.TH "steqr" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME steqr \- steqr: eig, QR iteration .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcsteqr\fP (compz, n, d, e, z, ldz, work, info)" .br .RI "\fBCSTEQR\fP " .ti -1c .RI "subroutine \fBdsteqr\fP (compz, n, d, e, z, ldz, work, info)" .br .RI "\fBDSTEQR\fP " .ti -1c .RI "subroutine \fBssteqr\fP (compz, n, d, e, z, ldz, work, info)" .br .RI "\fBSSTEQR\fP " .ti -1c .RI "subroutine \fBzsteqr\fP (compz, n, d, e, z, ldz, work, info)" .br .RI "\fBZSTEQR\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine csteqr (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)" .PP \fBCSTEQR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CSTEQR computes all eigenvalues and, optionally, eigenvectors of a !> symmetric tridiagonal matrix using the implicit QL or QR method\&. !> The eigenvectors of a full or band complex Hermitian matrix can also !> be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this !> matrix to tridiagonal form\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fICOMPZ\fP .PP .nf !> COMPZ is CHARACTER*1 !> = 'N': Compute eigenvalues only\&. !> = 'V': Compute eigenvalues and eigenvectors of the original !> Hermitian matrix\&. On entry, Z must contain the !> unitary matrix used to reduce the original matrix !> to tridiagonal form\&. !> = 'I': Compute eigenvalues and eigenvectors of the !> tridiagonal matrix\&. Z is initialized to the identity !> matrix\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix\&. N >= 0\&. !> .fi .PP .br \fID\fP .PP .nf !> D is REAL array, dimension (N) !> On entry, the diagonal elements of the tridiagonal matrix\&. !> On exit, if INFO = 0, the eigenvalues in ascending order\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is REAL array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix\&. !> On exit, E has been destroyed\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is COMPLEX array, dimension (LDZ, N) !> On entry, if COMPZ = 'V', then Z contains the unitary !> matrix used in the reduction to tridiagonal form\&. !> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the !> orthonormal eigenvectors of the original Hermitian matrix, !> and if COMPZ = 'I', Z contains the orthonormal eigenvectors !> of the symmetric tridiagonal matrix\&. !> If COMPZ = '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 !> eigenvectors are desired, then LDZ >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (max(1,2*N-2)) !> If COMPZ = 'N', then WORK 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: the algorithm has failed to find all the eigenvalues in !> a total of 30*N iterations; if INFO = i, then i !> elements of E have not converged to zero; on exit, D !> and E contain the elements of a symmetric tridiagonal !> matrix which is unitarily similar to the original !> matrix\&. !> .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 .PP Definition at line \fB131\fP of file \fBcsteqr\&.f\fP\&. .SS "subroutine dsteqr (character compz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)" .PP \fBDSTEQR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DSTEQR computes all eigenvalues and, optionally, eigenvectors of a !> symmetric tridiagonal matrix using the implicit QL or QR method\&. !> The eigenvectors of a full or band symmetric matrix can also be found !> if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to !> tridiagonal form\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fICOMPZ\fP .PP .nf !> COMPZ is CHARACTER*1 !> = 'N': Compute eigenvalues only\&. !> = 'V': Compute eigenvalues and eigenvectors of the original !> symmetric matrix\&. On entry, Z must contain the !> orthogonal matrix used to reduce the original matrix !> to tridiagonal form\&. !> = 'I': Compute eigenvalues and eigenvectors of the !> tridiagonal matrix\&. Z is initialized to the identity !> matrix\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix\&. N >= 0\&. !> .fi .PP .br \fID\fP .PP .nf !> D is DOUBLE PRECISION array, dimension (N) !> On entry, the diagonal elements of the tridiagonal matrix\&. !> On exit, if INFO = 0, the eigenvalues in ascending order\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is DOUBLE PRECISION array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix\&. !> On exit, E has been destroyed\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is DOUBLE PRECISION array, dimension (LDZ, N) !> On entry, if COMPZ = 'V', then Z contains the orthogonal !> matrix used in the reduction to tridiagonal form\&. !> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the !> orthonormal eigenvectors of the original symmetric matrix, !> and if COMPZ = 'I', Z contains the orthonormal eigenvectors !> of the symmetric tridiagonal matrix\&. !> If COMPZ = '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 !> eigenvectors are desired, then LDZ >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) !> If COMPZ = 'N', then WORK 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: the algorithm has failed to find all the eigenvalues in !> a total of 30*N iterations; if INFO = i, then i !> elements of E have not converged to zero; on exit, D !> and E contain the elements of a symmetric tridiagonal !> matrix which is orthogonally similar to the original !> matrix\&. !> .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 .PP Definition at line \fB130\fP of file \fBdsteqr\&.f\fP\&. .SS "subroutine ssteqr (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)" .PP \fBSSTEQR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SSTEQR computes all eigenvalues and, optionally, eigenvectors of a !> symmetric tridiagonal matrix using the implicit QL or QR method\&. !> The eigenvectors of a full or band symmetric matrix can also be found !> if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to !> tridiagonal form\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fICOMPZ\fP .PP .nf !> COMPZ is CHARACTER*1 !> = 'N': Compute eigenvalues only\&. !> = 'V': Compute eigenvalues and eigenvectors of the original !> symmetric matrix\&. On entry, Z must contain the !> orthogonal matrix used to reduce the original matrix !> to tridiagonal form\&. !> = 'I': Compute eigenvalues and eigenvectors of the !> tridiagonal matrix\&. Z is initialized to the identity !> matrix\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix\&. N >= 0\&. !> .fi .PP .br \fID\fP .PP .nf !> D is REAL array, dimension (N) !> On entry, the diagonal elements of the tridiagonal matrix\&. !> On exit, if INFO = 0, the eigenvalues in ascending order\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is REAL array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix\&. !> On exit, E has been destroyed\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is REAL array, dimension (LDZ, N) !> On entry, if COMPZ = 'V', then Z contains the orthogonal !> matrix used in the reduction to tridiagonal form\&. !> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the !> orthonormal eigenvectors of the original symmetric matrix, !> and if COMPZ = 'I', Z contains the orthonormal eigenvectors !> of the symmetric tridiagonal matrix\&. !> If COMPZ = '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 !> eigenvectors are desired, then LDZ >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (max(1,2*N-2)) !> If COMPZ = 'N', then WORK 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: the algorithm has failed to find all the eigenvalues in !> a total of 30*N iterations; if INFO = i, then i !> elements of E have not converged to zero; on exit, D !> and E contain the elements of a symmetric tridiagonal !> matrix which is orthogonally similar to the original !> matrix\&. !> .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 .PP Definition at line \fB130\fP of file \fBssteqr\&.f\fP\&. .SS "subroutine zsteqr (character compz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)" .PP \fBZSTEQR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a !> symmetric tridiagonal matrix using the implicit QL or QR method\&. !> The eigenvectors of a full or band complex Hermitian matrix can also !> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this !> matrix to tridiagonal form\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fICOMPZ\fP .PP .nf !> COMPZ is CHARACTER*1 !> = 'N': Compute eigenvalues only\&. !> = 'V': Compute eigenvalues and eigenvectors of the original !> Hermitian matrix\&. On entry, Z must contain the !> unitary matrix used to reduce the original matrix !> to tridiagonal form\&. !> = 'I': Compute eigenvalues and eigenvectors of the !> tridiagonal matrix\&. Z is initialized to the identity !> matrix\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix\&. N >= 0\&. !> .fi .PP .br \fID\fP .PP .nf !> D is DOUBLE PRECISION array, dimension (N) !> On entry, the diagonal elements of the tridiagonal matrix\&. !> On exit, if INFO = 0, the eigenvalues in ascending order\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is DOUBLE PRECISION array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix\&. !> On exit, E has been destroyed\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is COMPLEX*16 array, dimension (LDZ, N) !> On entry, if COMPZ = 'V', then Z contains the unitary !> matrix used in the reduction to tridiagonal form\&. !> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the !> orthonormal eigenvectors of the original Hermitian matrix, !> and if COMPZ = 'I', Z contains the orthonormal eigenvectors !> of the symmetric tridiagonal matrix\&. !> If COMPZ = '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 !> eigenvectors are desired, then LDZ >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) !> If COMPZ = 'N', then WORK 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: the algorithm has failed to find all the eigenvalues in !> a total of 30*N iterations; if INFO = i, then i !> elements of E have not converged to zero; on exit, D !> and E contain the elements of a symmetric tridiagonal !> matrix which is unitarily similar to the original !> matrix\&. !> .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 .PP Definition at line \fB131\fP of file \fBzsteqr\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.