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quantum-espresso/flib/lapack_mkl.f

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"configure" bug for pc cluster and intel 6 Make.rules_cpp => Rules.cpp, Make.rules_nocpp => Rules.nocpp lapack_mkl.f added, __MKL removed Make.{fujutsu,sxcross}, compile error in restart.f90 (Guido) electrons, punch_band, plot_bands: use the same format for reading and writing eigenvalues git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@119 c92efa57-630b-4861-b058-cf58834340f0
2003-03-10 22:49:21 +08:00
SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
*
* -- LAPACK AUXILIARY ROUTINE (VERSION 1.1) --
* UNIV. OF TENNESSEE, UNIV. OF CALIFORNIA BERKELEY, NAG LTD.,
* COURANT INSTITUTE, ARGONNE NATIONAL LAB, AND RICE UNIVERSITY
* OCTOBER 31, 1992
*
* .. SCALAR ARGUMENTS ..
DOUBLE PRECISION A, B, C, RT1, RT2
* ..
*
* PURPOSE
* =======
*
* DLAE2 COMPUTES THE EIGENVALUES OF A 2-BY-2 SYMMETRIC MATRIX
* [ A B ]
* [ B C ].
* ON RETURN, RT1 IS THE EIGENVALUE OF LARGER ABSOLUTE VALUE, AND RT2
* IS THE EIGENVALUE OF SMALLER ABSOLUTE VALUE.
*
* ARGUMENTS
* =========
*
* A (INPUT) DOUBLE PRECISION
* THE (1,1) ENTRY OF THE 2-BY-2 MATRIX.
*
* B (INPUT) DOUBLE PRECISION
* THE (1,2) AND (2,1) ENTRIES OF THE 2-BY-2 MATRIX.
*
* C (INPUT) DOUBLE PRECISION
* THE (2,2) ENTRY OF THE 2-BY-2 MATRIX.
*
* RT1 (OUTPUT) DOUBLE PRECISION
* THE EIGENVALUE OF LARGER ABSOLUTE VALUE.
*
* RT2 (OUTPUT) DOUBLE PRECISION
* THE EIGENVALUE OF SMALLER ABSOLUTE VALUE.
*
* FURTHER DETAILS
* ===============
*
* RT1 IS ACCURATE TO A FEW ULPS BARRING OVER/UNDERFLOW.
*
* RT2 MAY BE INACCURATE IF THERE IS MASSIVE CANCELLATION IN THE
* DETERMINANT A*C-B*B; HIGHER PRECISION OR CORRECTLY ROUNDED OR
* CORRECTLY TRUNCATED ARITHMETIC WOULD BE NEEDED TO COMPUTE RT2
* ACCURATELY IN ALL CASES.
*
* OVERFLOW IS POSSIBLE ONLY IF RT1 IS WITHIN A FACTOR OF 5 OF OVERFLOW.
* UNDERFLOW IS HARMLESS IF THE INPUT DATA IS 0 OR EXCEEDS
* UNDERFLOW_THRESHOLD / MACHEPS.
*
* =====================================================================
*
* .. PARAMETERS ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
DOUBLE PRECISION TWO
PARAMETER ( TWO = 2.0D0 )
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
DOUBLE PRECISION HALF
PARAMETER ( HALF = 0.5D0 )
* ..
* .. LOCAL SCALARS ..
DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB
* ..
* .. INTRINSIC FUNCTIONS ..
INTRINSIC ABS, SQRT
* ..
* .. EXECUTABLE STATEMENTS ..
*
* COMPUTE THE EIGENVALUES
*
SM = A + C
DF = A - C
ADF = ABS( DF )
TB = B + B
AB = ABS( TB )
IF( ABS( A ).GT.ABS( C ) ) THEN
ACMX = A
ACMN = C
ELSE
ACMX = C
ACMN = A
END IF
IF( ADF.GT.AB ) THEN
RT = ADF*SQRT( ONE+( AB / ADF )**2 )
ELSE IF( ADF.LT.AB ) THEN
RT = AB*SQRT( ONE+( ADF / AB )**2 )
ELSE
*
* INCLUDES CASE AB=ADF=0
*
RT = AB*SQRT( TWO )
END IF
IF( SM.LT.ZERO ) THEN
RT1 = HALF*( SM-RT )
*
* ORDER OF EXECUTION IMPORTANT.
* TO GET FULLY ACCURATE SMALLER EIGENVALUE,
* NEXT LINE NEEDS TO BE EXECUTED IN HIGHER PRECISION.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE IF( SM.GT.ZERO ) THEN
RT1 = HALF*( SM+RT )
*
* ORDER OF EXECUTION IMPORTANT.
* TO GET FULLY ACCURATE SMALLER EIGENVALUE,
* NEXT LINE NEEDS TO BE EXECUTED IN HIGHER PRECISION.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE
*
* INCLUDES CASE RT1 = RT2 = 0
*
RT1 = HALF*RT
RT2 = -HALF*RT
END IF
RETURN
*
* END OF DLAE2
*
END
SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
* -- LAPACK AUXILIARY ROUTINE (VERSION 1.1) --
* UNIV. OF TENNESSEE, UNIV. OF CALIFORNIA BERKELEY, NAG LTD.,
* COURANT INSTITUTE, ARGONNE NATIONAL LAB, AND RICE UNIVERSITY
* OCTOBER 31, 1992
*
* .. SCALAR ARGUMENTS ..
DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1
* ..
*
* PURPOSE
* =======
*
* DLAEV2 COMPUTES THE EIGENDECOMPOSITION OF A 2-BY-2 SYMMETRIC MATRIX
* [ A B ]
* [ B C ].
* ON RETURN, RT1 IS THE EIGENVALUE OF LARGER ABSOLUTE VALUE, RT2 IS THE
* EIGENVALUE OF SMALLER ABSOLUTE VALUE, AND (CS1,SN1) IS THE UNIT RIGHT
* EIGENVECTOR FOR RT1, GIVING THE DECOMPOSITION
*
* [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ]
* [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
*
* ARGUMENTS
* =========
*
* A (INPUT) DOUBLE PRECISION
* THE (1,1) ENTRY OF THE 2-BY-2 MATRIX.
*
* B (INPUT) DOUBLE PRECISION
* THE (1,2) ENTRY AND THE CONJUGATE OF THE (2,1) ENTRY OF THE
* 2-BY-2 MATRIX.
*
* C (INPUT) DOUBLE PRECISION
* THE (2,2) ENTRY OF THE 2-BY-2 MATRIX.
*
* RT1 (OUTPUT) DOUBLE PRECISION
* THE EIGENVALUE OF LARGER ABSOLUTE VALUE.
*
* RT2 (OUTPUT) DOUBLE PRECISION
* THE EIGENVALUE OF SMALLER ABSOLUTE VALUE.
*
* CS1 (OUTPUT) DOUBLE PRECISION
* SN1 (OUTPUT) DOUBLE PRECISION
* THE VECTOR (CS1, SN1) IS A UNIT RIGHT EIGENVECTOR FOR RT1.
*
* FURTHER DETAILS
* ===============
*
* RT1 IS ACCURATE TO A FEW ULPS BARRING OVER/UNDERFLOW.
*
* RT2 MAY BE INACCURATE IF THERE IS MASSIVE CANCELLATION IN THE
* DETERMINANT A*C-B*B; HIGHER PRECISION OR CORRECTLY ROUNDED OR
* CORRECTLY TRUNCATED ARITHMETIC WOULD BE NEEDED TO COMPUTE RT2
* ACCURATELY IN ALL CASES.
*
* CS1 AND SN1 ARE ACCURATE TO A FEW ULPS BARRING OVER/UNDERFLOW.
*
* OVERFLOW IS POSSIBLE ONLY IF RT1 IS WITHIN A FACTOR OF 5 OF OVERFLOW.
* UNDERFLOW IS HARMLESS IF THE INPUT DATA IS 0 OR EXCEEDS
* UNDERFLOW_THRESHOLD / MACHEPS.
*
* =====================================================================
*
* .. PARAMETERS ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
DOUBLE PRECISION TWO
PARAMETER ( TWO = 2.0D0 )
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
DOUBLE PRECISION HALF
PARAMETER ( HALF = 0.5D0 )
* ..
* .. LOCAL SCALARS ..
INTEGER SGN1, SGN2
DOUBLE PRECISION AB, ACMN, ACMX, ACS, ADF, CS, CT, DF, RT, SM,
$ TB, TN
* ..
* .. INTRINSIC FUNCTIONS ..
INTRINSIC ABS, SQRT
* ..
* .. EXECUTABLE STATEMENTS ..
*
* COMPUTE THE EIGENVALUES
*
SM = A + C
DF = A - C
ADF = ABS( DF )
TB = B + B
AB = ABS( TB )
IF( ABS( A ).GT.ABS( C ) ) THEN
ACMX = A
ACMN = C
ELSE
ACMX = C
ACMN = A
END IF
IF( ADF.GT.AB ) THEN
RT = ADF*SQRT( ONE+( AB / ADF )**2 )
ELSE IF( ADF.LT.AB ) THEN
RT = AB*SQRT( ONE+( ADF / AB )**2 )
ELSE
*
* INCLUDES CASE AB=ADF=0
*
RT = AB*SQRT( TWO )
END IF
IF( SM.LT.ZERO ) THEN
RT1 = HALF*( SM-RT )
SGN1 = -1
*
* ORDER OF EXECUTION IMPORTANT.
* TO GET FULLY ACCURATE SMALLER EIGENVALUE,
* NEXT LINE NEEDS TO BE EXECUTED IN HIGHER PRECISION.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE IF( SM.GT.ZERO ) THEN
RT1 = HALF*( SM+RT )
SGN1 = 1
*
* ORDER OF EXECUTION IMPORTANT.
* TO GET FULLY ACCURATE SMALLER EIGENVALUE,
* NEXT LINE NEEDS TO BE EXECUTED IN HIGHER PRECISION.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE
*
* INCLUDES CASE RT1 = RT2 = 0
*
RT1 = HALF*RT
RT2 = -HALF*RT
SGN1 = 1
END IF
*
* COMPUTE THE EIGENVECTOR
*
IF( DF.GE.ZERO ) THEN
CS = DF + RT
SGN2 = 1
ELSE
CS = DF - RT
SGN2 = -1
END IF
ACS = ABS( CS )
IF( ACS.GT.AB ) THEN
CT = -TB / CS
SN1 = ONE / SQRT( ONE+CT*CT )
CS1 = CT*SN1
ELSE
IF( AB.EQ.ZERO ) THEN
CS1 = ONE
SN1 = ZERO
ELSE
TN = -CS / TB
CS1 = ONE / SQRT( ONE+TN*TN )
SN1 = TN*CS1
END IF
END IF
IF( SGN1.EQ.SGN2 ) THEN
TN = CS1
CS1 = -SN1
SN1 = TN
END IF
RETURN
*
* END OF DLAEV2
*
END
INTEGER FUNCTION ILAENV ()
ILAENV=64
RETURN
END