.TH "steqr" 3 "Wed Feb 7 2024 11:30:40" "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

.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

.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

.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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.