hpevd(3)

📦

version 3.12.1 · 9 versions

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, in arch rolling

💖 NAME 💖

hpevd — {hp,sp}evd: eig, divide and conquer. that's the whole vibe bestie, no cap ✨

✨ SYNOPSIS ✨

🦋 Functions

subroutine chpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info) — CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💅
subroutine dspevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork, liwork, info) — DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💅
subroutine sspevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork, liwork, info) — SSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💅
subroutine zhpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info) — ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💅

💫 Detailed Description 💫

okay so this section is literally empty in the original — nothing under it, bestie, we move straight to the good part 🫶

🔥 Function Documentation 🔥

🎀 subroutine `chpevd`

subroutine chpevd (character jobz, character uplo, integer n, complex,
    dimension( * ) ap, real, dimension( * ) w, complex, dimension( ldz, * )
    z, integer ldz, complex, dimension( * ) work, integer lwork, real,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

🌟 Purpose:

CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. iconic behavior fr 🔥

🌸 Parameters

JOBZ — JOBZ is CHARACTER*1, so like, what do you actually want out of this:
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors.
UPLO — UPLO is CHARACTER*1, which triangle are we even talking about:
- = '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. (yes, zero is allowed, she's tiny but valid 💀)
AP — AP is COMPLEX array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. so yeah, your input? gone. she ate it 😭

W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. cute, sorted, organized, main character energy 👑
Z — Z is COMPLEX array, dimension (LDZ, N). If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced. (she said "don't talk to me" 🙈)
LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the required LWORK. she's a little snitch and that's a compliment 💅
LWORK — LWORK is INTEGER. The dimension of array WORK.
- If N <= 1, LWORK must be at least 1.
- If JOBZ = 'N' and N > 1, LWORK must be at least N.
- If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
- If LWORK = -1, then a workspace query is assumed; the routine only calculates the required 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. (the -1 trick is basically "hey queen, how much room do I need?" 🧚)
RWORK — RWORK is REAL array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
LRWORK — LRWORK is INTEGER. The dimension of 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 required 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.
IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
LIWORK — LIWORK is INTEGER. The dimension of array IWORK.
- If JOBZ = 'N' or 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 required 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.
INFO — INFO is INTEGER, the receipts 🧾
- = 0: successful exit (slay 🎉)
- < 0: if INFO = -i, the i-th argument had an illegal value. (you passed her something cursed, bestie)
- > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. (this one's the bad ending — she tried and she could NOT 😭)

🫶 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

⭐ Definition at line 192 of file `chpevd.f`.

🎀 subroutine `dspevd`

subroutine dspevd (character jobz, character uplo, integer n, double
    precision, dimension( * ) ap, double precision, dimension( * ) w, double
    precision, dimension( ldz, * ) z, integer ldz, double precision,
    dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

🌟 Purpose:

DSPEVD computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. same energy, double precision this time 💜

🌸 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.
AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

W — W is DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
Z — Z is DOUBLE PRECISION array, dimension (LDZ, N). If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced.
LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the required LWORK.
LWORK — 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.
- If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + N**2.
- If LWORK = -1, then a workspace query is assumed; the routine only calculates the required 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. (yup, no RWORK in this one — different routine, different baggage ✨)
IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
LIWORK —
LIWORK — okay so LIWORK is INTEGER, and it's literally the dimension of the IWORK array, bestie. If JOBZ = 'N' or N <= 1, then LIWORK has to be at least 1. If JOBZ = 'V' and N > 1, then LIWORK must be at least 3 + 5*N. And if LIWORK = -1, that's the workspace-query vibe: the routine only calculates the required sizes of the WORK and IWORK arrays, returns those values as the first entries of the WORK and IWORK arrays, and XERBLA does not issue any error message related to LWORK or LIWORK. Periodt. 💅
INFO — INFO is INTEGER, and here's the tea: = 0 means successful exit 🎉; < 0 means if INFO = -i, the i-th argument had an illegal value 🚨; and > 0 means if INFO = i, the algorithm failed to converge — specifically, i off-diagonal elements of an intermediate tridiagonal form did not converge to zero 😭. Not me being dramatic, that's just what it says.

👑 Author

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

📌 Definition

Definition at line 170 of file dspevd.f.

🦋 subroutine `sspevd`

   subroutine sspevd (character jobz, character uplo, integer n, real,
       dimension( * ) ap, real, dimension( * ) w, real, dimension( ldz, * ) z,
       integer ldz, real, dimension( * ) work, integer lwork, integer,
       dimension( * ) iwork, integer liwork, integer info)
        SSPEVD computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for OTHER matrices

SSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. Iconic. ✨

✨ Purpose

SSPEVD computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. Slay. 💖

🌸 Parameters

JOBZ — JOBZ is CHARACTER*1. = 'N': compute eigenvalues only; = 'V': compute eigenvalues and eigenvectors. Choose your fighter. 💅
UPLO — UPLO is CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. Pick a side, bestie. 🫶
N — N is INTEGER. The order of the matrix A. N >= 0. No negative nonsense. 🚫
AP — AP is REAL array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. That's the whole packed-storage moment. 💀
W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. So organized. 🌈
Z — Z is REAL array, dimension (LDZ, N). If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced. Ghosted. 👻
LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). Respect the dimension, fr fr. 📏
WORK — WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the required LWORK. Cute. ✨
LWORK — 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. If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the required 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. The math is mathing. 🧮
IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the required LIWORK. 💜
LIWORK — LIWORK is INTEGER. The dimension of the array IWORK. If JOBZ = 'N' or 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 required 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. Same energy, different array. 🎀
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 😵‍💫. No cap.

👑 Author

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

📌 Definition

Definition at line 170 of file sspevd.f.

🦋 subroutine `zhpevd`

   subroutine zhpevd (character jobz, character uplo, integer n, complex*16,
       dimension( * ) ap, double precision, dimension( * ) w, complex*16,
       dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work,
       integer lwork, double precision, dimension( * ) rwork, integer lrwork,
       integer, dimension( * ) iwork, integer liwork, integer info)
        ZHPEVD computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for OTHER matrices

ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. Complex Hermitian? We love to see it. 💖

✨ Purpose

ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. Main character algorithm energy. 👑

🌸 Parameters

JOBZ — JOBZ is CHARACTER*1. = 'N': compute eigenvalues only; = 'V': compute eigenvalues and eigenvectors. Pick your plotline. 💅
UPLO — UPLO is CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. Choose wisely, bestie. 🫶
N — N is INTEGER. The order of the matrix A. N >= 0. Keep it non-negative. ✨
AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. Same packed-storage saga, now with complex flavor. 🌸
W — W is DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. Sorted, slay. 🌈
Z — Z is COMPLEX*16 array, dimension (LDZ, N). If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced. Not referenced means not invited to the function. 🙈
LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). Rules are rules. 📏
WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the required LWORK. 💜
LWORK — LWORK is INTEGER. The dimension of array WORK. If N <= 1, LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least N. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N. If LWORK = -1, then a workspace query is assumed; the routine only calculates the required 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. The workspace query is lowkey iconic. ✨
RWORK — RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the required LRWORK. 🎀
LRWORK — LRWORK is INTEGER. The dimension of 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 required 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. Big workspace energy. 🔥
IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the required LIWORK. 🫶
LIWORK —

Okay bestie, back to the parameter list — here’s the tea on LIWORK and INFO, and they’re both giving “read me carefully” energy:

LIWORK — INTEGER, aka the dimension of array IWORK.
- If JOBZ = 'N' or 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 required 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.
INFO — INTEGER, the exit-status bestie. Here’s the breakdown:
- = 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 192 of file zhpevd.f.

👑 Author 👑 (the auto-generated encore)

Generated automatically by Doxygen for LAPACK from the source code.

Mwah! 💋 This little icon is from LAPACK Version 3.12.0, page hpevd(3) — footer date? Not shown, so she’s timeless, periodt. 🦋✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

hpevd(3)

💖 NAME 💖

✨ SYNOPSIS ✨

🦋 Functions

💫 Detailed Description 💫

🔥 Function Documentation 🔥

🎀 subroutine chpevd

🌟 Purpose:

🌸 Parameters

🫶 Author

⭐ Definition at line 192 of file chpevd.f.

🎀 subroutine dspevd

🌟 Purpose:

🌸 Parameters

👑 Author

📌 Definition

🦋 subroutine sspevd

✨ Purpose

🌸 Parameters

👑 Author

📌 Definition

🦋 subroutine zhpevd

✨ Purpose

🌸 Parameters

👑 Author 👑

👑 Author 👑 (the auto-generated encore)

🎀 subroutine `chpevd`

⭐ Definition at line 192 of file `chpevd.f`.

🎀 subroutine `dspevd`

🦋 subroutine `sspevd`

🦋 subroutine `zhpevd`