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- ____HHHHQQQQRRRR2222((((3333FFFF)))) ____HHHHQQQQRRRR2222((((3333FFFF))))
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- NNNNAAAAMMMMEEEE
- HQR2, SHQR2 - EISPACK routine. This subroutine finds the eigenvalues
- and eigenvectors of a REAL UPPER Hessenberg matrix by the QR method. The
- eigenvectors of a REAL GENERAL matrix can also be found if ELMHES and
- ELTRAN or ORTHES and ORTRAN have been used to reduce this general
- matrix to Hessenberg form and to accumulate the similarity
- transformations.
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- SSSSYYYYNNNNOOOOPPPPSSSSYYYYSSSS
- ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee hhhhqqqqrrrr2222((((nnnnmmmm,,,, nnnn,,,, lllloooowwww,,,, iiiigggghhhh,,,, hhhh,,,, wwwwrrrr,,,, wwwwiiii,,,, zzzz,,,, iiiieeeerrrrrrrr))))
- iiiinnnntttteeeeggggeeeerrrr nnnnmmmm,,,, nnnn,,,, lllloooowwww,,,, iiiigggghhhh,,,, iiiieeeerrrrrrrr
- ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn hhhh((((nnnnmmmm,,,,nnnn)))),,,, wwwwrrrr((((nnnn)))),,,, wwwwiiii((((nnnn)))),,,, zzzz((((nnnnmmmm,,,,nnnn))))
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- ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee sssshhhhqqqqrrrr2222((((nnnnmmmm,,,, nnnn,,,, lllloooowwww,,,, iiiigggghhhh,,,, hhhh,,,, wwwwrrrr,,,, wwwwiiii,,,, zzzz,,,, iiiieeeerrrrrrrr))))
- iiiinnnntttteeeeggggeeeerrrr nnnnmmmm,,,, nnnn,,,, lllloooowwww,,,, iiiigggghhhh,,,, iiiieeeerrrrrrrr
- rrrreeeeaaaallll hhhh((((nnnnmmmm,,,,nnnn)))),,,, wwwwrrrr((((nnnn)))),,,, wwwwiiii((((nnnn)))),,,, zzzz((((nnnnmmmm,,,,nnnn))))
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- DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
- On INPUT
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- NNNNMMMM must be set to the row dimension of two-dimensional array parameters
- as declared in the calling program dimension statement.
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- NNNN is the order of the matrix.
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- LLLLOOOOWWWW and IGH are integers determined by the balancing subroutine BALANC.
- If BALANC has not been used, set LOW=1, IGH=N.
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- HHHH contains the upper Hessenberg matrix.
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- ZZZZ contains the transformation matrix produced by ELTRAN after the
- reduction by ELMHES, or by ORTRAN after the reduction by ORTHES, if
- performed. If the eigenvectors of the Hessenberg matrix are desired, Z
- must contain the identity matrix. On OUTPUT
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- HHHH has been destroyed.
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- WWWWRRRR and WI contain the real and imaginary parts, respectively, of the
- eigenvalues. The eigenvalues are unordered except that complex conjugate
- pairs of values appear consecutively with the eigenvalue having the
- positive imaginary part first. If an error exit is made, the eigenvalues
- should be correct for indices IERR+1,...,N.
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- ZZZZ contains the real and imaginary parts of the eigenvectors. If the I-th
- eigenvalue is real, the I-th column of Z contains its eigenvector. If
- the I-th eigenvalue is complex with positive imaginary part, the I-th and
- (I+1)-th columns of Z contain the real and imaginary parts of its
- eigenvector. The eigenvectors are unnormalized. If an error exit is
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- PPPPaaaaggggeeee 1111
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- ____HHHHQQQQRRRR2222((((3333FFFF)))) ____HHHHQQQQRRRR2222((((3333FFFF))))
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- made, none of the eigenvectors has been found.
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- IIIIEEEERRRRRRRR is set to Zero for normal return, J if the J-th
- eigenvalue has not been
- determined after a total of 30*N iterations. Calls CDIV for complex
- division. Questions and comments should be directed to B. S. Garbow,
- APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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- PPPPaaaaggggeeee 2222
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