.TH "heevd" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME heevd \- {he,sy}evd: eig, divide and conquer .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcheevd\fP (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)" .br .RI "\fB CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices\fP " .ti -1c .RI "subroutine \fBdsyevd\fP (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)" .br .RI "\fB DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices\fP " .ti -1c .RI "subroutine \fBssyevd\fP (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)" .br .RI "\fB SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices\fP " .ti -1c .RI "subroutine \fBzheevd\fP (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)" .br .RI "\fB ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cheevd (character jobz, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)" .PP \fB CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A\&. If eigenvectors are desired, it uses a divide and conquer algorithm\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIW\fP .PP .nf W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The length of the array WORK\&. If N <= 1, LWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LWORK must be at least N + 1\&. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2\&. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK\&. .fi .PP .br \fILRWORK\fP .PP .nf LRWORK is INTEGER The dimension of the array RWORK\&. If N <= 1, LRWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LRWORK must be at least N\&. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2\&. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK 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 optimal LIWORK\&. .fi .PP .br \fILIWORK\fP .PP .nf LIWORK is INTEGER The dimension of the array IWORK\&. If N <= 1, LIWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LIWORK must be at least 1\&. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N\&. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK 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: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then 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)\&. .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 \fBFurther Details:\fP .RS 4 Modified description of INFO\&. Sven, 16 Feb 05\&. .RE .PP \fBContributors:\fP .RS 4 Jeff Rutter, Computer Science Division, University of California at Berkeley, USA .RE .PP .SS "subroutine dsyevd (character jobz, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)" .PP \fB DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A\&. If eigenvectors are desired, it uses a divide and conquer algorithm\&. Because of large use of BLAS of level 3, DSYEVD needs N**2 more workspace than DSYEVX\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .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 \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. If N <= 1, LWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1\&. If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2\&. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal 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 optimal LIWORK\&. .fi .PP .br \fILIWORK\fP .PP .nf LIWORK is INTEGER The dimension of the array IWORK\&. If N <= 1, LIWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LIWORK must be at least 1\&. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N\&. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal 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: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then 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)\&. .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 Jeff Rutter, Computer Science Division, University of California at Berkeley, USA .br Modified by Francoise Tisseur, University of Tennessee .br Modified description of INFO\&. Sven, 16 Feb 05\&. .br .RE .PP .SS "subroutine ssyevd (character jobz, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) w, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)" .PP \fB SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A\&. If eigenvectors are desired, it uses a divide and conquer algorithm\&. Because of large use of BLAS of level 3, SSYEVD needs N**2 more workspace than SSYEVX\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIW\fP .PP .nf W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. If N <= 1, LWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1\&. If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2\&. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal 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 optimal LIWORK\&. .fi .PP .br \fILIWORK\fP .PP .nf LIWORK is INTEGER The dimension of the array IWORK\&. If N <= 1, LIWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LIWORK must be at least 1\&. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N\&. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal 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: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then 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)\&. .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 Jeff Rutter, Computer Science Division, University of California at Berkeley, USA .br Modified by Francoise Tisseur, University of Tennessee .br Modified description of INFO\&. Sven, 16 Feb 05\&. .br .RE .PP .SS "subroutine zheevd (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 lrwork, integer, dimension( * ) iwork, integer liwork, integer info)" .PP \fB ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A\&. If eigenvectors are desired, it uses a divide and conquer algorithm\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .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 \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The length of the array WORK\&. If N <= 1, LWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LWORK must be at least N + 1\&. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2\&. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK\&. .fi .PP .br \fILRWORK\fP .PP .nf LRWORK is INTEGER The dimension of the array RWORK\&. If N <= 1, LRWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LRWORK must be at least N\&. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2\&. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK 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 optimal LIWORK\&. .fi .PP .br \fILIWORK\fP .PP .nf LIWORK is INTEGER The dimension of the array IWORK\&. If N <= 1, LIWORK must be at least 1\&. If JOBZ = 'N' and N > 1, LIWORK must be at least 1\&. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N\&. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK 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: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then 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)\&. .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 \fBFurther Details:\fP .RS 4 Modified description of INFO\&. Sven, 16 Feb 05\&. .RE .PP \fBContributors:\fP .RS 4 Jeff Rutter, Computer Science Division, University of California at Berkeley, USA .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.