Move LAPACK trunk into position.

1 files changed, 363 insertions, 0 deletions

diff --git a/SRC/clasr.f b/SRC/clasr.f
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+      SUBROUTINE CLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
+*
+*  -- LAPACK auxiliary routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      CHARACTER          DIRECT, PIVOT, SIDE
+      INTEGER            LDA, M, N
+*     ..
+*     .. Array Arguments ..
+      REAL               C( * ), S( * )
+      COMPLEX            A( LDA, * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  CLASR applies a sequence of real plane rotations to a complex matrix
+*  A, from either the left or the right.
+*
+*  When SIDE = 'L', the transformation takes the form
+*
+*     A := P*A
+*
+*  and when SIDE = 'R', the transformation takes the form
+*
+*     A := A*P**T
+*
+*  where P is an orthogonal matrix consisting of a sequence of z plane
+*  rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
+*  and P**T is the transpose of P.
+*  
+*  When DIRECT = 'F' (Forward sequence), then
+*  
+*     P = P(z-1) * ... * P(2) * P(1)
+*  
+*  and when DIRECT = 'B' (Backward sequence), then
+*  
+*     P = P(1) * P(2) * ... * P(z-1)
+*  
+*  where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
+*  
+*     R(k) = (  c(k)  s(k) )
+*          = ( -s(k)  c(k) ).
+*  
+*  When PIVOT = 'V' (Variable pivot), the rotation is performed
+*  for the plane (k,k+1), i.e., P(k) has the form
+*  
+*     P(k) = (  1                                            )
+*            (       ...                                     )
+*            (              1                                )
+*            (                   c(k)  s(k)                  )
+*            (                  -s(k)  c(k)                  )
+*            (                                1              )
+*            (                                     ...       )
+*            (                                            1  )
+*  
+*  where R(k) appears as a rank-2 modification to the identity matrix in
+*  rows and columns k and k+1.
+*  
+*  When PIVOT = 'T' (Top pivot), the rotation is performed for the
+*  plane (1,k+1), so P(k) has the form
+*  
+*     P(k) = (  c(k)                    s(k)                 )
+*            (         1                                     )
+*            (              ...                              )
+*            (                     1                         )
+*            ( -s(k)                    c(k)                 )
+*            (                                 1             )
+*            (                                      ...      )
+*            (                                             1 )
+*  
+*  where R(k) appears in rows and columns 1 and k+1.
+*  
+*  Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
+*  performed for the plane (k,z), giving P(k) the form
+*  
+*     P(k) = ( 1                                             )
+*            (      ...                                      )
+*            (             1                                 )
+*            (                  c(k)                    s(k) )
+*            (                         1                     )
+*            (                              ...              )
+*            (                                     1         )
+*            (                 -s(k)                    c(k) )
+*  
+*  where R(k) appears in rows and columns k and z.  The rotations are
+*  performed without ever forming P(k) explicitly.
+*
+*  Arguments
+*  =========
+*
+*  SIDE    (input) CHARACTER*1
+*          Specifies whether the plane rotation matrix P is applied to
+*          A on the left or the right.
+*          = 'L':  Left, compute A := P*A
+*          = 'R':  Right, compute A:= A*P**T
+*
+*  PIVOT   (input) CHARACTER*1
+*          Specifies the plane for which P(k) is a plane rotation
+*          matrix.
+*          = 'V':  Variable pivot, the plane (k,k+1)
+*          = 'T':  Top pivot, the plane (1,k+1)
+*          = 'B':  Bottom pivot, the plane (k,z)
+*
+*  DIRECT  (input) CHARACTER*1
+*          Specifies whether P is a forward or backward sequence of
+*          plane rotations.
+*          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
+*          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
+*
+*  M       (input) INTEGER
+*          The number of rows of the matrix A.  If m <= 1, an immediate
+*          return is effected.
+*
+*  N       (input) INTEGER
+*          The number of columns of the matrix A.  If n <= 1, an
+*          immediate return is effected.
+*
+*  C       (input) REAL array, dimension
+*                  (M-1) if SIDE = 'L'
+*                  (N-1) if SIDE = 'R'
+*          The cosines c(k) of the plane rotations.
+*
+*  S       (input) REAL array, dimension
+*                  (M-1) if SIDE = 'L'
+*                  (N-1) if SIDE = 'R'
+*          The sines s(k) of the plane rotations.  The 2-by-2 plane
+*          rotation part of the matrix P(k), R(k), has the form
+*          R(k) = (  c(k)  s(k) )
+*                 ( -s(k)  c(k) ).
+*
+*  A       (input/output) COMPLEX array, dimension (LDA,N)
+*          The M-by-N matrix A.  On exit, A is overwritten by P*A if
+*          SIDE = 'R' or by A*P**T if SIDE = 'L'.
+*
+*  LDA     (input) INTEGER
+*          The leading dimension of the array A.  LDA >= max(1,M).
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ONE, ZERO
+      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I, INFO, J
+      REAL               CTEMP, STEMP
+      COMPLEX            TEMP
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters
+*
+      INFO = 0
+      IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
+         INFO = 1
+      ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
+     $         'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
+         INFO = 2
+      ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
+     $          THEN
+         INFO = 3
+      ELSE IF( M.LT.0 ) THEN
+         INFO = 4
+      ELSE IF( N.LT.0 ) THEN
+         INFO = 5
+      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
+         INFO = 9
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CLASR ', INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
+     $   RETURN
+      IF( LSAME( SIDE, 'L' ) ) THEN
+*
+*        Form  P * A
+*
+         IF( LSAME( PIVOT, 'V' ) ) THEN
+            IF( LSAME( DIRECT, 'F' ) ) THEN
+               DO 20 J = 1, M - 1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 10 I = 1, N
+                        TEMP = A( J+1, I )
+                        A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
+                        A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
+   10                CONTINUE
+                  END IF
+   20          CONTINUE
+            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
+               DO 40 J = M - 1, 1, -1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 30 I = 1, N
+                        TEMP = A( J+1, I )
+                        A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
+                        A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
+   30                CONTINUE
+                  END IF
+   40          CONTINUE
+            END IF
+         ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
+            IF( LSAME( DIRECT, 'F' ) ) THEN
+               DO 60 J = 2, M
+                  CTEMP = C( J-1 )
+                  STEMP = S( J-1 )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 50 I = 1, N
+                        TEMP = A( J, I )
+                        A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
+                        A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
+   50                CONTINUE
+                  END IF
+   60          CONTINUE
+            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
+               DO 80 J = M, 2, -1
+                  CTEMP = C( J-1 )
+                  STEMP = S( J-1 )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 70 I = 1, N
+                        TEMP = A( J, I )
+                        A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
+                        A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
+   70                CONTINUE
+                  END IF
+   80          CONTINUE
+            END IF
+         ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
+            IF( LSAME( DIRECT, 'F' ) ) THEN
+               DO 100 J = 1, M - 1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 90 I = 1, N
+                        TEMP = A( J, I )
+                        A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
+                        A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
+   90                CONTINUE
+                  END IF
+  100          CONTINUE
+            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
+               DO 120 J = M - 1, 1, -1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 110 I = 1, N
+                        TEMP = A( J, I )
+                        A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
+                        A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
+  110                CONTINUE
+                  END IF
+  120          CONTINUE
+            END IF
+         END IF
+      ELSE IF( LSAME( SIDE, 'R' ) ) THEN
+*
+*        Form A * P'
+*
+         IF( LSAME( PIVOT, 'V' ) ) THEN
+            IF( LSAME( DIRECT, 'F' ) ) THEN
+               DO 140 J = 1, N - 1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 130 I = 1, M
+                        TEMP = A( I, J+1 )
+                        A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
+                        A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
+  130                CONTINUE
+                  END IF
+  140          CONTINUE
+            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
+               DO 160 J = N - 1, 1, -1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 150 I = 1, M
+                        TEMP = A( I, J+1 )
+                        A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
+                        A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
+  150                CONTINUE
+                  END IF
+  160          CONTINUE
+            END IF
+         ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
+            IF( LSAME( DIRECT, 'F' ) ) THEN
+               DO 180 J = 2, N
+                  CTEMP = C( J-1 )
+                  STEMP = S( J-1 )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 170 I = 1, M
+                        TEMP = A( I, J )
+                        A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
+                        A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
+  170                CONTINUE
+                  END IF
+  180          CONTINUE
+            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
+               DO 200 J = N, 2, -1
+                  CTEMP = C( J-1 )
+                  STEMP = S( J-1 )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 190 I = 1, M
+                        TEMP = A( I, J )
+                        A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
+                        A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
+  190                CONTINUE
+                  END IF
+  200          CONTINUE
+            END IF
+         ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
+            IF( LSAME( DIRECT, 'F' ) ) THEN
+               DO 220 J = 1, N - 1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 210 I = 1, M
+                        TEMP = A( I, J )
+                        A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
+                        A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
+  210                CONTINUE
+                  END IF
+  220          CONTINUE
+            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
+               DO 240 J = N - 1, 1, -1
+                  CTEMP = C( J )
+                  STEMP = S( J )
+                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
+                     DO 230 I = 1, M
+                        TEMP = A( I, J )
+                        A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
+                        A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
+  230                CONTINUE
+                  END IF
+  240          CONTINUE
+            END IF
+         END IF
+      END IF
+*
+      RETURN
+*
+*     End of CLASR
+*
+      END