# laed0 - Man Page

laed0: D&C step: top level solver

## Synopsis

### Functions

subroutine **claed0** (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info)**CLAED0** used by CSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

subroutine **dlaed0** (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info)**DLAED0** used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

subroutine **slaed0** (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info)**SLAED0** used by SSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

subroutine **zlaed0** (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info)**ZLAED0** used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

## Detailed Description

## Function Documentation

### subroutine claed0 (integer qsiz, integer n, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldq, * ) q, integer ldq, complex, dimension( ldqs, * ) qstore, integer ldqs, real, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)

**CLAED0** used by CSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

**Purpose:**

Using the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix.

**Parameters***QSIZ*QSIZ is INTEGER The dimension of the unitary matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.

*N*N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.

*D*D is REAL array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, the eigenvalues in ascending order.

*E*E is REAL array, dimension (N-1) On entry, the off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

*Q*Q is COMPLEX array, dimension (LDQ,N) On entry, Q must contain an QSIZ x N matrix whose columns unitarily orthonormal. It is a part of the unitary matrix that reduces the full dense Hermitian matrix to a (reducible) symmetric tridiagonal matrix.

*LDQ*LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).

*IWORK*IWORK is INTEGER array, the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N ( lg( N ) = smallest integer k such that 2^k >= N )

*RWORK*RWORK is REAL array, dimension (1 + 3*N + 2*N*lg N + 3*N**2) ( lg( N ) = smallest integer k such that 2^k >= N )

*QSTORE*QSTORE is COMPLEX array, dimension (LDQS, N) Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

*LDQS*LDQS is INTEGER The leading dimension of the array QSTORE. LDQS >= max(1,N).

*INFO*INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **143** of file **claed0.f**.

### subroutine dlaed0 (integer icompq, integer qsiz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( ldqs, * ) qstore, integer ldqs, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

**DLAED0** used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

**Purpose:**

DLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

**Parameters***ICOMPQ*ICOMPQ is INTEGER = 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 2: Compute eigenvalues and eigenvectors of tridiagonal matrix.

*QSIZ*QSIZ is INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.

*N*N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.

*D*D is DOUBLE PRECISION array, dimension (N) On entry, the main diagonal of the tridiagonal matrix. On exit, its eigenvalues.

*E*E is DOUBLE PRECISION array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

*Q*Q is DOUBLE PRECISION array, dimension (LDQ, N) On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ = 0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a subset of the columns of the orthogonal matrix used to reduce the full matrix to tridiagonal form corresponding to the subset of the full matrix which is being decomposed at this time. If ICOMPQ = 2 On entry, Q will be the identity matrix. On exit, Q contains the eigenvectors of the tridiagonal matrix.

*LDQ*LDQ is INTEGER The leading dimension of the array Q. If eigenvectors are desired, then LDQ >= max(1,N). In any case, LDQ >= 1.

*QSTORE*QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) Referenced only when ICOMPQ = 1. Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

*LDQS*LDQS is INTEGER The leading dimension of the array QSTORE. If ICOMPQ = 1, then LDQS >= max(1,N). In any case, LDQS >= 1.

*WORK*WORK is DOUBLE PRECISION array, If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must be at least 4*N + N**2.

*IWORK*IWORK is INTEGER array, If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 + 5*N.

*INFO*INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line **170** of file **dlaed0.f**.

### subroutine slaed0 (integer icompq, integer qsiz, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldq, * ) q, integer ldq, real, dimension( ldqs, * ) qstore, integer ldqs, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

**SLAED0** used by SSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

**Purpose:**

SLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

**Parameters***ICOMPQ*ICOMPQ is INTEGER = 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 2: Compute eigenvalues and eigenvectors of tridiagonal matrix.

*QSIZ*QSIZ is INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.

*N*N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.

*D*D is REAL array, dimension (N) On entry, the main diagonal of the tridiagonal matrix. On exit, its eigenvalues.

*E*E is REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

*Q*Q is REAL array, dimension (LDQ, N) On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ = 0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a subset of the columns of the orthogonal matrix used to reduce the full matrix to tridiagonal form corresponding to the subset of the full matrix which is being decomposed at this time. If ICOMPQ = 2 On entry, Q will be the identity matrix. On exit, Q contains the eigenvectors of the tridiagonal matrix.

*LDQ*LDQ is INTEGER The leading dimension of the array Q. If eigenvectors are desired, then LDQ >= max(1,N). In any case, LDQ >= 1.

*QSTORE*QSTORE is REAL array, dimension (LDQS, N) Referenced only when ICOMPQ = 1. Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

*LDQS*LDQS is INTEGER The leading dimension of the array QSTORE. If ICOMPQ = 1, then LDQS >= max(1,N). In any case, LDQS >= 1.

*WORK*WORK is REAL array, If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must be at least 4*N + N**2.

*IWORK*IWORK is INTEGER array, If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 + 5*N.

*INFO*INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line **170** of file **slaed0.f**.

### subroutine zlaed0 (integer qsiz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( ldqs, * ) qstore, integer ldqs, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)

**ZLAED0** used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

**Purpose:**

Using the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix.

**Parameters***QSIZ*QSIZ is INTEGER The dimension of the unitary matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.

*N*N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.

*D*D is DOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, the eigenvalues in ascending order.

*E*E is DOUBLE PRECISION array, dimension (N-1) On entry, the off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

*Q*Q is COMPLEX*16 array, dimension (LDQ,N) On entry, Q must contain an QSIZ x N matrix whose columns unitarily orthonormal. It is a part of the unitary matrix that reduces the full dense Hermitian matrix to a (reducible) symmetric tridiagonal matrix.

*LDQ*LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).

*IWORK*IWORK is INTEGER array, the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N ( lg( N ) = smallest integer k such that 2^k >= N )

*RWORK*RWORK is DOUBLE PRECISION array, dimension (1 + 3*N + 2*N*lg N + 3*N**2) ( lg( N ) = smallest integer k such that 2^k >= N )

*QSTORE*QSTORE is COMPLEX*16 array, dimension (LDQS, N) Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

*LDQS*LDQS is INTEGER The leading dimension of the array QSTORE. LDQS >= max(1,N).

*INFO***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **143** of file **zlaed0.f**.

## Author

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