--- rpl/lapack/lapack/dlantr.f 2012/08/22 09:48:18 1.10 +++ rpl/lapack/lapack/dlantr.f 2020/05/21 21:45:59 1.18 @@ -1,26 +1,26 @@ -*> \brief \b DLANTR +*> \brief \b DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular 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 DLANTR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> +*> Download DLANTR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> *> [TXT] -*> \endhtmlonly +*> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, * WORK ) -* +* * .. Scalar Arguments .. * CHARACTER DIAG, NORM, UPLO * INTEGER LDA, M, N @@ -28,7 +28,7 @@ * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. -* +* * *> \par Purpose: * ============= @@ -128,12 +128,12 @@ * 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 * @@ -141,11 +141,12 @@ DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, $ 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 LDA, M, N @@ -163,17 +164,20 @@ * .. Local Scalars .. LOGICAL UDIAG INTEGER I, J - 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 + INTRINSIC ABS, MIN, SQRT * .. * .. Executable Statements .. * @@ -188,13 +192,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, MIN( M, J-1 ) - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J + 1, M - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF @@ -203,13 +209,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N DO 50 I = 1, MIN( M, J ) - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1, N DO 70 I = J, M - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE 80 CONTINUE END IF @@ -233,7 +241,7 @@ SUM = SUM + ABS( A( 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 @@ -248,7 +256,7 @@ SUM = SUM + ABS( A( 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 @@ -301,43 +309,62 @@ END IF VALUE = ZERO DO 280 I = 1, M - VALUE = MAX( VALUE, WORK( I ) ) + SUM = WORK( I ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 280 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 = MIN( M, N ) + SSQ( 1 ) = ONE + SSQ( 2 ) = MIN( M, N ) DO 290 J = 2, N - CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 290 CONTINUE ELSE - SCALE = ZERO - SUM = ONE + SSQ( 1 ) = ZERO + SSQ( 2 ) = ONE DO 300 J = 1, N - CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 300 CONTINUE END IF ELSE IF( LSAME( DIAG, 'U' ) ) THEN - SCALE = ONE - SUM = MIN( M, N ) + SSQ( 1 ) = ONE + SSQ( 2 ) = MIN( M, N ) DO 310 J = 1, N - CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE, - $ SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 310 CONTINUE ELSE - SCALE = ZERO - SUM = ONE + SSQ( 1 ) = ZERO + SSQ( 2 ) = ONE DO 320 J = 1, N - CALL DLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM ) + COLSSQ( 1 ) = ZERO + COLSSQ( 2 ) = ONE + CALL DLASSQ( M-J+1, A( J, J ), 1, + $ COLSSQ( 1 ), COLSSQ( 2 ) ) + CALL DCOMBSSQ( SSQ, COLSSQ ) 320 CONTINUE END IF END IF - VALUE = SCALE*SQRT( SUM ) + VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * DLANTR = VALUE