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OpenLibm/slatec/ulsia.f
Viral B. Shah c977aa998f Add Makefile.extras to build libopenlibm-extras. 
Replace amos with slatec
2012-12-31 16:37:05 -05:00

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*DECK ULSIA
SUBROUTINE ULSIA (A, MDA, M, N, B, MDB, NB, RE, AE, KEY, MODE, NP,
+ KRANK, KSURE, RNORM, W, LW, IWORK, LIW, INFO)
C***BEGIN PROLOGUE ULSIA
C***PURPOSE Solve an underdetermined linear system of equations by
C performing an LQ factorization of the matrix using
C Householder transformations. Emphasis is put on detecting
C possible rank deficiency.
C***LIBRARY SLATEC
C***CATEGORY D9
C***TYPE SINGLE PRECISION (ULSIA-S, DULSIA-D)
C***KEYWORDS LINEAR LEAST SQUARES, LQ FACTORIZATION,
C UNDERDETERMINED LINEAR SYSTEM
C***AUTHOR Manteuffel, T. A., (LANL)
C***DESCRIPTION
C
C ULSIA computes the minimal length solution(s) to the problem AX=B
C where A is an M by N matrix with M.LE.N and B is the M by NB
C matrix of right hand sides. User input bounds on the uncertainty
C in the elements of A are used to detect numerical rank deficiency.
C The algorithm employs a row and column pivot strategy to
C minimize the growth of uncertainty and round-off errors.
C
C ULSIA requires (MDA+1)*N + (MDB+1)*NB + 6*M dimensioned space
C
C ******************************************************************
C * *
C * WARNING - All input arrays are changed on exit. *
C * *
C ******************************************************************
C
C Input..
C
C A(,) Linear coefficient matrix of AX=B, with MDA the
C MDA,M,N actual first dimension of A in the calling program.
C M is the row dimension (no. of EQUATIONS of the
C problem) and N the col dimension (no. of UNKNOWNS).
C Must have MDA.GE.M and M.LE.N.
C
C B(,) Right hand side(s), with MDB the actual first
C MDB,NB dimension of B in the calling program. NB is the
C number of M by 1 right hand sides. Since the
C solution is returned in B, must have MDB.GE.N. If
C NB = 0, B is never accessed.
C
C ******************************************************************
C * *
C * Note - Use of RE and AE are what make this *
C * code significantly different from *
C * other linear least squares solvers. *
C * However, the inexperienced user is *
C * advised to set RE=0.,AE=0.,KEY=0. *
C * *
C ******************************************************************
C
C RE(),AE(),KEY
C RE() RE() is a vector of length N such that RE(I) is
C the maximum relative uncertainty in row I of
C the matrix A. The values of RE() must be between
C 0 and 1. A minimum of 10*machine precision will
C be enforced.
C
C AE() AE() is a vector of length N such that AE(I) is
C the maximum absolute uncertainty in row I of
C the matrix A. The values of AE() must be greater
C than or equal to 0.
C
C KEY For ease of use, RE and AE may be input as either
C vectors or scalars. If a scalar is input, the algo-
C rithm will use that value for each column of A.
C The parameter KEY indicates whether scalars or
C vectors are being input.
C KEY=0 RE scalar AE scalar
C KEY=1 RE vector AE scalar
C KEY=2 RE scalar AE vector
C KEY=3 RE vector AE vector
C
C
C MODE The integer MODE indicates how the routine
C is to react if rank deficiency is detected.
C If MODE = 0 return immediately, no solution
C 1 compute truncated solution
C 2 compute minimal length least squares sol
C The inexperienced user is advised to set MODE=0
C
C NP The first NP rows of A will not be interchanged
C with other rows even though the pivot strategy
C would suggest otherwise.
C The inexperienced user is advised to set NP=0.
C
C WORK() A real work array dimensioned 5*M. However, if
C RE or AE have been specified as vectors, dimension
C WORK 4*M. If both RE and AE have been specified
C as vectors, dimension WORK 3*M.
C
C LW Actual dimension of WORK
C
C IWORK() Integer work array dimensioned at least N+M.
C
C LIW Actual dimension of IWORK.
C
C
C INFO Is a flag which provides for the efficient
C solution of subsequent problems involving the
C same A but different B.
C If INFO = 0 original call
C INFO = 1 subsequent calls
C On subsequent calls, the user must supply A, KRANK,
C LW, IWORK, LIW, and the first 2*M locations of WORK
C as output by the original call to ULSIA. MODE must
C be equal to the value of MODE in the original call.
C If MODE.LT.2, only the first N locations of WORK
C are accessed. AE, RE, KEY, and NP are not accessed.
C
C
C
C
C Output..
C
C A(,) Contains the lower triangular part of the reduced
C matrix and the transformation information. It togeth
C with the first M elements of WORK (see below)
C completely specify the LQ factorization of A.
C
C B(,) Contains the N by NB solution matrix for X.
C
C KRANK,KSURE The numerical rank of A, based upon the relative
C and absolute bounds on uncertainty, is bounded
C above by KRANK and below by KSURE. The algorithm
C returns a solution based on KRANK. KSURE provides
C an indication of the precision of the rank.
C
C RNORM() Contains the Euclidean length of the NB residual
C vectors B(I)-AX(I), I=1,NB. If the matrix A is of
C full rank, then RNORM=0.0.
C
C WORK() The first M locations of WORK contain values
C necessary to reproduce the Householder
C transformation.
C
C IWORK() The first N locations contain the order in
C which the columns of A were used. The next
C M locations contain the order in which the
C rows of A were used.
C
C INFO Flag to indicate status of computation on completion
C -1 Parameter error(s)
C 0 - Rank deficient, no solution
C 1 - Rank deficient, truncated solution
C 2 - Rank deficient, minimal length least squares sol
C 3 - Numerical rank 0, zero solution
C 4 - Rank .LT. NP
C 5 - Full rank
C
C***REFERENCES T. Manteuffel, An interval analysis approach to rank
C determination in linear least squares problems,
C Report SAND80-0655, Sandia Laboratories, June 1980.
C***ROUTINES CALLED R1MACH, U11US, U12US, XERMSG
C***REVISION HISTORY (YYMMDD)
C 810801 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 891009 Removed unreferenced variable. (WRB)
C 891009 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 900510 Fixed an error message. (RWC)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE ULSIA
DIMENSION A(MDA,*),B(MDB,*),RE(*),AE(*),RNORM(*),W(*)
INTEGER IWORK(*)
C
C***FIRST EXECUTABLE STATEMENT ULSIA
IF(INFO.LT.0 .OR. INFO.GT.1) GO TO 514
IT=INFO
INFO=-1
IF(NB.EQ.0 .AND. IT.EQ.1) GO TO 501
IF(M.LT.1) GO TO 502
IF(N.LT.1) GO TO 503
IF(N.LT.M) GO TO 504
IF(MDA.LT.M) GO TO 505
IF(LIW.LT.M+N) GO TO 506
IF(MODE.LT.0 .OR. MODE.GT.3) GO TO 515
IF(NB.EQ.0) GO TO 4
IF(NB.LT.0) GO TO 507
IF(MDB.LT.N) GO TO 508
IF(IT.EQ.0) GO TO 4
GO TO 400
4 IF(KEY.LT.0.OR.KEY.GT.3) GO TO 509
IF(KEY.EQ.0 .AND. LW.LT.5*M) GO TO 510
IF(KEY.EQ.1 .AND. LW.LT.4*M) GO TO 510
IF(KEY.EQ.2 .AND. LW.LT.4*M) GO TO 510
IF(KEY.EQ.3 .AND. LW.LT.3*M) GO TO 510
IF(NP.LT.0 .OR. NP.GT.M) GO TO 516
C
EPS=10.*R1MACH(4)
M1=1
M2=M1+M
M3=M2+M
M4=M3+M
M5=M4+M
C
IF(KEY.EQ.1) GO TO 100
IF(KEY.EQ.2) GO TO 200
IF(KEY.EQ.3) GO TO 300
C
IF(RE(1).LT.0.0) GO TO 511
IF(RE(1).GT.1.0) GO TO 512
IF(RE(1).LT.EPS) RE(1)=EPS
IF(AE(1).LT.0.0) GO TO 513
DO 20 I=1,M
W(M4-1+I)=RE(1)
W(M5-1+I)=AE(1)
20 CONTINUE
CALL U11US(A,MDA,M,N,W(M4),W(M5),MODE,NP,KRANK,KSURE,
1 W(M1),W(M2),W(M3),IWORK(M1),IWORK(M2))
GO TO 400
C
100 CONTINUE
IF(AE(1).LT.0.0) GO TO 513
DO 120 I=1,M
IF(RE(I).LT.0.0) GO TO 511
IF(RE(I).GT.1.0) GO TO 512
IF(RE(I).LT.EPS) RE(I)=EPS
W(M4-1+I)=AE(1)
120 CONTINUE
CALL U11US(A,MDA,M,N,RE,W(M4),MODE,NP,KRANK,KSURE,
1 W(M1),W(M2),W(M3),IWORK(M1),IWORK(M2))
GO TO 400
C
200 CONTINUE
IF(RE(1).LT.0.0) GO TO 511
IF(RE(1).GT.1.0) GO TO 512
IF(RE(1).LT.EPS) RE(1)=EPS
DO 220 I=1,M
W(M4-1+I)=RE(1)
IF(AE(I).LT.0.0) GO TO 513
220 CONTINUE
CALL U11US(A,MDA,M,N,W(M4),AE,MODE,NP,KRANK,KSURE,
1 W(M1),W(M2),W(M3),IWORK(M1),IWORK(M2))
GO TO 400
C
300 CONTINUE
DO 320 I=1,M
IF(RE(I).LT.0.0) GO TO 511
IF(RE(I).GT.1.0) GO TO 512
IF(RE(I).LT.EPS) RE(I)=EPS
IF(AE(I).LT.0.0) GO TO 513
320 CONTINUE
CALL U11US(A,MDA,M,N,RE,AE,MODE,NP,KRANK,KSURE,
1 W(M1),W(M2),W(M3),IWORK(M1),IWORK(M2))
C
C DETERMINE INFO
C
400 IF(KRANK.NE.M) GO TO 402
INFO=5
GO TO 410
402 IF(KRANK.NE.0) GO TO 404
INFO=3
GO TO 410
404 IF(KRANK.GE.NP) GO TO 406
INFO=4
RETURN
406 INFO=MODE
IF(MODE.EQ.0) RETURN
410 IF(NB.EQ.0) RETURN
C
C
C SOLUTION PHASE
C
M1=1
M2=M1+M
M3=M2+M
IF(INFO.EQ.2) GO TO 420
IF(LW.LT.M2-1) GO TO 510
CALL U12US(A,MDA,M,N,B,MDB,NB,MODE,KRANK,
1 RNORM,W(M1),W(M1),IWORK(M1),IWORK(M2))
RETURN
C
420 IF(LW.LT.M3-1) GO TO 510
CALL U12US(A,MDA,M,N,B,MDB,NB,MODE,KRANK,
1 RNORM,W(M1),W(M2),IWORK(M1),IWORK(M2))
RETURN
C
C ERROR MESSAGES
C
501 CALL XERMSG ('SLATEC', 'ULSIA',
+ 'SOLUTION ONLY (INFO=1) BUT NO RIGHT HAND SIDE (NB=0)', 1, 0)
RETURN
502 CALL XERMSG ('SLATEC', 'ULSIA', 'M.LT.1', 2, 1)
RETURN
503 CALL XERMSG ('SLATEC', 'ULSIA', 'N.LT.1', 2, 1)
RETURN
504 CALL XERMSG ('SLATEC', 'ULSIA', 'N.LT.M', 2, 1)
RETURN
505 CALL XERMSG ('SLATEC', 'ULSIA', 'MDA.LT.M', 2, 1)
RETURN
506 CALL XERMSG ('SLATEC', 'ULSIA', 'LIW.LT.M+N', 2, 1)
RETURN
507 CALL XERMSG ('SLATEC', 'ULSIA', 'NB.LT.0', 2, 1)
RETURN
508 CALL XERMSG ('SLATEC', 'ULSIA', 'MDB.LT.N', 2, 1)
RETURN
509 CALL XERMSG ('SLATEC', 'ULSIA', 'KEY OUT OF RANGE', 2, 1)
RETURN
510 CALL XERMSG ('SLATEC', 'ULSIA', 'INSUFFICIENT WORK SPACE', 8, 1)
INFO=-1
RETURN
511 CALL XERMSG ('SLATEC', 'ULSIA', 'RE(I) .LT. 0', 2, 1)
RETURN
512 CALL XERMSG ('SLATEC', 'ULSIA', 'RE(I) .GT. 1', 2, 1)
RETURN
513 CALL XERMSG ('SLATEC', 'ULSIA', 'AE(I) .LT. 0', 2, 1)
RETURN
514 CALL XERMSG ('SLATEC', 'ULSIA', 'INFO OUT OF RANGE', 2, 1)
RETURN
515 CALL XERMSG ('SLATEC', 'ULSIA', 'MODE OUT OF RANGE', 2, 1)
RETURN
516 CALL XERMSG ('SLATEC', 'ULSIA', 'NP OUT OF RANGE', 2, 1)
RETURN
END
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