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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
-*
-* -- LAPACK auxiliary routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- CHARACTER NORM, UPLO
- INTEGER N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION AP( * ), WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DLANSP returns the value of the one norm, or the Frobenius norm, or
-* the infinity norm, or the element of largest absolute value of a
-* real symmetric matrix A, supplied in packed form.
-*
-* Description
-* ===========
-*
-* DLANSP returns the value
-*
-* DLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
-* (
-* ( norm1(A), NORM = '1', 'O' or 'o'
-* (
-* ( normI(A), NORM = 'I' or 'i'
-* (
-* ( normF(A), NORM = 'F', 'f', 'E' or 'e'
-*
-* where norm1 denotes the one norm of a matrix (maximum column sum),
-* normI denotes the infinity norm of a matrix (maximum row sum) and
-* normF denotes the Frobenius norm of a matrix (square root of sum of
-* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*
-* Arguments
-* =========
-*
-* NORM (input) CHARACTER*1
-* Specifies the value to be returned in DLANSP as described
-* above.
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* symmetric matrix A is supplied.
-* = 'U': Upper triangular part of A is supplied
-* = 'L': Lower triangular part of A is supplied
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0. When N = 0, DLANSP is
-* set to zero.
-*
-* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
-* The upper or lower triangle of the symmetric matrix A, packed
-* columnwise in a linear array. The j-th column of A is stored
-* in the array AP as follows:
-* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
-* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
-* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
-* WORK is not referenced.
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ONE, ZERO
- PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
-* ..
-* .. Local Scalars ..
- INTEGER I, J, K
- DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
-* ..
-* .. External Subroutines ..
- EXTERNAL DLASSQ
-* ..
-* .. External Functions ..
- LOGICAL LSAME
- EXTERNAL LSAME
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX, SQRT
-* ..
-* .. Executable Statements ..
-*
- IF( N.EQ.0 ) THEN
- VALUE = ZERO
- ELSE IF( LSAME( NORM, 'M' ) ) THEN
-*
-* Find max(abs(A(i,j))).
-*
- VALUE = ZERO
- IF( LSAME( UPLO, 'U' ) ) THEN
- K = 1
- DO 20 J = 1, N
- DO 10 I = K, K + J - 1
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
- 10 CONTINUE
- K = K + J
- 20 CONTINUE
- ELSE
- K = 1
- DO 40 J = 1, N
- DO 30 I = K, K + N - J
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
- 30 CONTINUE
- K = K + N - J + 1
- 40 CONTINUE
- END IF
- ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
- $ ( NORM.EQ.'1' ) ) THEN
-*
-* Find normI(A) ( = norm1(A), since A is symmetric).
-*
- VALUE = ZERO
- K = 1
- IF( LSAME( UPLO, 'U' ) ) THEN
- DO 60 J = 1, N
- SUM = ZERO
- DO 50 I = 1, J - 1
- ABSA = ABS( AP( K ) )
- SUM = SUM + ABSA
- WORK( I ) = WORK( I ) + ABSA
- K = K + 1
- 50 CONTINUE
- WORK( J ) = SUM + ABS( AP( K ) )
- K = K + 1
- 60 CONTINUE
- DO 70 I = 1, N
- VALUE = MAX( VALUE, WORK( I ) )
- 70 CONTINUE
- ELSE
- DO 80 I = 1, N
- WORK( I ) = ZERO
- 80 CONTINUE
- DO 100 J = 1, N
- SUM = WORK( J ) + ABS( AP( K ) )
- K = K + 1
- DO 90 I = J + 1, N
- ABSA = ABS( AP( K ) )
- SUM = SUM + ABSA
- WORK( I ) = WORK( I ) + ABSA
- K = K + 1
- 90 CONTINUE
- VALUE = MAX( VALUE, SUM )
- 100 CONTINUE
- END IF
- ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
-*
-* Find normF(A).
-*
- SCALE = ZERO
- SUM = ONE
- K = 2
- IF( LSAME( UPLO, 'U' ) ) THEN
- DO 110 J = 2, N
- CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
- K = K + J
- 110 CONTINUE
- ELSE
- DO 120 J = 1, N - 1
- CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
- K = K + N - J + 1
- 120 CONTINUE
- END IF
- SUM = 2*SUM
- K = 1
- DO 130 I = 1, N
- IF( AP( K ).NE.ZERO ) THEN
- ABSA = ABS( AP( K ) )
- IF( SCALE.LT.ABSA ) THEN
- SUM = ONE + SUM*( SCALE / ABSA )**2
- SCALE = ABSA
- ELSE
- SUM = SUM + ( ABSA / SCALE )**2
- END IF
- END IF
- IF( LSAME( UPLO, 'U' ) ) THEN
- K = K + I + 1
- ELSE
- K = K + N - I + 1
- END IF
- 130 CONTINUE
- VALUE = SCALE*SQRT( SUM )
- END IF
-*
- DLANSP = VALUE
- RETURN
-*
-* End of DLANSP
-*
- END