.TH "SRC/dspgvd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/dspgvd.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBdspgvd\fP (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, iwork, liwork, info)" .br .RI "\fBDSPGVD\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine dspgvd (integer itype, character jobz, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) bp, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)" .PP \fBDSPGVD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DSPGVD computes all the eigenvalues, and optionally, the 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 format, and B is also !> positive definite\&. !> If eigenvectors are desired, it uses a divide and conquer algorithm\&. !> !> .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 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangles of A and B are stored; !> = 'L': Lower triangles of A and B are stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrices A and B\&. N >= 0\&. !> .fi .PP .br \fIAP\fP .PP .nf !> AP is DOUBLE PRECISION 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 DOUBLE PRECISION 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 \fIW\fP .PP .nf !> W is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is DOUBLE PRECISION array, dimension (LDZ, N) !> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of !> eigenvectors\&. 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 JOBZ = 'N', then Z is not referenced\&. !> .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 DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the required LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> If N <= 1, LWORK >= 1\&. !> If JOBZ = 'N' and N > 1, LWORK >= 2*N\&. !> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the required sizes of the WORK and IWORK !> arrays, returns these values as the first entries of the WORK !> and IWORK arrays, and no error message related to LWORK or !> LIWORK is issued by XERBLA\&. !> .fi .PP .br \fIIWORK\fP .PP .nf !> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) !> On exit, if INFO = 0, IWORK(1) returns the required LIWORK\&. !> .fi .PP .br \fILIWORK\fP .PP .nf !> LIWORK is INTEGER !> The dimension of the array IWORK\&. !> If JOBZ = 'N' or N <= 1, LIWORK >= 1\&. !> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N\&. !> !> If LIWORK = -1, then a workspace query is assumed; the !> routine only calculates the required sizes of the WORK and !> IWORK arrays, returns these values as the first entries of !> the WORK and IWORK arrays, and no error message related to !> LWORK or LIWORK is issued by XERBLA\&. !> .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: DPPTRF or DSPEVD returned an error code: !> <= N: if INFO = i, DSPEVD failed to converge; !> i off-diagonal elements of an intermediate !> tridiagonal form did not converge to zero; !> > N: if INFO = N + i, for 1 <= i <= N, then the leading !> principal minor of order i of B is not positive\&. !> 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 \fBContributors:\fP .RS 4 Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA .RE .PP .PP Definition at line \fB202\fP of file \fBdspgvd\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.