Annotation of rpl/lapack/lapack/dpbtrs.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER UPLO
! 10: INTEGER INFO, KD, LDAB, LDB, N, NRHS
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DPBTRS solves a system of linear equations A*X = B with a symmetric
! 20: * positive definite band matrix A using the Cholesky factorization
! 21: * A = U**T*U or A = L*L**T computed by DPBTRF.
! 22: *
! 23: * Arguments
! 24: * =========
! 25: *
! 26: * UPLO (input) CHARACTER*1
! 27: * = 'U': Upper triangular factor stored in AB;
! 28: * = 'L': Lower triangular factor stored in AB.
! 29: *
! 30: * N (input) INTEGER
! 31: * The order of the matrix A. N >= 0.
! 32: *
! 33: * KD (input) INTEGER
! 34: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 35: * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 36: *
! 37: * NRHS (input) INTEGER
! 38: * The number of right hand sides, i.e., the number of columns
! 39: * of the matrix B. NRHS >= 0.
! 40: *
! 41: * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
! 42: * The triangular factor U or L from the Cholesky factorization
! 43: * A = U**T*U or A = L*L**T of the band matrix A, stored in the
! 44: * first KD+1 rows of the array. The j-th column of U or L is
! 45: * stored in the j-th column of the array AB as follows:
! 46: * if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
! 47: * if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
! 48: *
! 49: * LDAB (input) INTEGER
! 50: * The leading dimension of the array AB. LDAB >= KD+1.
! 51: *
! 52: * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
! 53: * On entry, the right hand side matrix B.
! 54: * On exit, the solution matrix X.
! 55: *
! 56: * LDB (input) INTEGER
! 57: * The leading dimension of the array B. LDB >= max(1,N).
! 58: *
! 59: * INFO (output) INTEGER
! 60: * = 0: successful exit
! 61: * < 0: if INFO = -i, the i-th argument had an illegal value
! 62: *
! 63: * =====================================================================
! 64: *
! 65: * .. Local Scalars ..
! 66: LOGICAL UPPER
! 67: INTEGER J
! 68: * ..
! 69: * .. External Functions ..
! 70: LOGICAL LSAME
! 71: EXTERNAL LSAME
! 72: * ..
! 73: * .. External Subroutines ..
! 74: EXTERNAL DTBSV, XERBLA
! 75: * ..
! 76: * .. Intrinsic Functions ..
! 77: INTRINSIC MAX
! 78: * ..
! 79: * .. Executable Statements ..
! 80: *
! 81: * Test the input parameters.
! 82: *
! 83: INFO = 0
! 84: UPPER = LSAME( UPLO, 'U' )
! 85: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 86: INFO = -1
! 87: ELSE IF( N.LT.0 ) THEN
! 88: INFO = -2
! 89: ELSE IF( KD.LT.0 ) THEN
! 90: INFO = -3
! 91: ELSE IF( NRHS.LT.0 ) THEN
! 92: INFO = -4
! 93: ELSE IF( LDAB.LT.KD+1 ) THEN
! 94: INFO = -6
! 95: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 96: INFO = -8
! 97: END IF
! 98: IF( INFO.NE.0 ) THEN
! 99: CALL XERBLA( 'DPBTRS', -INFO )
! 100: RETURN
! 101: END IF
! 102: *
! 103: * Quick return if possible
! 104: *
! 105: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 106: $ RETURN
! 107: *
! 108: IF( UPPER ) THEN
! 109: *
! 110: * Solve A*X = B where A = U'*U.
! 111: *
! 112: DO 10 J = 1, NRHS
! 113: *
! 114: * Solve U'*X = B, overwriting B with X.
! 115: *
! 116: CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
! 117: $ LDAB, B( 1, J ), 1 )
! 118: *
! 119: * Solve U*X = B, overwriting B with X.
! 120: *
! 121: CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
! 122: $ LDAB, B( 1, J ), 1 )
! 123: 10 CONTINUE
! 124: ELSE
! 125: *
! 126: * Solve A*X = B where A = L*L'.
! 127: *
! 128: DO 20 J = 1, NRHS
! 129: *
! 130: * Solve L*X = B, overwriting B with X.
! 131: *
! 132: CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
! 133: $ LDAB, B( 1, J ), 1 )
! 134: *
! 135: * Solve L'*X = B, overwriting B with X.
! 136: *
! 137: CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
! 138: $ LDAB, B( 1, J ), 1 )
! 139: 20 CONTINUE
! 140: END IF
! 141: *
! 142: RETURN
! 143: *
! 144: * End of DPBTRS
! 145: *
! 146: END
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