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Diffstat (limited to '2.3-1/src/fortran/lapack/dsytd2.f')
| -rw-r--r-- | 2.3-1/src/fortran/lapack/dsytd2.f | 248 |
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diff --git a/2.3-1/src/fortran/lapack/dsytd2.f b/2.3-1/src/fortran/lapack/dsytd2.f new file mode 100644 index 00000000..c696818e --- /dev/null +++ b/2.3-1/src/fortran/lapack/dsytd2.f @@ -0,0 +1,248 @@ + SUBROUTINE DSYTD2( UPLO, N, A, LDA, 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, LDA, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) +* .. +* +* Purpose +* ======= +* +* DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal +* form T by an orthogonal similarity transformation: Q' * A * Q = T. +* +* Arguments +* ========= +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* symmetric matrix A is stored: +* = 'U': Upper triangular +* = 'L': Lower triangular +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) +* On entry, the symmetric matrix A. If UPLO = 'U', the leading +* n-by-n upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading n-by-n lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* 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. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* 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 +* A(1:i-1,i+1), and tau 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 A(i+2:n,i), +* and tau in TAU(i). +* +* The contents of A on exit are illustrated by the following examples +* with n = 5: +* +* if UPLO = 'U': if UPLO = 'L': +* +* ( d e v2 v3 v4 ) ( d ) +* ( d e v3 v4 ) ( e d ) +* ( d e v4 ) ( v1 e d ) +* ( d e ) ( v1 v2 e d ) +* ( d ) ( v1 v2 v3 e d ) +* +* where d and e denote diagonal and off-diagonal elements of T, and vi +* denotes an element of the vector defining H(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 + DOUBLE PRECISION ALPHA, TAUI +* .. +* .. External Subroutines .. + EXTERNAL DAXPY, DLARFG, DSYMV, DSYR2, XERBLA +* .. +* .. External Functions .. + LOGICAL LSAME + DOUBLE PRECISION DDOT + EXTERNAL LSAME, DDOT +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. 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 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -4 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSYTD2', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.LE.0 ) + $ RETURN +* + IF( UPPER ) THEN +* +* Reduce the upper triangle of A +* + 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, A( I, I+1 ), A( 1, I+1 ), 1, TAUI ) + E( I ) = A( I, I+1 ) +* + IF( TAUI.NE.ZERO ) THEN +* +* Apply H(i) from both sides to A(1:i,1:i) +* + A( I, I+1 ) = ONE +* +* Compute x := tau * A * v storing x in TAU(1:i) +* + CALL DSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO, + $ TAU, 1 ) +* +* Compute w := x - 1/2 * tau * (x'*v) * v +* + ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, A( 1, I+1 ), 1 ) + CALL DAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 ) +* +* Apply the transformation as a rank-2 update: +* A := A - v * w' - w * v' +* + CALL DSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A, + $ LDA ) +* + A( I, I+1 ) = E( I ) + END IF + D( I+1 ) = A( I+1, I+1 ) + TAU( I ) = TAUI + 10 CONTINUE + D( 1 ) = A( 1, 1 ) + ELSE +* +* Reduce the lower triangle of A +* + DO 20 I = 1, N - 1 +* +* Generate elementary reflector H(i) = I - tau * v * v' +* to annihilate A(i+2:n,i) +* + CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1, + $ TAUI ) + E( I ) = A( I+1, I ) +* + IF( TAUI.NE.ZERO ) THEN +* +* Apply H(i) from both sides to A(i+1:n,i+1:n) +* + A( I+1, I ) = ONE +* +* Compute x := tau * A * v storing y in TAU(i:n-1) +* + CALL DSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA, + $ A( I+1, I ), 1, ZERO, TAU( I ), 1 ) +* +* Compute w := x - 1/2 * tau * (x'*v) * v +* + ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, A( I+1, I ), + $ 1 ) + CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 ) +* +* Apply the transformation as a rank-2 update: +* A := A - v * w' - w * v' +* + CALL DSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1, + $ A( I+1, I+1 ), LDA ) +* + A( I+1, I ) = E( I ) + END IF + D( I ) = A( I, I ) + TAU( I ) = TAUI + 20 CONTINUE + D( N ) = A( N, N ) + END IF +* + RETURN +* +* End of DSYTD2 +* + END |