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

blas/srotm.f

@@ -0,0 +1,148 @@
+      SUBROUTINE SROTM(N,SX,INCX,SY,INCY,SPARAM)
+*     .. Scalar Arguments ..
+      INTEGER INCX,INCY,N
+*     ..
+*     .. Array Arguments ..
+      REAL SPARAM(5),SX(*),SY(*)
+*     ..
+*
+*  Purpose
+*  =======
+*
+*     APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
+*
+*     (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN
+*     (DX**T)
+*
+*     SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
+*     LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY.
+*     WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS..
+*
+*     SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0
+*
+*       (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0)
+*     H=(          )    (          )    (          )    (          )
+*       (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0).
+*     SEE  SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM.
+*
+*
+*  Arguments
+*  =========
+*
+*  N      (input) INTEGER
+*         number of elements in input vector(s)
+*
+*  SX     (input/output) REAL array, dimension N
+*         double precision vector with N elements
+*
+*  INCX   (input) INTEGER
+*         storage spacing between elements of SX
+*
+*  SY     (input/output) REAL array, dimension N
+*         double precision vector with N elements
+*
+*  INCY   (input) INTEGER
+*         storage spacing between elements of SY
+*
+*  SPARAM (input/output)  REAL array, dimension 5
+*     SPARAM(1)=SFLAG
+*     SPARAM(2)=SH11
+*     SPARAM(3)=SH21
+*     SPARAM(4)=SH12
+*     SPARAM(5)=SH22
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      REAL SFLAG,SH11,SH12,SH21,SH22,TWO,W,Z,ZERO
+      INTEGER I,KX,KY,NSTEPS
+*     ..
+*     .. Data statements ..
+      DATA ZERO,TWO/0.E0,2.E0/
+*     ..
+*
+      SFLAG = SPARAM(1)
+      IF (N.LE.0 .OR. (SFLAG+TWO.EQ.ZERO)) GO TO 140
+      IF (.NOT. (INCX.EQ.INCY.AND.INCX.GT.0)) GO TO 70
+*
+      NSTEPS = N*INCX
+      IF (SFLAG) 50,10,30
+   10 CONTINUE
+      SH12 = SPARAM(4)
+      SH21 = SPARAM(3)
+      DO 20 I = 1,NSTEPS,INCX
+          W = SX(I)
+          Z = SY(I)
+          SX(I) = W + Z*SH12
+          SY(I) = W*SH21 + Z
+   20 CONTINUE
+      GO TO 140
+   30 CONTINUE
+      SH11 = SPARAM(2)
+      SH22 = SPARAM(5)
+      DO 40 I = 1,NSTEPS,INCX
+          W = SX(I)
+          Z = SY(I)
+          SX(I) = W*SH11 + Z
+          SY(I) = -W + SH22*Z
+   40 CONTINUE
+      GO TO 140
+   50 CONTINUE
+      SH11 = SPARAM(2)
+      SH12 = SPARAM(4)
+      SH21 = SPARAM(3)
+      SH22 = SPARAM(5)
+      DO 60 I = 1,NSTEPS,INCX
+          W = SX(I)
+          Z = SY(I)
+          SX(I) = W*SH11 + Z*SH12
+          SY(I) = W*SH21 + Z*SH22
+   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 (SFLAG) 120,80,100
+   80 CONTINUE
+      SH12 = SPARAM(4)
+      SH21 = SPARAM(3)
+      DO 90 I = 1,N
+          W = SX(KX)
+          Z = SY(KY)
+          SX(KX) = W + Z*SH12
+          SY(KY) = W*SH21 + Z
+          KX = KX + INCX
+          KY = KY + INCY
+   90 CONTINUE
+      GO TO 140
+  100 CONTINUE
+      SH11 = SPARAM(2)
+      SH22 = SPARAM(5)
+      DO 110 I = 1,N
+          W = SX(KX)
+          Z = SY(KY)
+          SX(KX) = W*SH11 + Z
+          SY(KY) = -W + SH22*Z
+          KX = KX + INCX
+          KY = KY + INCY
+  110 CONTINUE
+      GO TO 140
+  120 CONTINUE
+      SH11 = SPARAM(2)
+      SH12 = SPARAM(4)
+      SH21 = SPARAM(3)
+      SH22 = SPARAM(5)
+      DO 130 I = 1,N
+          W = SX(KX)
+          Z = SY(KY)
+          SX(KX) = W*SH11 + Z*SH12
+          SY(KY) = W*SH21 + Z*SH22
+          KX = KX + INCX
+          KY = KY + INCY
+  130 CONTINUE
+  140 CONTINUE
+      RETURN
+      END