--- name: "heev" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/heev" --- # heev(3) {he,sy}ev: eig, QR iteration ## NAME heev - {he,sy}ev: eig, QR iteration ## SYNOPSIS ### Functions subroutine **cheev** (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)\ **CHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices** subroutine **dsyev** (jobz, uplo, n, a, lda, w, work, lwork, info)\ **DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices** subroutine **ssyev** (jobz, uplo, n, a, lda, w, work, lwork, info)\ **SSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices** subroutine **zheev** (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)\ **ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices** ## Detailed Description ## Function Documentation ### subroutine cheev (character jobz, character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, real, dimension( \* ) w, complex, dimension( \* ) work, integer lwork, real, dimension( \* ) rwork, integer info) **CHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices** **Purpose:** ``` !> !> CHEEV computes all eigenvalues and, optionally, eigenvectors of a !> complex Hermitian matrix A. !> ``` **Parameters** *JOBZ* ``` !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !> ``` *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX array, dimension (LDA, N) !> On entry, the Hermitian matrix A. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A. !> On exit, if JOBZ = 'V', then if INFO = 0, A contains the !> orthonormal eigenvectors of the matrix A. !> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') !> or the upper triangle (if UPLO='U') of A, including the !> diagonal, is destroyed. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *W* ``` !> W is REAL array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> ``` *LWORK* ``` !> LWORK is INTEGER !> The length of the array WORK. LWORK >= max(1,2*N-1). !> For optimal efficiency, LWORK >= (NB+1)*N, !> where NB is the blocksize for CHETRD returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> ``` *RWORK* ``` !> RWORK is REAL array, dimension (max(1, 3*N-2)) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the algorithm failed to converge; i !> off-diagonal elements of an intermediate tridiagonal !> form did not converge to zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **138** of file **cheev.f**. ### subroutine dsyev (character jobz, character uplo, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) w, double precision, dimension( \* ) work, integer lwork, integer info) **DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices** **Purpose:** ``` !> !> DSYEV computes all eigenvalues and, optionally, eigenvectors of a !> real symmetric matrix A. !> ``` **Parameters** *JOBZ* ``` !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !> ``` *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is DOUBLE PRECISION array, dimension (LDA, N) !> On entry, the symmetric matrix A. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A. !> On exit, if JOBZ = 'V', then if INFO = 0, A contains the !> orthonormal eigenvectors of the matrix A. !> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') !> or the upper triangle (if UPLO='U') of A, including the !> diagonal, is destroyed. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *W* ``` !> W is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> ``` *WORK* ``` !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> ``` *LWORK* ``` !> LWORK is INTEGER !> The length of the array WORK. LWORK >= max(1,3*N-1). !> For optimal efficiency, LWORK >= (NB+2)*N, !> where NB is the blocksize for DSYTRD returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the algorithm failed to converge; i !> off-diagonal elements of an intermediate tridiagonal !> form did not converge to zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **131** of file **dsyev.f**. ### subroutine ssyev (character jobz, character uplo, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) w, real, dimension( \* ) work, integer lwork, integer info) **SSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices** **Purpose:** ``` !> !> SSYEV computes all eigenvalues and, optionally, eigenvectors of a !> real symmetric matrix A. !> ``` **Parameters** *JOBZ* ``` !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !> ``` *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is REAL array, dimension (LDA, N) !> On entry, the symmetric matrix A. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A. !> On exit, if JOBZ = 'V', then if INFO = 0, A contains the !> orthonormal eigenvectors of the matrix A. !> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') !> or the upper triangle (if UPLO='U') of A, including the !> diagonal, is destroyed. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *W* ``` !> W is REAL array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> ``` *WORK* ``` !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> ``` *LWORK* ``` !> LWORK is INTEGER !> The length of the array WORK. LWORK >= max(1,3*N-1). !> For optimal efficiency, LWORK >= (NB+2)*N, !> where NB is the blocksize for SSYTRD returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the algorithm failed to converge; i !> off-diagonal elements of an intermediate tridiagonal !> form did not converge to zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **131** of file **ssyev.f**. ### subroutine zheev (character jobz, character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) w, complex\*16, dimension( \* ) work, integer lwork, double precision, dimension( \* ) rwork, integer info) **ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices** **Purpose:** ``` !> !> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a !> complex Hermitian matrix A. !> ``` **Parameters** *JOBZ* ``` !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !> ``` *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX*16 array, dimension (LDA, N) !> On entry, the Hermitian matrix A. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A. !> On exit, if JOBZ = 'V', then if INFO = 0, A contains the !> orthonormal eigenvectors of the matrix A. !> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') !> or the upper triangle (if UPLO='U') of A, including the !> diagonal, is destroyed. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *W* ``` !> W is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> ``` *LWORK* ``` !> LWORK is INTEGER !> The length of the array WORK. LWORK >= max(1,2*N-1). !> For optimal efficiency, LWORK >= (NB+1)*N, !> where NB is the blocksize for ZHETRD returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> ``` *RWORK* ``` !> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the algorithm failed to converge; i !> off-diagonal elements of an intermediate tridiagonal !> form did not converge to zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **138** of file **zheev.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.