Annotation of rpl/lapack/lapack/dlaqz1.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DLAQZ1
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAQZ1 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqz1.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqz1.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqz1.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAQZ1( A, LDA, B, LDB, SR1, SR2, SI, BETA1, BETA2,
! 22: * $ V )
! 23: * IMPLICIT NONE
! 24: *
! 25: * Arguments
! 26: * INTEGER, INTENT( IN ) :: LDA, LDB
! 27: * DOUBLE PRECISION, INTENT( IN ) :: A( LDA, * ), B( LDB, * ), SR1,
! 28: * $ SR2, SI, BETA1, BETA2
! 29: * DOUBLE PRECISION, INTENT( OUT ) :: V( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> Given a 3-by-3 matrix pencil (A,B), DLAQZ1 sets v to a
! 39: *> scalar multiple of the first column of the product
! 40: *>
! 41: *> (*) K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1).
! 42: *>
! 43: *> It is assumed that either
! 44: *>
! 45: *> 1) sr1 = sr2
! 46: *> or
! 47: *> 2) si = 0.
! 48: *>
! 49: *> This is useful for starting double implicit shift bulges
! 50: *> in the QZ algorithm.
! 51: *> \endverbatim
! 52: *
! 53: *
! 54: * Arguments:
! 55: * ==========
! 56: *
! 57: *> \param[in] A
! 58: *> \verbatim
! 59: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 60: *> The 3-by-3 matrix A in (*).
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] LDA
! 64: *> \verbatim
! 65: *> LDA is INTEGER
! 66: *> The leading dimension of A as declared in
! 67: *> the calling procedure.
! 68: *> \endverbatim
! 69: *
! 70: *> \param[in] B
! 71: *> \verbatim
! 72: *> B is DOUBLE PRECISION array, dimension (LDB,N)
! 73: *> The 3-by-3 matrix B in (*).
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] LDB
! 77: *> \verbatim
! 78: *> LDB is INTEGER
! 79: *> The leading dimension of B as declared in
! 80: *> the calling procedure.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] SR1
! 84: *> \verbatim
! 85: *> SR1 is DOUBLE PRECISION
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] SR2
! 89: *> \verbatim
! 90: *> SR2 is DOUBLE PRECISION
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[in] SI
! 94: *> \verbatim
! 95: *> SI is DOUBLE PRECISION
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[in] BETA1
! 99: *> \verbatim
! 100: *> BETA1 is DOUBLE PRECISION
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] BETA2
! 104: *> \verbatim
! 105: *> BETA2 is DOUBLE PRECISION
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] V
! 109: *> \verbatim
! 110: *> V is DOUBLE PRECISION array, dimension (N)
! 111: *> A scalar multiple of the first column of the
! 112: *> matrix K in (*).
! 113: *> \endverbatim
! 114: *
! 115: * Authors:
! 116: * ========
! 117: *
! 118: *> \author Thijs Steel, KU Leuven
! 119: *
! 120: *> \date May 2020
! 121: *
! 122: *> \ingroup doubleGEcomputational
! 123: *>
! 124: * =====================================================================
! 125: SUBROUTINE DLAQZ1( A, LDA, B, LDB, SR1, SR2, SI, BETA1, BETA2,
! 126: $ V )
! 127: IMPLICIT NONE
! 128: *
! 129: * Arguments
! 130: INTEGER, INTENT( IN ) :: LDA, LDB
! 131: DOUBLE PRECISION, INTENT( IN ) :: A( LDA, * ), B( LDB, * ), SR1,
! 132: $ SR2, SI, BETA1, BETA2
! 133: DOUBLE PRECISION, INTENT( OUT ) :: V( * )
! 134: *
! 135: * Parameters
! 136: DOUBLE PRECISION :: ZERO, ONE, HALF
! 137: PARAMETER( ZERO = 0.0D0, ONE = 1.0D0, HALF = 0.5D0 )
! 138: *
! 139: * Local scalars
! 140: DOUBLE PRECISION :: W( 2 ), SAFMIN, SAFMAX, SCALE1, SCALE2
! 141: *
! 142: * External Functions
! 143: DOUBLE PRECISION, EXTERNAL :: DLAMCH
! 144: LOGICAL, EXTERNAL :: DISNAN
! 145: *
! 146: SAFMIN = DLAMCH( 'SAFE MINIMUM' )
! 147: SAFMAX = ONE/SAFMIN
! 148: *
! 149: * Calculate first shifted vector
! 150: *
! 151: W( 1 ) = BETA1*A( 1, 1 )-SR1*B( 1, 1 )
! 152: W( 2 ) = BETA1*A( 2, 1 )-SR1*B( 2, 1 )
! 153: SCALE1 = SQRT( ABS( W( 1 ) ) ) * SQRT( ABS( W( 2 ) ) )
! 154: IF( SCALE1 .GE. SAFMIN .AND. SCALE1 .LE. SAFMAX ) THEN
! 155: W( 1 ) = W( 1 )/SCALE1
! 156: W( 2 ) = W( 2 )/SCALE1
! 157: END IF
! 158: *
! 159: * Solve linear system
! 160: *
! 161: W( 2 ) = W( 2 )/B( 2, 2 )
! 162: W( 1 ) = ( W( 1 )-B( 1, 2 )*W( 2 ) )/B( 1, 1 )
! 163: SCALE2 = SQRT( ABS( W( 1 ) ) ) * SQRT( ABS( W( 2 ) ) )
! 164: IF( SCALE2 .GE. SAFMIN .AND. SCALE2 .LE. SAFMAX ) THEN
! 165: W( 1 ) = W( 1 )/SCALE2
! 166: W( 2 ) = W( 2 )/SCALE2
! 167: END IF
! 168: *
! 169: * Apply second shift
! 170: *
! 171: V( 1 ) = BETA2*( A( 1, 1 )*W( 1 )+A( 1, 2 )*W( 2 ) )-SR2*( B( 1,
! 172: $ 1 )*W( 1 )+B( 1, 2 )*W( 2 ) )
! 173: V( 2 ) = BETA2*( A( 2, 1 )*W( 1 )+A( 2, 2 )*W( 2 ) )-SR2*( B( 2,
! 174: $ 1 )*W( 1 )+B( 2, 2 )*W( 2 ) )
! 175: V( 3 ) = BETA2*( A( 3, 1 )*W( 1 )+A( 3, 2 )*W( 2 ) )-SR2*( B( 3,
! 176: $ 1 )*W( 1 )+B( 3, 2 )*W( 2 ) )
! 177: *
! 178: * Account for imaginary part
! 179: *
! 180: V( 1 ) = V( 1 )+SI*SI*B( 1, 1 )/SCALE1/SCALE2
! 181: *
! 182: * Check for overflow
! 183: *
! 184: IF( ABS( V( 1 ) ).GT.SAFMAX .OR. ABS( V( 2 ) ) .GT. SAFMAX .OR.
! 185: $ ABS( V( 3 ) ).GT.SAFMAX .OR. DISNAN( V( 1 ) ) .OR.
! 186: $ DISNAN( V( 2 ) ) .OR. DISNAN( V( 3 ) ) ) THEN
! 187: V( 1 ) = ZERO
! 188: V( 2 ) = ZERO
! 189: V( 3 ) = ZERO
! 190: END IF
! 191: *
! 192: * End of DLAQZ1
! 193: *
! 194: END SUBROUTINE
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