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