SRC/sspevd.f(3)

🎀 SRC/sspevd.f(3) 🎀

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🌸 NAME 🌸

SRC/sspevd.f

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🦋 SYNOPSIS 🦋

💫 Functions/Subroutines 💫

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

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💖 Function/Subroutine Documentation 💖

   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. ✨

🦋 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. 🧚

✨ 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 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. 🫶
• W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• 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.
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — WORK is REAL 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. 🔥
• 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. 🌟
• 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 170 of file sspevd.f.

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🧚 Author 🧚

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