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- ____QQQQZZZZIIIITTTT((((3333FFFF)))) ____QQQQZZZZIIIITTTT((((3333FFFF))))
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- NNNNAAAAMMMMEEEE
- QZIT, SQZIT - EISPACK routine. This subroutine is the second step of
- the QZ algorithm for solving generalized matrix eigenvalue problems,
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- SSSSYYYYNNNNOOOOPPPPSSSSYYYYSSSS
- ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee qqqqzzzziiiitttt((((nnnnmmmm,,,, nnnn,,,, aaaa,,,, bbbb,,,, eeeeppppssss1111,,,, mmmmaaaattttzzzz,,,, zzzz,,,, iiiieeeerrrrrrrr))))
- iiiinnnntttteeeeggggeeeerrrr nnnnmmmm,,,, nnnn,,,, iiiieeeerrrrrrrr
- ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn eeeeppppssss1111
- ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn aaaa((((nnnnmmmm,,,,nnnn)))),,,, bbbb((((nnnnmmmm,,,,nnnn)))),,,, zzzz((((nnnnmmmm,,,,nnnn))))
- llllooooggggiiiiccccaaaallll mmmmaaaattttzzzz
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- ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssqqqqzzzziiiitttt((((nnnnmmmm,,,, nnnn,,,, aaaa,,,, bbbb,,,, eeeeppppssss1111,,,, mmmmaaaattttzzzz,,,, zzzz,,,, iiiieeeerrrrrrrr))))
- iiiinnnntttteeeeggggeeeerrrr nnnnmmmm,,,, nnnn,,,, iiiieeeerrrrrrrr
- rrrreeeeaaaallll eeeeppppssss1111
- rrrreeeeaaaallll aaaa((((nnnnmmmm,,,,nnnn)))),,,, bbbb((((nnnnmmmm,,,,nnnn)))),,,, zzzz((((nnnnmmmm,,,,nnnn))))
- llllooooggggiiiiccccaaaallll mmmmaaaattttzzzz
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- DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
- This subroutine accepts a pair of REAL matrices, one of them in upper
- Hessenberg form and the other in upper triangular form. It reduces the
- Hessenberg matrix to quasi-triangular form using orthogonal
- transformations while maintaining the triangular form of the other
- matrix. It is usually preceded by QZHES and followed by QZVAL and,
- possibly, QZVEC.
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- 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 matrices.
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- AAAA contains a real upper Hessenberg matrix.
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- BBBB contains a real upper triangular matrix.
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- EEEEPPPPSSSS1111 is a tolerance used to determine negligible elements. EPS1 = 0.0 (or
- negative) may be input, in which case an element will be neglected only
- if it is less than roundoff error times the norm of its matrix. If the
- input EPS1 is positive, then an element will be considered negligible if
- it is less than EPS1 times the norm of its matrix. A positive value of
- EPS1 may result in faster execution, but less accurate results.
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- MMMMAAAATTTTZZZZ should be set to .TRUE. If the right hand transformations are to be
- accumulated for later use in computing eigenvectors, and to .FALSE.
- otherwise.
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- ZZZZ contains, if MATZ has been set to .TRUE., the transformation matrix
- produced in the reduction by QZHES, if performed, or else the identity
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- PPPPaaaaggggeeee 1111
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- ____QQQQZZZZIIIITTTT((((3333FFFF)))) ____QQQQZZZZIIIITTTT((((3333FFFF))))
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- matrix. If MATZ has been set to .FALSE., Z is not referenced. On Output
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- AAAA has been reduced to quasi-triangular form. The elements below the
- first subdiagonal are still zero and no two consecutive subdiagonal
- elements are nonzero.
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- BBBB is still in upper triangular form, although its elements have been
- altered. The location B(N,1) is used to store EPS1 times the norm of B
- for later use by QZVAL and QZVEC.
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- ZZZZ contains the product of the right hand transformations (for both steps)
- if MATZ has been set to .TRUE.
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- IIIIEEEERRRRRRRR is set to ZERO for normal return, J if neither
- A(J,J-1) nor A(J-1,J-2) has become
- zero after a total of 30*N iterations. 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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