--- rpl/lapack/lapack/dlantp.f 2011/11/21 22:19:32 1.9 +++ rpl/lapack/lapack/dlantp.f 2020/05/21 21:45:59 1.18 @@ -1,25 +1,25 @@ -*> \brief \b DLANTP +*> \brief \b DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. * * =========== DOCUMENTATION =========== * -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * *> \htmlonly -*> Download DLANTP + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> +*> Download DLANTP + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> *> [TXT] -*> \endhtmlonly +*> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK ) -* +* * .. Scalar Arguments .. * CHARACTER DIAG, NORM, UPLO * INTEGER N @@ -27,7 +27,7 @@ * .. Array Arguments .. * DOUBLE PRECISION AP( * ), WORK( * ) * .. -* +* * *> \par Purpose: * ============= @@ -112,23 +112,24 @@ * Authors: * ======== * -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -*> \date November 2011 +*> \date December 2016 * *> \ingroup doubleOTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK ) * -* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK auxiliary 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..-- -* November 2011 +* December 2016 * + IMPLICIT NONE * .. Scalar Arguments .. CHARACTER DIAG, NORM, UPLO INTEGER N @@ -146,17 +147,20 @@ * .. Local Scalars .. LOGICAL UDIAG INTEGER I, J, K - DOUBLE PRECISION SCALE, SUM, VALUE + DOUBLE PRECISION SUM, VALUE * .. -* .. External Subroutines .. - EXTERNAL DLASSQ +* .. Local Arrays .. + DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN +* .. +* .. External Subroutines .. + EXTERNAL DLASSQ, DCOMBSSQ * .. * .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SQRT + INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * @@ -172,14 +176,16 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = K, K + J - 2 - VALUE = MAX( VALUE, ABS( AP( I ) ) ) + SUM = ABS( AP( I ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE K = K + J 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = K + 1, K + N - J - VALUE = MAX( VALUE, ABS( AP( I ) ) ) + SUM = ABS( AP( I ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE K = K + N - J + 1 40 CONTINUE @@ -189,14 +195,16 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N DO 50 I = K, K + J - 1 - VALUE = MAX( VALUE, ABS( AP( I ) ) ) + SUM = ABS( AP( I ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 50 CONTINUE K = K + J 60 CONTINUE ELSE DO 80 J = 1, N DO 70 I = K, K + N - J - VALUE = MAX( VALUE, ABS( AP( I ) ) ) + SUM = ABS( AP( I ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE K = K + N - J + 1 80 CONTINUE @@ -223,7 +231,7 @@ 100 CONTINUE END IF K = K + J - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 110 CONTINUE ELSE DO 140 J = 1, N @@ -239,7 +247,7 @@ 130 CONTINUE END IF K = K + N - J + 1 - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 140 CONTINUE END IF ELSE IF( LSAME( NORM, 'I' ) ) THEN @@ -296,50 +304,70 @@ END IF VALUE = ZERO DO 270 I = 1, N - VALUE = MAX( VALUE, WORK( I ) ) + SUM = WORK( I ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 270 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). +* SSQ(1) is scale +* SSQ(2) is sum-of-squares +* For better accuracy, sum each column separately. * IF( LSAME( UPLO, 'U' ) ) THEN IF( LSAME( DIAG, 'U' ) ) THEN - SCALE = ONE - SUM = N + SSQ( 1 ) = ONE + SSQ( 2 ) = N K = 2 DO 280 J = 2, N - CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( J-1, AP( K ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) K = K + J 280 CONTINUE ELSE - SCALE = ZERO - SUM = ONE + SSQ( 1 ) = ZERO + SSQ( 2 ) = ONE K = 1 DO 290 J = 1, N - CALL DLASSQ( J, AP( K ), 1, SCALE, SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( J, AP( K ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) K = K + J 290 CONTINUE END IF ELSE IF( LSAME( DIAG, 'U' ) ) THEN - SCALE = ONE - SUM = N + SSQ( 1 ) = ONE + SSQ( 2 ) = N K = 2 DO 300 J = 1, N - 1 - CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( N-J, AP( K ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) K = K + N - J + 1 300 CONTINUE ELSE - SCALE = ZERO - SUM = ONE + SSQ( 1 ) = ZERO + SSQ( 2 ) = ONE K = 1 DO 310 J = 1, N - CALL DLASSQ( N-J+1, AP( K ), 1, SCALE, SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( N-J+1, AP( K ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) K = K + N - J + 1 310 CONTINUE END IF END IF - VALUE = SCALE*SQRT( SUM ) + VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * DLANTP = VALUE