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DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK ) |
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* |
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* -- LAPACK auxiliary routine (version 3.2) -- |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2006 |
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* |
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* .. Scalar Arguments .. |
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CHARACTER NORM |
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INTEGER LDA, M, N |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION A( LDA, * ), WORK( * ) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* DLANGE returns the value of the one norm, or the Frobenius norm, or |
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* the infinity norm, or the element of largest absolute value of a |
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* real matrix A. |
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* |
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* Description |
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* =========== |
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* |
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* DLANGE returns the value |
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* |
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* DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm' |
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* ( |
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* ( norm1(A), NORM = '1', 'O' or 'o' |
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* ( |
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* ( normI(A), NORM = 'I' or 'i' |
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* ( |
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* ( normF(A), NORM = 'F', 'f', 'E' or 'e' |
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* |
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* where norm1 denotes the one norm of a matrix (maximum column sum), |
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* normI denotes the infinity norm of a matrix (maximum row sum) and |
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* normF denotes the Frobenius norm of a matrix (square root of sum of |
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* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. |
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* |
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* Arguments |
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* ========= |
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* |
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* NORM (input) CHARACTER*1 |
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* Specifies the value to be returned in DLANGE as described |
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* above. |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. When M = 0, |
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* DLANGE is set to zero. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= 0. When N = 0, |
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* DLANGE is set to zero. |
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* |
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* A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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* The m by n matrix A. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(M,1). |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), |
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* where LWORK >= M when NORM = 'I'; otherwise, WORK is not |
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* referenced. |
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* |
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* ===================================================================== |
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* |
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* .. Parameters .. |
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DOUBLE PRECISION ONE, ZERO |
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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* .. |
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* .. Local Scalars .. |
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INTEGER I, J |
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DOUBLE PRECISION SCALE, SUM, VALUE |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL DLASSQ |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC ABS, MAX, MIN, SQRT |
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* .. |
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* .. Executable Statements .. |
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* |
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IF( MIN( M, N ).EQ.0 ) THEN |
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VALUE = ZERO |
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ELSE IF( LSAME( NORM, 'M' ) ) THEN |
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* |
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* Find max(abs(A(i,j))). |
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* |
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VALUE = ZERO |
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DO 20 J = 1, N |
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DO 10 I = 1, M |
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VALUE = MAX( VALUE, ABS( A( I, J ) ) ) |
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10 CONTINUE |
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20 CONTINUE |
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ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN |
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* |
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* Find norm1(A). |
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* |
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VALUE = ZERO |
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DO 40 J = 1, N |
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SUM = ZERO |
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DO 30 I = 1, M |
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SUM = SUM + ABS( A( I, J ) ) |
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30 CONTINUE |
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VALUE = MAX( VALUE, SUM ) |
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40 CONTINUE |
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ELSE IF( LSAME( NORM, 'I' ) ) THEN |
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* |
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* Find normI(A). |
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* |
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DO 50 I = 1, M |
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WORK( I ) = ZERO |
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50 CONTINUE |
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DO 70 J = 1, N |
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DO 60 I = 1, M |
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WORK( I ) = WORK( I ) + ABS( A( I, J ) ) |
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60 CONTINUE |
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70 CONTINUE |
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VALUE = ZERO |
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DO 80 I = 1, M |
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VALUE = MAX( VALUE, WORK( I ) ) |
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80 CONTINUE |
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ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
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* |
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* Find normF(A). |
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* |
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SCALE = ZERO |
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SUM = ONE |
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DO 90 J = 1, N |
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CALL DLASSQ( M, A( 1, J ), 1, SCALE, SUM ) |
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90 CONTINUE |
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VALUE = SCALE*SQRT( SUM ) |
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END IF |
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* |
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DLANGE = VALUE |
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RETURN |
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* |
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* End of DLANGE |
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* |
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END |