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# Expert Driver Routines for Standard Eigenvalue Problems

• CALL LA_SYEVX / LA_HEEVX ( A, W, JOBZ=jobz, UPLO=uplo, VL=vl, VU=vu, &
IL=il, IU=iu, M=m, IFAIL=ifail, ABSTOL=abstol, INFO=info )
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric/complex Hermitian matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
• CALL LA_SPEVX / LA_HPEVX ( AP, W, UPLO=uplo, Z=z, VL=vl, VU=vu, &
IL=il, IU=iu, M=m, IFAIL=ifail, ABSTOL=abstol, INFO=info )
Computes all the eigenvalues and, optionally, eigenvectors of a real symmetric / complex Hermitian matrix A in packed storage. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
• CALL LA_SBEVX / LA_HBEVX ( AB, W, UPLO=uplo, Z=z, VL=vl, VU=vu, &
IL=il, IU=iu, M=m, IFAIL=ifail, Q=q, ABSTOL=abstol, INFO=info )
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric / complex Hermitian band matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
• CALL LA_STEVX ( D, E, W, Z=z, VL=vl, VU=vu, IL=il, IU=iu, M=m, &
IFAIL=ifail, ABSTOL=abstol, INFO=info )
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
• CALL LA_GEESX (A, <w>, VS=vs, SELECT=select, SDIM=sdim, RCONDE=rconde, &
RCONDV=rcondv, INFO=info )
Computes for a non-symmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. Optionally, it also orders the eigenvalues on the diagonal of the real Schur form so that selected eigenvalues are at the top left; computes a reciprocal condition number for the average of the selected eigenvalues, and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues. <w> is either WR, WI or W.
• CALL LA_GEEVX ( A, <w>, VL=vl, VR=vr, BALANC=balanc, ILO=ilo, IHI=ihi, &
SCALE=scale, ABNRM=abnrm, RCONDE=rconde, &
RCONDV=rcondv, INFO=info )
Computes for a non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. Optionally also, it computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors (ILO, IHI, SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues (RCONDE), and reciprocal condition numbers for the right eigenvectors (RCONDV). <w> is either WR, WI or W.

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Minka Marinova 2000-09-07