--- rpl/lapack/lapack/dlantb.f 2011/11/21 20:42:56 1.8 +++ rpl/lapack/lapack/dlantb.f 2020/05/21 21:45:59 1.18 @@ -1,26 +1,26 @@ -*> \brief \b DLANTB +*> \brief \b DLANTB 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 band matrix. * * =========== 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 DLANTB + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> +*> Download DLANTB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> *> [TXT] -*> \endhtmlonly +*> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB, * LDAB, WORK ) -* +* * .. Scalar Arguments .. * CHARACTER DIAG, NORM, UPLO * INTEGER K, LDAB, N @@ -28,7 +28,7 @@ * .. Array Arguments .. * DOUBLE PRECISION AB( LDAB, * ), WORK( * ) * .. -* +* * *> \par Purpose: * ============= @@ -127,12 +127,12 @@ * 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 * @@ -140,11 +140,12 @@ DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB, $ LDAB, 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 K, LDAB, N @@ -162,14 +163,17 @@ * .. Local Scalars .. LOGICAL UDIAG INTEGER I, J, L - 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, MIN, SQRT @@ -187,13 +191,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = MAX( K+2-J, 1 ), K - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = 2, MIN( N+1-J, K+1 ) - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF @@ -202,13 +208,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N DO 50 I = MAX( K+2-J, 1 ), K + 1 - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1, N DO 70 I = 1, MIN( N+1-J, K+1 ) - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE 80 CONTINUE END IF @@ -232,7 +240,7 @@ SUM = SUM + ABS( AB( I, J ) ) 100 CONTINUE END IF - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 110 CONTINUE ELSE DO 140 J = 1, N @@ -247,7 +255,7 @@ SUM = SUM + ABS( AB( I, J ) ) 130 CONTINUE END IF - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 140 CONTINUE END IF ELSE IF( LSAME( NORM, 'I' ) ) THEN @@ -301,51 +309,67 @@ END IF END IF 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 IF( K.GT.0 ) THEN DO 280 J = 2, N + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE CALL DLASSQ( MIN( J-1, K ), - $ AB( MAX( K+2-J, 1 ), J ), 1, SCALE, - $ SUM ) + $ AB( MAX( K+2-J, 1 ), J ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 280 CONTINUE END IF ELSE - SCALE = ZERO - SUM = ONE + SSQ( 1 ) = ZERO + SSQ( 2 ) = ONE DO 290 J = 1, N + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE CALL DLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ), - $ 1, SCALE, SUM ) + $ 1, COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 290 CONTINUE END IF ELSE IF( LSAME( DIAG, 'U' ) ) THEN - SCALE = ONE - SUM = N + SSQ( 1 ) = ONE + SSQ( 2 ) = N IF( K.GT.0 ) THEN DO 300 J = 1, N - 1 - CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE, - $ SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 300 CONTINUE END IF ELSE - SCALE = ZERO - SUM = ONE + SSQ( 1 ) = ZERO + SSQ( 2 ) = ONE DO 310 J = 1, N - CALL DLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE, - $ SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 310 CONTINUE END IF END IF - VALUE = SCALE*SQRT( SUM ) + VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * DLANTB = VALUE