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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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- SUBROUTINE DSPTRD( UPLO, N, AP, D, E, TAU, INFO )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- CHARACTER UPLO
- INTEGER INFO, N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION AP( * ), D( * ), E( * ), TAU( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DSPTRD reduces a real symmetric matrix A stored in packed form to
-* symmetric tridiagonal form T by an orthogonal similarity
-* transformation: Q**T * A * Q = T.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of A is stored;
-* = 'L': Lower triangle of A is stored.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
-* On entry, 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.
-* On exit, if UPLO = 'U', the diagonal and first superdiagonal
-* of A are overwritten by the corresponding elements of the
-* tridiagonal matrix T, and the elements above the first
-* superdiagonal, with the array TAU, represent the orthogonal
-* matrix Q as a product of elementary reflectors; if UPLO
-* = 'L', the diagonal and first subdiagonal of A are over-
-* written by the corresponding elements of the tridiagonal
-* matrix T, and the elements below the first subdiagonal, with
-* the array TAU, represent the orthogonal matrix Q as a product
-* of elementary reflectors. See Further Details.
-*
-* D (output) DOUBLE PRECISION array, dimension (N)
-* The diagonal elements of the tridiagonal matrix T:
-* D(i) = A(i,i).
-*
-* E (output) DOUBLE PRECISION array, dimension (N-1)
-* The off-diagonal elements of the tridiagonal matrix T:
-* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
-*
-* TAU (output) DOUBLE PRECISION array, dimension (N-1)
-* The scalar factors of the elementary reflectors (see Further
-* Details).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
-* Further Details
-* ===============
-*
-* If UPLO = 'U', the matrix Q is represented as a product of elementary
-* reflectors
-*
-* Q = H(n-1) . . . H(2) H(1).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a real scalar, and v is a real vector with
-* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
-* overwriting A(1:i-1,i+1), and tau is stored in TAU(i).
-*
-* If UPLO = 'L', the matrix Q is represented as a product of elementary
-* reflectors
-*
-* Q = H(1) H(2) . . . H(n-1).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a real scalar, and v is a real vector with
-* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
-* overwriting A(i+2:n,i), and tau is stored in TAU(i).
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ONE, ZERO, HALF
- PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0,
- $ HALF = 1.0D0 / 2.0D0 )
-* ..
-* .. Local Scalars ..
- LOGICAL UPPER
- INTEGER I, I1, I1I1, II
- DOUBLE PRECISION ALPHA, TAUI
-* ..
-* .. External Subroutines ..
- EXTERNAL DAXPY, DLARFG, DSPMV, DSPR2, XERBLA
-* ..
-* .. External Functions ..
- LOGICAL LSAME
- DOUBLE PRECISION DDOT
- EXTERNAL LSAME, DDOT
-* ..
-* .. Executable Statements ..
-*
-* Test the input parameters
-*
- INFO = 0
- UPPER = LSAME( UPLO, 'U' )
- IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
- INFO = -1
- ELSE IF( N.LT.0 ) THEN
- INFO = -2
- END IF
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'DSPTRD', -INFO )
- RETURN
- END IF
-*
-* Quick return if possible
-*
- IF( N.LE.0 )
- $ RETURN
-*
- IF( UPPER ) THEN
-*
-* Reduce the upper triangle of A.
-* I1 is the index in AP of A(1,I+1).
-*
- I1 = N*( N-1 ) / 2 + 1
- DO 10 I = N - 1, 1, -1
-*
-* Generate elementary reflector H(i) = I - tau * v * v'
-* to annihilate A(1:i-1,i+1)
-*
- CALL DLARFG( I, AP( I1+I-1 ), AP( I1 ), 1, TAUI )
- E( I ) = AP( I1+I-1 )
-*
- IF( TAUI.NE.ZERO ) THEN
-*
-* Apply H(i) from both sides to A(1:i,1:i)
-*
- AP( I1+I-1 ) = ONE
-*
-* Compute y := tau * A * v storing y in TAU(1:i)
-*
- CALL DSPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
- $ 1 )
-*
-* Compute w := y - 1/2 * tau * (y'*v) * v
-*
- ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, AP( I1 ), 1 )
- CALL DAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
-*
-* Apply the transformation as a rank-2 update:
-* A := A - v * w' - w * v'
-*
- CALL DSPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP )
-*
- AP( I1+I-1 ) = E( I )
- END IF
- D( I+1 ) = AP( I1+I )
- TAU( I ) = TAUI
- I1 = I1 - I
- 10 CONTINUE
- D( 1 ) = AP( 1 )
- ELSE
-*
-* Reduce the lower triangle of A. II is the index in AP of
-* A(i,i) and I1I1 is the index of A(i+1,i+1).
-*
- II = 1
- DO 20 I = 1, N - 1
- I1I1 = II + N - I + 1
-*
-* Generate elementary reflector H(i) = I - tau * v * v'
-* to annihilate A(i+2:n,i)
-*
- CALL DLARFG( N-I, AP( II+1 ), AP( II+2 ), 1, TAUI )
- E( I ) = AP( II+1 )
-*
- IF( TAUI.NE.ZERO ) THEN
-*
-* Apply H(i) from both sides to A(i+1:n,i+1:n)
-*
- AP( II+1 ) = ONE
-*
-* Compute y := tau * A * v storing y in TAU(i:n-1)
-*
- CALL DSPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1,
- $ ZERO, TAU( I ), 1 )
-*
-* Compute w := y - 1/2 * tau * (y'*v) * v
-*
- ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, AP( II+1 ),
- $ 1 )
- CALL DAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 )
-*
-* Apply the transformation as a rank-2 update:
-* A := A - v * w' - w * v'
-*
- CALL DSPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1,
- $ AP( I1I1 ) )
-*
- AP( II+1 ) = E( I )
- END IF
- D( I ) = AP( II )
- TAU( I ) = TAUI
- II = I1I1
- 20 CONTINUE
- D( N ) = AP( II )
- END IF
-*
- RETURN
-*
-* End of DSPTRD
-*
- END