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118 lines
4 KiB
Fortran
118 lines
4 KiB
Fortran
*DECK H12
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SUBROUTINE H12 (MODE, LPIVOT, L1, M, U, IUE, UP, C, ICE, ICV, NCV)
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C***BEGIN PROLOGUE H12
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C***SUBSIDIARY
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C***PURPOSE Subsidiary to HFTI, LSEI and WNNLS
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C***LIBRARY SLATEC
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C***TYPE SINGLE PRECISION (H12-S, DH12-D)
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C***AUTHOR (UNKNOWN)
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C***DESCRIPTION
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C
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C C.L.Lawson and R.J.Hanson, Jet Propulsion Laboratory, 1973 Jun 12
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C to appear in 'Solving Least Squares Problems', Prentice-Hall, 1974
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C
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C Construction and/or application of a single
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C Householder transformation.. Q = I + U*(U**T)/B
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C
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C MODE = 1 or 2 to select algorithm H1 or H2 .
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C LPIVOT is the index of the pivot element.
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C L1,M If L1 .LE. M the transformation will be constructed to
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C zero elements indexed from L1 through M. If L1 GT. M
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C THE SUBROUTINE DOES AN IDENTITY TRANSFORMATION.
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C U(),IUE,UP On entry to H1 U() contains the pivot vector.
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C IUE is the storage increment between elements.
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C On exit from H1 U() and UP
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C contain quantities defining the vector U of the
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C Householder transformation. On entry to H2 U()
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C and UP should contain quantities previously computed
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C by H1. These will not be modified by H2.
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C C() On entry to H1 or H2 C() contains a matrix which will be
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C regarded as a set of vectors to which the Householder
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C transformation is to be applied. On exit C() contains the
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C set of transformed vectors.
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C ICE Storage increment between elements of vectors in C().
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C ICV Storage increment between vectors in C().
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C NCV Number of vectors in C() to be transformed. If NCV .LE. 0
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C no operations will be done on C().
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C
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C***SEE ALSO HFTI, LSEI, WNNLS
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C***ROUTINES CALLED SAXPY, SDOT, SSWAP
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C***REVISION HISTORY (YYMMDD)
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C 790101 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890831 Modified array declarations. (WRB)
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900328 Added TYPE section. (WRB)
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C***END PROLOGUE H12
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DIMENSION U(IUE,*), C(*)
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C***FIRST EXECUTABLE STATEMENT H12
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ONE=1.
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C
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IF (0.GE.LPIVOT.OR.LPIVOT.GE.L1.OR.L1.GT.M) RETURN
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CL=ABS(U(1,LPIVOT))
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IF (MODE.EQ.2) GO TO 60
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C ****** CONSTRUCT THE TRANSFORMATION. ******
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DO 10 J=L1,M
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10 CL=MAX(ABS(U(1,J)),CL)
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IF (CL) 130,130,20
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20 CLINV=ONE/CL
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SM=(U(1,LPIVOT)*CLINV)**2
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DO 30 J=L1,M
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30 SM=SM+(U(1,J)*CLINV)**2
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CL=CL*SQRT(SM)
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IF (U(1,LPIVOT)) 50,50,40
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40 CL=-CL
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50 UP=U(1,LPIVOT)-CL
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U(1,LPIVOT)=CL
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GO TO 70
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C ****** APPLY THE TRANSFORMATION I+U*(U**T)/B TO C. ******
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C
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60 IF (CL) 130,130,70
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70 IF (NCV.LE.0) RETURN
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B=UP*U(1,LPIVOT)
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C B MUST BE NONPOSITIVE HERE. IF B = 0., RETURN.
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C
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IF (B) 80,130,130
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80 B=ONE/B
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MML1P2=M-L1+2
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IF (MML1P2.GT.20) GO TO 140
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I2=1-ICV+ICE*(LPIVOT-1)
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INCR=ICE*(L1-LPIVOT)
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DO 120 J=1,NCV
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I2=I2+ICV
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I3=I2+INCR
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I4=I3
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SM=C(I2)*UP
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DO 90 I=L1,M
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SM=SM+C(I3)*U(1,I)
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90 I3=I3+ICE
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IF (SM) 100,120,100
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100 SM=SM*B
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C(I2)=C(I2)+SM*UP
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DO 110 I=L1,M
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C(I4)=C(I4)+SM*U(1,I)
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110 I4=I4+ICE
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120 CONTINUE
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130 RETURN
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140 CONTINUE
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L1M1=L1-1
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KL1=1+(L1M1-1)*ICE
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KL2=KL1
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KLP=1+(LPIVOT-1)*ICE
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UL1M1=U(1,L1M1)
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U(1,L1M1)=UP
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IF (LPIVOT.EQ.L1M1) GO TO 150
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CALL SSWAP(NCV,C(KL1),ICV,C(KLP),ICV)
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150 CONTINUE
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DO 160 J=1,NCV
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SM=SDOT(MML1P2,U(1,L1M1),IUE,C(KL1),ICE)
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SM=SM*B
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CALL SAXPY (MML1P2,SM,U(1,L1M1),IUE,C(KL1),ICE)
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KL1=KL1+ICV
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160 CONTINUE
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U(1,L1M1)=UL1M1
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IF (LPIVOT.EQ.L1M1) RETURN
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KL1=KL2
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CALL SSWAP(NCV,C(KL1),ICV,C(KLP),ICV)
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RETURN
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END
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