Annotation of rpl/lapack/lapack/ztbtrs.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
! 2: $ LDB, INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER DIAG, TRANS, UPLO
! 11: INTEGER INFO, KD, LDAB, LDB, N, NRHS
! 12: * ..
! 13: * .. Array Arguments ..
! 14: COMPLEX*16 AB( LDAB, * ), B( LDB, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZTBTRS solves a triangular system of the form
! 21: *
! 22: * A * X = B, A**T * X = B, or A**H * X = B,
! 23: *
! 24: * where A is a triangular band matrix of order N, and B is an
! 25: * N-by-NRHS matrix. A check is made to verify that A is nonsingular.
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * UPLO (input) CHARACTER*1
! 31: * = 'U': A is upper triangular;
! 32: * = 'L': A is lower triangular.
! 33: *
! 34: * TRANS (input) CHARACTER*1
! 35: * Specifies the form of the system of equations:
! 36: * = 'N': A * X = B (No transpose)
! 37: * = 'T': A**T * X = B (Transpose)
! 38: * = 'C': A**H * X = B (Conjugate transpose)
! 39: *
! 40: * DIAG (input) CHARACTER*1
! 41: * = 'N': A is non-unit triangular;
! 42: * = 'U': A is unit triangular.
! 43: *
! 44: * N (input) INTEGER
! 45: * The order of the matrix A. N >= 0.
! 46: *
! 47: * KD (input) INTEGER
! 48: * The number of superdiagonals or subdiagonals of the
! 49: * triangular band matrix A. KD >= 0.
! 50: *
! 51: * NRHS (input) INTEGER
! 52: * The number of right hand sides, i.e., the number of columns
! 53: * of the matrix B. NRHS >= 0.
! 54: *
! 55: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
! 56: * The upper or lower triangular band matrix A, stored in the
! 57: * first kd+1 rows of AB. The j-th column of A is stored
! 58: * in the j-th column of the array AB as follows:
! 59: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 60: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 61: * If DIAG = 'U', the diagonal elements of A are not referenced
! 62: * and are assumed to be 1.
! 63: *
! 64: * LDAB (input) INTEGER
! 65: * The leading dimension of the array AB. LDAB >= KD+1.
! 66: *
! 67: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 68: * On entry, the right hand side matrix B.
! 69: * On exit, if INFO = 0, the solution matrix X.
! 70: *
! 71: * LDB (input) INTEGER
! 72: * The leading dimension of the array B. LDB >= max(1,N).
! 73: *
! 74: * INFO (output) INTEGER
! 75: * = 0: successful exit
! 76: * < 0: if INFO = -i, the i-th argument had an illegal value
! 77: * > 0: if INFO = i, the i-th diagonal element of A is zero,
! 78: * indicating that the matrix is singular and the
! 79: * solutions X have not been computed.
! 80: *
! 81: * =====================================================================
! 82: *
! 83: * .. Parameters ..
! 84: COMPLEX*16 ZERO
! 85: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
! 86: * ..
! 87: * .. Local Scalars ..
! 88: LOGICAL NOUNIT, UPPER
! 89: INTEGER J
! 90: * ..
! 91: * .. External Functions ..
! 92: LOGICAL LSAME
! 93: EXTERNAL LSAME
! 94: * ..
! 95: * .. External Subroutines ..
! 96: EXTERNAL XERBLA, ZTBSV
! 97: * ..
! 98: * .. Intrinsic Functions ..
! 99: INTRINSIC MAX
! 100: * ..
! 101: * .. Executable Statements ..
! 102: *
! 103: * Test the input parameters.
! 104: *
! 105: INFO = 0
! 106: NOUNIT = LSAME( DIAG, 'N' )
! 107: UPPER = LSAME( UPLO, 'U' )
! 108: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 109: INFO = -1
! 110: ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
! 111: $ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
! 112: INFO = -2
! 113: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
! 114: INFO = -3
! 115: ELSE IF( N.LT.0 ) THEN
! 116: INFO = -4
! 117: ELSE IF( KD.LT.0 ) THEN
! 118: INFO = -5
! 119: ELSE IF( NRHS.LT.0 ) THEN
! 120: INFO = -6
! 121: ELSE IF( LDAB.LT.KD+1 ) THEN
! 122: INFO = -8
! 123: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 124: INFO = -10
! 125: END IF
! 126: IF( INFO.NE.0 ) THEN
! 127: CALL XERBLA( 'ZTBTRS', -INFO )
! 128: RETURN
! 129: END IF
! 130: *
! 131: * Quick return if possible
! 132: *
! 133: IF( N.EQ.0 )
! 134: $ RETURN
! 135: *
! 136: * Check for singularity.
! 137: *
! 138: IF( NOUNIT ) THEN
! 139: IF( UPPER ) THEN
! 140: DO 10 INFO = 1, N
! 141: IF( AB( KD+1, INFO ).EQ.ZERO )
! 142: $ RETURN
! 143: 10 CONTINUE
! 144: ELSE
! 145: DO 20 INFO = 1, N
! 146: IF( AB( 1, INFO ).EQ.ZERO )
! 147: $ RETURN
! 148: 20 CONTINUE
! 149: END IF
! 150: END IF
! 151: INFO = 0
! 152: *
! 153: * Solve A * X = B, A**T * X = B, or A**H * X = B.
! 154: *
! 155: DO 30 J = 1, NRHS
! 156: CALL ZTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 )
! 157: 30 CONTINUE
! 158: *
! 159: RETURN
! 160: *
! 161: * End of ZTBTRS
! 162: *
! 163: END
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