*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