--- /dev/null
+*DECK RWUPDT
+ SUBROUTINE RWUPDT (N, R, LDR, W, B, ALPHA, COS, SIN)
+C***BEGIN PROLOGUE RWUPDT
+C***SUBSIDIARY
+C***PURPOSE Subsidiary to SNLS1 and SNLS1E
+C***LIBRARY SLATEC
+C***TYPE SINGLE PRECISION (RWUPDT-S, DWUPDT-D)
+C***AUTHOR (UNKNOWN)
+C***DESCRIPTION
+C
+C Given an N by N upper triangular matrix R, this subroutine
+C computes the QR decomposition of the matrix formed when a row
+C is added to R. If the row is specified by the vector W, then
+C RWUPDT determines an orthogonal matrix Q such that when the
+C N+1 by N matrix composed of R augmented by W is premultiplied
+C by (Q TRANSPOSE), the resulting matrix is upper trapezoidal.
+C The orthogonal matrix Q is the product of N transformations
+C
+C G(1)*G(2)* ... *G(N)
+C
+C where G(I) is a Givens rotation in the (I,N+1) plane which
+C eliminates elements in the I-th plane. RWUPDT also
+C computes the product (Q TRANSPOSE)*C where C is the
+C (N+1)-vector (b,alpha). Q itself is not accumulated, rather
+C the information to recover the G rotations is supplied.
+C
+C The subroutine statement is
+C
+C SUBROUTINE RWUPDT(N,R,LDR,W,B,ALPHA,COS,SIN)
+C
+C where
+C
+C N is a positive integer input variable set to the order of R.
+C
+C R is an N by N array. On input the upper triangular part of
+C R must contain the matrix to be updated. On output R
+C contains the updated triangular matrix.
+C
+C LDR is a positive integer input variable not less than N
+C which specifies the leading dimension of the array R.
+C
+C W is an input array of length N which must contain the row
+C vector to be added to R.
+C
+C B is an array of length N. On input B must contain the
+C first N elements of the vector C. On output B contains
+C the first N elements of the vector (Q TRANSPOSE)*C.
+C
+C ALPHA is a variable. On input ALPHA must contain the
+C (N+1)-st element of the vector C. On output ALPHA contains
+C the (N+1)-st element of the vector (Q TRANSPOSE)*C.
+C
+C COS is an output array of length N which contains the
+C cosines of the transforming Givens rotations.
+C
+C SIN is an output array of length N which contains the
+C sines of the transforming Givens rotations.
+C
+C***SEE ALSO SNLS1, SNLS1E
+C***ROUTINES CALLED (NONE)
+C***REVISION HISTORY (YYMMDD)
+C 800301 DATE WRITTEN
+C 890831 Modified array declarations. (WRB)
+C 891214 Prologue converted to Version 4.0 format. (BAB)
+C 900326 Removed duplicate information from DESCRIPTION section.
+C (WRB)
+C 900328 Added TYPE section. (WRB)
+C***END PROLOGUE RWUPDT
+ INTEGER N,LDR
+ REAL ALPHA
+ REAL R(LDR,*),W(*),B(*),COS(*),SIN(*)
+ INTEGER I,J,JM1
+ REAL COTAN,ONE,P5,P25,ROWJ,TAN,TEMP,ZERO
+ SAVE ONE, P5, P25, ZERO
+ DATA ONE,P5,P25,ZERO /1.0E0,5.0E-1,2.5E-1,0.0E0/
+C***FIRST EXECUTABLE STATEMENT RWUPDT
+ DO 60 J = 1, N
+ ROWJ = W(J)
+ JM1 = J - 1
+C
+C APPLY THE PREVIOUS TRANSFORMATIONS TO
+C R(I,J), I=1,2,...,J-1, AND TO W(J).
+C
+ IF (JM1 .LT. 1) GO TO 20
+ DO 10 I = 1, JM1
+ TEMP = COS(I)*R(I,J) + SIN(I)*ROWJ
+ ROWJ = -SIN(I)*R(I,J) + COS(I)*ROWJ
+ R(I,J) = TEMP
+ 10 CONTINUE
+ 20 CONTINUE
+C
+C DETERMINE A GIVENS ROTATION WHICH ELIMINATES W(J).
+C
+ COS(J) = ONE
+ SIN(J) = ZERO
+ IF (ROWJ .EQ. ZERO) GO TO 50
+ IF (ABS(R(J,J)) .GE. ABS(ROWJ)) GO TO 30
+ COTAN = R(J,J)/ROWJ
+ SIN(J) = P5/SQRT(P25+P25*COTAN**2)
+ COS(J) = SIN(J)*COTAN
+ GO TO 40
+ 30 CONTINUE
+ TAN = ROWJ/R(J,J)
+ COS(J) = P5/SQRT(P25+P25*TAN**2)
+ SIN(J) = COS(J)*TAN
+ 40 CONTINUE
+C
+C APPLY THE CURRENT TRANSFORMATION TO R(J,J), B(J), AND ALPHA.
+C
+ R(J,J) = COS(J)*R(J,J) + SIN(J)*ROWJ
+ TEMP = COS(J)*B(J) + SIN(J)*ALPHA
+ ALPHA = -SIN(J)*B(J) + COS(J)*ALPHA
+ B(J) = TEMP
+ 50 CONTINUE
+ 60 CONTINUE
+ RETURN
+C
+C LAST CARD OF SUBROUTINE RWUPDT.
+C
+ END
git://source.jalview.org / jabaws.git / blobdiff