version 1.17, 2018/05/29 07:18:27
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version 1.18, 2020/05/21 21:46:08
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* December 2016 |
* December 2016 |
* |
* |
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IMPLICIT NONE |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM, UPLO |
CHARACTER NORM, UPLO |
INTEGER N |
INTEGER N |
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* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
INTEGER I, J, K |
INTEGER I, J, K |
DOUBLE PRECISION ABSA, SCALE, SUM, VALUE |
DOUBLE PRECISION ABSA, SUM, VALUE |
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* .. |
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* .. Local Arrays .. |
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DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME, DISNAN |
LOGICAL LSAME, DISNAN |
EXTERNAL LSAME, DISNAN |
EXTERNAL LSAME, DISNAN |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZLASSQ |
EXTERNAL ZLASSQ, DCOMBSSQ |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DBLE, DIMAG, SQRT |
INTRINSIC ABS, DBLE, DIMAG, SQRT |
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ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
* |
* |
* Find normF(A). |
* Find normF(A). |
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* SSQ(1) is scale |
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* SSQ(2) is sum-of-squares |
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* For better accuracy, sum each column separately. |
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* |
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SSQ( 1 ) = ZERO |
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SSQ( 2 ) = ONE |
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* |
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* Sum off-diagonals |
* |
* |
SCALE = ZERO |
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SUM = ONE |
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K = 2 |
K = 2 |
IF( LSAME( UPLO, 'U' ) ) THEN |
IF( LSAME( UPLO, 'U' ) ) THEN |
DO 110 J = 2, N |
DO 110 J = 2, N |
CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM ) |
COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
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CALL ZLASSQ( J-1, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) ) |
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CALL DCOMBSSQ( SSQ, COLSSQ ) |
K = K + J |
K = K + J |
110 CONTINUE |
110 CONTINUE |
ELSE |
ELSE |
DO 120 J = 1, N - 1 |
DO 120 J = 1, N - 1 |
CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM ) |
COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
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CALL ZLASSQ( N-J, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) ) |
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CALL DCOMBSSQ( SSQ, COLSSQ ) |
K = K + N - J + 1 |
K = K + N - J + 1 |
120 CONTINUE |
120 CONTINUE |
END IF |
END IF |
SUM = 2*SUM |
SSQ( 2 ) = 2*SSQ( 2 ) |
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* |
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* Sum diagonal |
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* |
K = 1 |
K = 1 |
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COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
DO 130 I = 1, N |
DO 130 I = 1, N |
IF( DBLE( AP( K ) ).NE.ZERO ) THEN |
IF( DBLE( AP( K ) ).NE.ZERO ) THEN |
ABSA = ABS( DBLE( AP( K ) ) ) |
ABSA = ABS( DBLE( AP( K ) ) ) |
IF( SCALE.LT.ABSA ) THEN |
IF( COLSSQ( 1 ).LT.ABSA ) THEN |
SUM = ONE + SUM*( SCALE / ABSA )**2 |
COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2 |
SCALE = ABSA |
COLSSQ( 1 ) = ABSA |
ELSE |
ELSE |
SUM = SUM + ( ABSA / SCALE )**2 |
COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2 |
END IF |
END IF |
END IF |
END IF |
IF( DIMAG( AP( K ) ).NE.ZERO ) THEN |
IF( DIMAG( AP( K ) ).NE.ZERO ) THEN |
ABSA = ABS( DIMAG( AP( K ) ) ) |
ABSA = ABS( DIMAG( AP( K ) ) ) |
IF( SCALE.LT.ABSA ) THEN |
IF( COLSSQ( 1 ).LT.ABSA ) THEN |
SUM = ONE + SUM*( SCALE / ABSA )**2 |
COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2 |
SCALE = ABSA |
COLSSQ( 1 ) = ABSA |
ELSE |
ELSE |
SUM = SUM + ( ABSA / SCALE )**2 |
COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2 |
END IF |
END IF |
END IF |
END IF |
IF( LSAME( UPLO, 'U' ) ) THEN |
IF( LSAME( UPLO, 'U' ) ) THEN |
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K = K + N - I + 1 |
K = K + N - I + 1 |
END IF |
END IF |
130 CONTINUE |
130 CONTINUE |
VALUE = SCALE*SQRT( SUM ) |
CALL DCOMBSSQ( SSQ, COLSSQ ) |
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VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) |
END IF |
END IF |
* |
* |
ZLANSP = VALUE |
ZLANSP = VALUE |