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120 lines
4.2 KiB
Fortran
120 lines
4.2 KiB
Fortran
*DECK SSPEV
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SUBROUTINE SSPEV (A, N, E, V, LDV, WORK, JOB, INFO)
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C***BEGIN PROLOGUE SSPEV
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C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors
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C of a real symmetric matrix stored in packed form.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4A1
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C***TYPE SINGLE PRECISION (SSPEV-S)
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C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK, PACKED, SYMMETRIC
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C***AUTHOR Kahaner, D. K., (NBS)
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C Moler, C. B., (U. of New Mexico)
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C Stewart, G. W., (U. of Maryland)
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C***DESCRIPTION
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C
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C Abstract
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C SSPEV computes the eigenvalues and, optionally, the eigenvectors
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C of a real symmetric matrix stored in packed form.
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C
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C Call Sequence Parameters-
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C (The values of parameters marked with * (star) will be changed
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C by SSPEV.)
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C
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C A* REAL(N*(N+1)/2)
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C real symmetric packed input matrix. Contains upper
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C triangle and diagonal of A, by column (elements
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C 11, 12, 22, 13, 23, 33, ...).
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C
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C N INTEGER
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C set by the user to
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C the order of the matrix A.
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C
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C E* REAL(N)
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C on return from SSPEV, E contains the eigenvalues of A.
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C See also INFO below.
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C
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C V* REAL(LDV,N)
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C on return from SSPEV, if the user has set JOB
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C = 0 V is not referenced.
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C = nonzero the N eigenvectors of A are stored in the
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C first N columns of V. See also INFO below.
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C
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C LDV INTEGER
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C set by the user to
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C the leading dimension of the array V if JOB is also
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C set nonzero. In that case, N must be .LE. LDV.
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C If JOB is set to zero, LDV is not referenced.
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C
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C WORK* REAL(2N)
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C temporary storage vector. Contents changed by SSPEV.
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C
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C JOB INTEGER
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C set by the user to
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C = 0 eigenvalues only to be calculated by SSPEV.
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C Neither V nor LDV are referenced.
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C = nonzero eigenvalues and vectors to be calculated.
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C In this case, A & V must be distinct arrays.
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C Also, if LDA .GT. LDV, SSPEV changes all the
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C elements of A thru column N. If LDA < LDV,
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C SSPEV changes all the elements of V through
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C column N. If LDA=LDV, only A(I,J) and V(I,
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C J) for I,J = 1,...,N are changed by SSPEV.
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C
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C INFO* INTEGER
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C on return from SSPEV, the value of INFO is
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C = 0 for normal return.
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C = K if the eigenvalue iteration fails to converge.
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C Eigenvalues and vectors 1 through K-1 are correct.
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C
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C
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C Error Messages-
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C No. 1 recoverable N is greater than LDV and JOB is nonzero
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C No. 2 recoverable N is less than one
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED IMTQL2, TQLRAT, TRBAK3, TRED3, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 800808 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C***END PROLOGUE SSPEV
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INTEGER I,INFO,J,LDV,M,N
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REAL A(*),E(*),V(LDV,*),WORK(*)
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C***FIRST EXECUTABLE STATEMENT SSPEV
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IF (N .GT. LDV) CALL XERMSG ('SLATEC', 'SSPEV', 'N .GT. LDV.',
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+ 1, 1)
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IF(N .GT. LDV) RETURN
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IF (N .LT. 1) CALL XERMSG ('SLATEC', 'SSPEV', 'N .LT. 1', 2, 1)
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IF(N .LT. 1) RETURN
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C
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C CHECK N=1 CASE
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C
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E(1) = A(1)
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INFO = 0
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IF(N .EQ. 1) RETURN
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C
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IF(JOB.NE.0) GO TO 20
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C
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C EIGENVALUES ONLY
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C
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CALL TRED3(N,1,A,E,WORK(1),WORK(N+1))
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CALL TQLRAT(N,E,WORK(N+1),INFO)
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RETURN
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C
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C EIGENVALUES AND EIGENVECTORS
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C
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20 CALL TRED3(N,1,A,E,WORK(1),WORK(1))
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DO 30 I = 1, N
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DO 25 J = 1, N
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25 V(I,J) = 0.
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30 V(I,I) = 1.
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CALL IMTQL2(LDV,N,E,WORK,V,INFO)
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M = N
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IF(INFO .NE. 0) M = INFO - 1
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CALL TRBAK3(LDV,N,1,A,M,V)
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RETURN
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END
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