Annotation of rpl/lapack/lapack/dtptri.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTPTRI( UPLO, DIAG, N, AP, 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 DIAG, UPLO
! 10: INTEGER INFO, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION AP( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DTPTRI computes the inverse of a real upper or lower triangular
! 20: * matrix A stored in packed format.
! 21: *
! 22: * Arguments
! 23: * =========
! 24: *
! 25: * UPLO (input) CHARACTER*1
! 26: * = 'U': A is upper triangular;
! 27: * = 'L': A is lower triangular.
! 28: *
! 29: * DIAG (input) CHARACTER*1
! 30: * = 'N': A is non-unit triangular;
! 31: * = 'U': A is unit triangular.
! 32: *
! 33: * N (input) INTEGER
! 34: * The order of the matrix A. N >= 0.
! 35: *
! 36: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 37: * On entry, the upper or lower triangular matrix A, stored
! 38: * columnwise in a linear array. The j-th column of A is stored
! 39: * in the array AP as follows:
! 40: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 41: * if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
! 42: * See below for further details.
! 43: * On exit, the (triangular) inverse of the original matrix, in
! 44: * the same packed storage format.
! 45: *
! 46: * INFO (output) INTEGER
! 47: * = 0: successful exit
! 48: * < 0: if INFO = -i, the i-th argument had an illegal value
! 49: * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
! 50: * matrix is singular and its inverse can not be computed.
! 51: *
! 52: * Further Details
! 53: * ===============
! 54: *
! 55: * A triangular matrix A can be transferred to packed storage using one
! 56: * of the following program segments:
! 57: *
! 58: * UPLO = 'U': UPLO = 'L':
! 59: *
! 60: * JC = 1 JC = 1
! 61: * DO 2 J = 1, N DO 2 J = 1, N
! 62: * DO 1 I = 1, J DO 1 I = J, N
! 63: * AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
! 64: * 1 CONTINUE 1 CONTINUE
! 65: * JC = JC + J JC = JC + N - J + 1
! 66: * 2 CONTINUE 2 CONTINUE
! 67: *
! 68: * =====================================================================
! 69: *
! 70: * .. Parameters ..
! 71: DOUBLE PRECISION ONE, ZERO
! 72: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 73: * ..
! 74: * .. Local Scalars ..
! 75: LOGICAL NOUNIT, UPPER
! 76: INTEGER J, JC, JCLAST, JJ
! 77: DOUBLE PRECISION AJJ
! 78: * ..
! 79: * .. External Functions ..
! 80: LOGICAL LSAME
! 81: EXTERNAL LSAME
! 82: * ..
! 83: * .. External Subroutines ..
! 84: EXTERNAL DSCAL, DTPMV, XERBLA
! 85: * ..
! 86: * .. Executable Statements ..
! 87: *
! 88: * Test the input parameters.
! 89: *
! 90: INFO = 0
! 91: UPPER = LSAME( UPLO, 'U' )
! 92: NOUNIT = LSAME( DIAG, 'N' )
! 93: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 94: INFO = -1
! 95: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
! 96: INFO = -2
! 97: ELSE IF( N.LT.0 ) THEN
! 98: INFO = -3
! 99: END IF
! 100: IF( INFO.NE.0 ) THEN
! 101: CALL XERBLA( 'DTPTRI', -INFO )
! 102: RETURN
! 103: END IF
! 104: *
! 105: * Check for singularity if non-unit.
! 106: *
! 107: IF( NOUNIT ) THEN
! 108: IF( UPPER ) THEN
! 109: JJ = 0
! 110: DO 10 INFO = 1, N
! 111: JJ = JJ + INFO
! 112: IF( AP( JJ ).EQ.ZERO )
! 113: $ RETURN
! 114: 10 CONTINUE
! 115: ELSE
! 116: JJ = 1
! 117: DO 20 INFO = 1, N
! 118: IF( AP( JJ ).EQ.ZERO )
! 119: $ RETURN
! 120: JJ = JJ + N - INFO + 1
! 121: 20 CONTINUE
! 122: END IF
! 123: INFO = 0
! 124: END IF
! 125: *
! 126: IF( UPPER ) THEN
! 127: *
! 128: * Compute inverse of upper triangular matrix.
! 129: *
! 130: JC = 1
! 131: DO 30 J = 1, N
! 132: IF( NOUNIT ) THEN
! 133: AP( JC+J-1 ) = ONE / AP( JC+J-1 )
! 134: AJJ = -AP( JC+J-1 )
! 135: ELSE
! 136: AJJ = -ONE
! 137: END IF
! 138: *
! 139: * Compute elements 1:j-1 of j-th column.
! 140: *
! 141: CALL DTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
! 142: $ AP( JC ), 1 )
! 143: CALL DSCAL( J-1, AJJ, AP( JC ), 1 )
! 144: JC = JC + J
! 145: 30 CONTINUE
! 146: *
! 147: ELSE
! 148: *
! 149: * Compute inverse of lower triangular matrix.
! 150: *
! 151: JC = N*( N+1 ) / 2
! 152: DO 40 J = N, 1, -1
! 153: IF( NOUNIT ) THEN
! 154: AP( JC ) = ONE / AP( JC )
! 155: AJJ = -AP( JC )
! 156: ELSE
! 157: AJJ = -ONE
! 158: END IF
! 159: IF( J.LT.N ) THEN
! 160: *
! 161: * Compute elements j+1:n of j-th column.
! 162: *
! 163: CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J,
! 164: $ AP( JCLAST ), AP( JC+1 ), 1 )
! 165: CALL DSCAL( N-J, AJJ, AP( JC+1 ), 1 )
! 166: END IF
! 167: JCLAST = JC
! 168: JC = JC - N + J - 2
! 169: 40 CONTINUE
! 170: END IF
! 171: *
! 172: RETURN
! 173: *
! 174: * End of DTPTRI
! 175: *
! 176: END
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