.TH "sspgvx.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME sspgvx.f \- .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBsspgvx\fP (ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO)" .br .RI "\fI\fBSSPGST\fP \fP" .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine sspgvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )BP, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)" .PP \fBSSPGST\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SSPGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric, stored in packed storage, and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fIITYPE\fP .PP .nf ITYPE is INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x .fi .PP .br \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. .fi .PP .br \fIRANGE\fP .PP .nf RANGE is CHARACTER*1 = 'A': all eigenvalues will be found. = 'V': all eigenvalues in the half-open interval (VL,VU] will be found. = 'I': the IL-th through IU-th eigenvalues will be found. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A and B are stored; = 'L': Lower triangle of A and B are stored. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix pencil (A,B). N >= 0. .fi .PP .br \fIAP\fP .PP .nf AP is REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed. .fi .PP .br \fIBP\fP .PP .nf BP is REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B. .fi .PP .br \fIVL\fP .PP .nf VL is REAL .fi .PP .br \fIVU\fP .PP .nf VU is REAL If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. .fi .PP .br \fIIL\fP .PP .nf IL is INTEGER .fi .PP .br \fIIU\fP .PP .nf IU is INTEGER If RANGE='I', the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. .fi .PP .br \fIABSTOL\fP .PP .nf ABSTOL is REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). .fi .PP .br \fIM\fP .PP .nf M is INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. .fi .PP .br \fIW\fP .PP .nf W is REAL array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order. .fi .PP .br \fIZ\fP .PP .nf Z is REAL array, dimension (LDZ, max(1,M)) If JOBZ = 'N', then Z is not referenced. If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. .fi .PP .br \fILDZ\fP .PP .nf LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (8*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (5*N) .fi .PP .br \fIIFAIL\fP .PP .nf IFAIL is INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: SPPTRF or SSPEVX returned an error code: <= N: if INFO = i, SSPEVX failed to converge; i eigenvectors failed to converge. Their indices are stored in array IFAIL. > N: if INFO = N + i, for 1 <= i <= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 November 2011 .RE .PP \fBContributors: \fP .RS 4 Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA .RE .PP .PP Definition at line 262 of file sspgvx\&.f\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.