Annotation of rpl/lapack/lapack/zpbtf2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, 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, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: COMPLEX*16 AB( LDAB, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZPBTF2 computes the Cholesky factorization of a complex Hermitian
! 20: * positive definite band matrix A.
! 21: *
! 22: * The factorization has the form
! 23: * A = U' * U , if UPLO = 'U', or
! 24: * A = L * L', if UPLO = 'L',
! 25: * where U is an upper triangular matrix, U' is the conjugate transpose
! 26: * of U, and L is lower triangular.
! 27: *
! 28: * This is the unblocked version of the algorithm, calling Level 2 BLAS.
! 29: *
! 30: * Arguments
! 31: * =========
! 32: *
! 33: * UPLO (input) CHARACTER*1
! 34: * Specifies whether the upper or lower triangular part of the
! 35: * Hermitian matrix A is stored:
! 36: * = 'U': Upper triangular
! 37: * = 'L': Lower triangular
! 38: *
! 39: * N (input) INTEGER
! 40: * The order of the matrix A. N >= 0.
! 41: *
! 42: * KD (input) INTEGER
! 43: * The number of super-diagonals of the matrix A if UPLO = 'U',
! 44: * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
! 45: *
! 46: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
! 47: * On entry, the upper or lower triangle of the Hermitian band
! 48: * matrix A, stored in the first KD+1 rows of the array. The
! 49: * j-th column of A is stored in the j-th column of the array AB
! 50: * as follows:
! 51: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 52: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 53: *
! 54: * On exit, if INFO = 0, the triangular factor U or L from the
! 55: * Cholesky factorization A = U'*U or A = L*L' of the band
! 56: * matrix A, in the same storage format as A.
! 57: *
! 58: * LDAB (input) INTEGER
! 59: * The leading dimension of the array AB. LDAB >= KD+1.
! 60: *
! 61: * INFO (output) INTEGER
! 62: * = 0: successful exit
! 63: * < 0: if INFO = -k, the k-th argument had an illegal value
! 64: * > 0: if INFO = k, the leading minor of order k is not
! 65: * positive definite, and the factorization could not be
! 66: * completed.
! 67: *
! 68: * Further Details
! 69: * ===============
! 70: *
! 71: * The band storage scheme is illustrated by the following example, when
! 72: * N = 6, KD = 2, and UPLO = 'U':
! 73: *
! 74: * On entry: On exit:
! 75: *
! 76: * * * a13 a24 a35 a46 * * u13 u24 u35 u46
! 77: * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
! 78: * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
! 79: *
! 80: * Similarly, if UPLO = 'L' the format of A is as follows:
! 81: *
! 82: * On entry: On exit:
! 83: *
! 84: * a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
! 85: * a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
! 86: * a31 a42 a53 a64 * * l31 l42 l53 l64 * *
! 87: *
! 88: * Array elements marked * are not used by the routine.
! 89: *
! 90: * =====================================================================
! 91: *
! 92: * .. Parameters ..
! 93: DOUBLE PRECISION ONE, ZERO
! 94: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 95: * ..
! 96: * .. Local Scalars ..
! 97: LOGICAL UPPER
! 98: INTEGER J, KLD, KN
! 99: DOUBLE PRECISION AJJ
! 100: * ..
! 101: * .. External Functions ..
! 102: LOGICAL LSAME
! 103: EXTERNAL LSAME
! 104: * ..
! 105: * .. External Subroutines ..
! 106: EXTERNAL XERBLA, ZDSCAL, ZHER, ZLACGV
! 107: * ..
! 108: * .. Intrinsic Functions ..
! 109: INTRINSIC DBLE, MAX, MIN, SQRT
! 110: * ..
! 111: * .. Executable Statements ..
! 112: *
! 113: * Test the input parameters.
! 114: *
! 115: INFO = 0
! 116: UPPER = LSAME( UPLO, 'U' )
! 117: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 118: INFO = -1
! 119: ELSE IF( N.LT.0 ) THEN
! 120: INFO = -2
! 121: ELSE IF( KD.LT.0 ) THEN
! 122: INFO = -3
! 123: ELSE IF( LDAB.LT.KD+1 ) THEN
! 124: INFO = -5
! 125: END IF
! 126: IF( INFO.NE.0 ) THEN
! 127: CALL XERBLA( 'ZPBTF2', -INFO )
! 128: RETURN
! 129: END IF
! 130: *
! 131: * Quick return if possible
! 132: *
! 133: IF( N.EQ.0 )
! 134: $ RETURN
! 135: *
! 136: KLD = MAX( 1, LDAB-1 )
! 137: *
! 138: IF( UPPER ) THEN
! 139: *
! 140: * Compute the Cholesky factorization A = U'*U.
! 141: *
! 142: DO 10 J = 1, N
! 143: *
! 144: * Compute U(J,J) and test for non-positive-definiteness.
! 145: *
! 146: AJJ = DBLE( AB( KD+1, J ) )
! 147: IF( AJJ.LE.ZERO ) THEN
! 148: AB( KD+1, J ) = AJJ
! 149: GO TO 30
! 150: END IF
! 151: AJJ = SQRT( AJJ )
! 152: AB( KD+1, J ) = AJJ
! 153: *
! 154: * Compute elements J+1:J+KN of row J and update the
! 155: * trailing submatrix within the band.
! 156: *
! 157: KN = MIN( KD, N-J )
! 158: IF( KN.GT.0 ) THEN
! 159: CALL ZDSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD )
! 160: CALL ZLACGV( KN, AB( KD, J+1 ), KLD )
! 161: CALL ZHER( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD,
! 162: $ AB( KD+1, J+1 ), KLD )
! 163: CALL ZLACGV( KN, AB( KD, J+1 ), KLD )
! 164: END IF
! 165: 10 CONTINUE
! 166: ELSE
! 167: *
! 168: * Compute the Cholesky factorization A = L*L'.
! 169: *
! 170: DO 20 J = 1, N
! 171: *
! 172: * Compute L(J,J) and test for non-positive-definiteness.
! 173: *
! 174: AJJ = DBLE( AB( 1, J ) )
! 175: IF( AJJ.LE.ZERO ) THEN
! 176: AB( 1, J ) = AJJ
! 177: GO TO 30
! 178: END IF
! 179: AJJ = SQRT( AJJ )
! 180: AB( 1, J ) = AJJ
! 181: *
! 182: * Compute elements J+1:J+KN of column J and update the
! 183: * trailing submatrix within the band.
! 184: *
! 185: KN = MIN( KD, N-J )
! 186: IF( KN.GT.0 ) THEN
! 187: CALL ZDSCAL( KN, ONE / AJJ, AB( 2, J ), 1 )
! 188: CALL ZHER( 'Lower', KN, -ONE, AB( 2, J ), 1,
! 189: $ AB( 1, J+1 ), KLD )
! 190: END IF
! 191: 20 CONTINUE
! 192: END IF
! 193: RETURN
! 194: *
! 195: 30 CONTINUE
! 196: INFO = J
! 197: RETURN
! 198: *
! 199: * End of ZPBTF2
! 200: *
! 201: END
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