import reference BLAS routines which are not already implemented in Eigen : modified givens rotations, and packed and banded storages

blas/drotm.f

@@ -0,0 +1,147 @@
+      SUBROUTINE DROTM(N,DX,INCX,DY,INCY,DPARAM)
+*     .. Scalar Arguments ..
+      INTEGER INCX,INCY,N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION DPARAM(5),DX(*),DY(*)
+*     ..
+*
+*  Purpose
+*  =======
+*
+*     APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
+*
+*     (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN
+*     (DY**T)
+*
+*     DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
+*     LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY.
+*     WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
+*
+*     DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0
+*
+*       (DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0)
+*     H=(          )    (          )    (          )    (          )
+*       (DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0).
+*     SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM.
+*
+*  Arguments
+*  =========
+*
+*  N      (input) INTEGER
+*         number of elements in input vector(s)
+*
+*  DX     (input/output) DOUBLE PRECISION array, dimension N
+*         double precision vector with N elements
+*
+*  INCX   (input) INTEGER
+*         storage spacing between elements of DX
+*
+*  DY     (input/output) DOUBLE PRECISION array, dimension N
+*         double precision vector with N elements
+*
+*  INCY   (input) INTEGER
+*         storage spacing between elements of DY
+*
+*  DPARAM (input/output)  DOUBLE PRECISION array, dimension 5 
+*     DPARAM(1)=DFLAG
+*     DPARAM(2)=DH11
+*     DPARAM(3)=DH21
+*     DPARAM(4)=DH12
+*     DPARAM(5)=DH22
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      DOUBLE PRECISION DFLAG,DH11,DH12,DH21,DH22,TWO,W,Z,ZERO
+      INTEGER I,KX,KY,NSTEPS
+*     ..
+*     .. Data statements ..
+      DATA ZERO,TWO/0.D0,2.D0/
+*     ..
+*
+      DFLAG = DPARAM(1)
+      IF (N.LE.0 .OR. (DFLAG+TWO.EQ.ZERO)) GO TO 140
+      IF (.NOT. (INCX.EQ.INCY.AND.INCX.GT.0)) GO TO 70
+*
+      NSTEPS = N*INCX
+      IF (DFLAG) 50,10,30
+   10 CONTINUE
+      DH12 = DPARAM(4)
+      DH21 = DPARAM(3)
+      DO 20 I = 1,NSTEPS,INCX
+          W = DX(I)
+          Z = DY(I)
+          DX(I) = W + Z*DH12
+          DY(I) = W*DH21 + Z
+   20 CONTINUE
+      GO TO 140
+   30 CONTINUE
+      DH11 = DPARAM(2)
+      DH22 = DPARAM(5)
+      DO 40 I = 1,NSTEPS,INCX
+          W = DX(I)
+          Z = DY(I)
+          DX(I) = W*DH11 + Z
+          DY(I) = -W + DH22*Z
+   40 CONTINUE
+      GO TO 140
+   50 CONTINUE
+      DH11 = DPARAM(2)
+      DH12 = DPARAM(4)
+      DH21 = DPARAM(3)
+      DH22 = DPARAM(5)
+      DO 60 I = 1,NSTEPS,INCX
+          W = DX(I)
+          Z = DY(I)
+          DX(I) = W*DH11 + Z*DH12
+          DY(I) = W*DH21 + Z*DH22
+   60 CONTINUE
+      GO TO 140
+   70 CONTINUE
+      KX = 1
+      KY = 1
+      IF (INCX.LT.0) KX = 1 + (1-N)*INCX
+      IF (INCY.LT.0) KY = 1 + (1-N)*INCY
+*
+      IF (DFLAG) 120,80,100
+   80 CONTINUE
+      DH12 = DPARAM(4)
+      DH21 = DPARAM(3)
+      DO 90 I = 1,N
+          W = DX(KX)
+          Z = DY(KY)
+          DX(KX) = W + Z*DH12
+          DY(KY) = W*DH21 + Z
+          KX = KX + INCX
+          KY = KY + INCY
+   90 CONTINUE
+      GO TO 140
+  100 CONTINUE
+      DH11 = DPARAM(2)
+      DH22 = DPARAM(5)
+      DO 110 I = 1,N
+          W = DX(KX)
+          Z = DY(KY)
+          DX(KX) = W*DH11 + Z
+          DY(KY) = -W + DH22*Z
+          KX = KX + INCX
+          KY = KY + INCY
+  110 CONTINUE
+      GO TO 140
+  120 CONTINUE
+      DH11 = DPARAM(2)
+      DH12 = DPARAM(4)
+      DH21 = DPARAM(3)
+      DH22 = DPARAM(5)
+      DO 130 I = 1,N
+          W = DX(KX)
+          Z = DY(KY)
+          DX(KX) = W*DH11 + Z*DH12
+          DY(KY) = W*DH21 + Z*DH22
+          KX = KX + INCX
+          KY = KY + INCY
+  130 CONTINUE
+  140 CONTINUE
+      RETURN
+      END