. Parameters .. @@ -169,12 +230,11 @@ * .. * .. 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 DLASSQ @@ -187,25 +247,28 @@ IF( N.EQ.0 ) THEN DLANSF = ZERO RETURN + ELSE IF( N.EQ.1 ) THEN + DLANSF = ABS( A(0) ) + RETURN END IF * * set noe = 1 if n is odd. if n is even set noe=0 * NOE = 1 IF( MOD( N, 2 ).EQ.0 ) - + NOE = 0 + $ NOE = 0 * * set ifm = 0 when form='T or 't' and 1 otherwise * IFM = 1 IF( LSAME( TRANSR, 'T' ) ) - + 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 @@ -235,14 +298,18 @@ * A is n by k DO J = 0, K - 1 DO I = 0, 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 * xpose case; A is k by n DO J = 0, 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 END IF @@ -252,20 +319,24 @@ * A is n+1 by k DO J = 0, K - 1 DO I = 0, 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 * xpose case; A is k by n+1 DO J = 0, 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 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 symmetric). * @@ -289,7 +360,7 @@ * -> 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( A( I+J*LDA ) ) * -> A(j,j) @@ -305,8 +376,12 @@ 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 K = K + 1 @@ -343,8 +418,12 @@ 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 @@ -377,8 +456,12 @@ 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 DO I = K, N - 1 @@ -411,8 +494,12 @@ 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 @@ -473,8 +560,12 @@ 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 K = K + 1 @@ -534,8 +625,12 @@ 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 @@ -603,8 +698,12 @@ * 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 DO I = K, N - 1 @@ -672,8 +771,12 @@ 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 @@ -724,7 +827,7 @@ ELSE * A is xpose IF( ILU.EQ.0 ) THEN -* A' is upper +* A**T is upper DO J = 1, K - 2 CALL DLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S ) * U at A(0,k) @@ -735,7 +838,7 @@ END DO DO J = 0, K - 2 CALL DLASSQ( 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 @@ -745,7 +848,7 @@ CALL DLASSQ( K, A( 0+( K-1 )*LDA ), LDA+1, SCALE, S ) * tri L at A(0,k-1) ELSE -* A' is lower +* A**T is lower DO J = 1, K - 1 CALL DLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) * U at A(0,0) @@ -806,7 +909,7 @@ ELSE * A is xpose IF( ILU.EQ.0 ) THEN -* A' is upper +* A**T is upper DO J = 1, K - 1 CALL DLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S ) * U at A(0,k+1) @@ -817,7 +920,7 @@ END DO DO J = 0, K - 2 CALL DLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE, - + S ) + $ S ) * L at A(0,k) END DO S = S + S @@ -827,7 +930,7 @@ CALL DLASSQ( K, A( 0+K*LDA ), LDA+1, SCALE, S ) * tri L at A(0,k) ELSE -* A' is lower +* A**T is lower DO J = 1, K - 1 CALL DLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S ) * U at A(0,1)