177 lines
5.0 KiB
FortranFixed
177 lines
5.0 KiB
FortranFixed
SUBROUTINE CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER IUPLO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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REAL D( * )
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COMPLEX B( LDB, * ), E( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CPTTS2 solves a tridiagonal system of the form
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* A * X = B
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* using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF.
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* D is a diagonal matrix specified in the vector D, U (or L) is a unit
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* bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
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* the vector E, and X and B are N by NRHS matrices.
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*
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* Arguments
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* =========
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*
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* IUPLO (input) INTEGER
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* Specifies the form of the factorization and whether the
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* vector E is the superdiagonal of the upper bidiagonal factor
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* U or the subdiagonal of the lower bidiagonal factor L.
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* = 1: A = U'*D*U, E is the superdiagonal of U
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* = 0: A = L*D*L', E is the subdiagonal of L
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*
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* N (input) INTEGER
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* The order of the tridiagonal matrix A. N >= 0.
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*
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* NRHS (input) INTEGER
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* The number of right hand sides, i.e., the number of columns
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* of the matrix B. NRHS >= 0.
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*
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* D (input) REAL array, dimension (N)
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* The n diagonal elements of the diagonal matrix D from the
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* factorization A = U'*D*U or A = L*D*L'.
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*
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* E (input) COMPLEX array, dimension (N-1)
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* If IUPLO = 1, the (n-1) superdiagonal elements of the unit
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* bidiagonal factor U from the factorization A = U'*D*U.
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* If IUPLO = 0, the (n-1) subdiagonal elements of the unit
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* bidiagonal factor L from the factorization A = L*D*L'.
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*
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* B (input/output) REAL array, dimension (LDB,NRHS)
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* On entry, the right hand side vectors B for the system of
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* linear equations.
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* On exit, the solution vectors, X.
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*
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* LDB (input) INTEGER
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* The leading dimension of the array B. LDB >= max(1,N).
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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INTEGER I, J
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* ..
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* .. External Subroutines ..
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EXTERNAL CSSCAL
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CONJG
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.LE.1 ) THEN
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IF( N.EQ.1 )
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$ CALL CSSCAL( NRHS, 1. / D( 1 ), B, LDB )
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RETURN
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END IF
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*
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IF( IUPLO.EQ.1 ) THEN
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*
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* Solve A * X = B using the factorization A = U'*D*U,
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* overwriting each right hand side vector with its solution.
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*
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IF( NRHS.LE.2 ) THEN
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J = 1
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5 CONTINUE
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*
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* Solve U' * x = b.
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*
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DO 10 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
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10 CONTINUE
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*
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* Solve D * U * x = b.
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*
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DO 20 I = 1, N
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B( I, J ) = B( I, J ) / D( I )
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20 CONTINUE
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DO 30 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) - B( I+1, J )*E( I )
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30 CONTINUE
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IF( J.LT.NRHS ) THEN
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J = J + 1
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GO TO 5
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END IF
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ELSE
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DO 60 J = 1, NRHS
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*
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* Solve U' * x = b.
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*
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DO 40 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
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40 CONTINUE
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*
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* Solve D * U * x = b.
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*
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B( N, J ) = B( N, J ) / D( N )
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DO 50 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
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50 CONTINUE
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60 CONTINUE
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END IF
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ELSE
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*
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* Solve A * X = B using the factorization A = L*D*L',
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* overwriting each right hand side vector with its solution.
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*
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IF( NRHS.LE.2 ) THEN
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J = 1
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65 CONTINUE
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*
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* Solve L * x = b.
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*
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DO 70 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
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70 CONTINUE
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*
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* Solve D * L' * x = b.
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*
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DO 80 I = 1, N
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B( I, J ) = B( I, J ) / D( I )
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80 CONTINUE
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DO 90 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) - B( I+1, J )*CONJG( E( I ) )
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90 CONTINUE
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IF( J.LT.NRHS ) THEN
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J = J + 1
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GO TO 65
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END IF
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ELSE
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DO 120 J = 1, NRHS
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*
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* Solve L * x = b.
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*
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DO 100 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
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100 CONTINUE
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*
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* Solve D * L' * x = b.
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*
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B( N, J ) = B( N, J ) / D( N )
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DO 110 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) / D( I ) -
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$ B( I+1, J )*CONJG( E( I ) )
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110 CONTINUE
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120 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of CPTTS2
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*
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END
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