Move LAPACK trunk into position.

1 files changed, 227 insertions, 0 deletions

diff --git a/SRC/ssptrd.f b/SRC/ssptrd.f
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+      SUBROUTINE SSPTRD( 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 ..
+      REAL               AP( * ), D( * ), E( * ), TAU( * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  SSPTRD 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) REAL 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) REAL array, dimension (N)
+*          The diagonal elements of the tridiagonal matrix T:
+*          D(i) = A(i,i).
+*
+*  E       (output) REAL 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) REAL 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 ..
+      REAL               ONE, ZERO, HALF
+      PARAMETER          ( ONE = 1.0, ZERO = 0.0, HALF = 1.0 / 2.0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            I, I1, I1I1, II
+      REAL               ALPHA, TAUI
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           SAXPY, SLARFG, SSPMV, SSPR2, XERBLA
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      REAL               SDOT
+      EXTERNAL           LSAME, SDOT
+*     ..
+*     .. 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( 'SSPTRD', -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 SLARFG( 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 SSPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
+     $                     1 )
+*
+*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*
+               ALPHA = -HALF*TAUI*SDOT( I, TAU, 1, AP( I1 ), 1 )
+               CALL SAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
+*
+*              Apply the transformation as a rank-2 update:
+*                 A := A - v * w' - w * v'
+*
+               CALL SSPR2( 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 SLARFG( 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 SSPMV( 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*SDOT( N-I, TAU( I ), 1, AP( II+1 ),
+     $                 1 )
+               CALL SAXPY( 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 SSPR2( 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 SSPTRD
+*
+      END