Annotation of rpl/lapack/lapack/dlantr.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
! 2: $ WORK )
! 3: *
! 4: * -- LAPACK auxiliary 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, NORM, UPLO
! 11: INTEGER LDA, M, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION A( LDA, * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DLANTR returns the value of the one norm, or the Frobenius norm, or
! 21: * the infinity norm, or the element of largest absolute value of a
! 22: * trapezoidal or triangular matrix A.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * DLANTR returns the value
! 28: *
! 29: * DLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 30: * (
! 31: * ( norm1(A), NORM = '1', 'O' or 'o'
! 32: * (
! 33: * ( normI(A), NORM = 'I' or 'i'
! 34: * (
! 35: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 36: *
! 37: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 38: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 39: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 40: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 41: *
! 42: * Arguments
! 43: * =========
! 44: *
! 45: * NORM (input) CHARACTER*1
! 46: * Specifies the value to be returned in DLANTR as described
! 47: * above.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * Specifies whether the matrix A is upper or lower trapezoidal.
! 51: * = 'U': Upper trapezoidal
! 52: * = 'L': Lower trapezoidal
! 53: * Note that A is triangular instead of trapezoidal if M = N.
! 54: *
! 55: * DIAG (input) CHARACTER*1
! 56: * Specifies whether or not the matrix A has unit diagonal.
! 57: * = 'N': Non-unit diagonal
! 58: * = 'U': Unit diagonal
! 59: *
! 60: * M (input) INTEGER
! 61: * The number of rows of the matrix A. M >= 0, and if
! 62: * UPLO = 'U', M <= N. When M = 0, DLANTR is set to zero.
! 63: *
! 64: * N (input) INTEGER
! 65: * The number of columns of the matrix A. N >= 0, and if
! 66: * UPLO = 'L', N <= M. When N = 0, DLANTR is set to zero.
! 67: *
! 68: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
! 69: * The trapezoidal matrix A (A is triangular if M = N).
! 70: * If UPLO = 'U', the leading m by n upper trapezoidal part of
! 71: * the array A contains the upper trapezoidal matrix, and the
! 72: * strictly lower triangular part of A is not referenced.
! 73: * If UPLO = 'L', the leading m by n lower trapezoidal part of
! 74: * the array A contains the lower trapezoidal matrix, and the
! 75: * strictly upper triangular part of A is not referenced. Note
! 76: * that when DIAG = 'U', the diagonal elements of A are not
! 77: * referenced and are assumed to be one.
! 78: *
! 79: * LDA (input) INTEGER
! 80: * The leading dimension of the array A. LDA >= max(M,1).
! 81: *
! 82: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 83: * where LWORK >= M when NORM = 'I'; otherwise, WORK is not
! 84: * referenced.
! 85: *
! 86: * =====================================================================
! 87: *
! 88: * .. Parameters ..
! 89: DOUBLE PRECISION ONE, ZERO
! 90: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 91: * ..
! 92: * .. Local Scalars ..
! 93: LOGICAL UDIAG
! 94: INTEGER I, J
! 95: DOUBLE PRECISION SCALE, SUM, VALUE
! 96: * ..
! 97: * .. External Subroutines ..
! 98: EXTERNAL DLASSQ
! 99: * ..
! 100: * .. External Functions ..
! 101: LOGICAL LSAME
! 102: EXTERNAL LSAME
! 103: * ..
! 104: * .. Intrinsic Functions ..
! 105: INTRINSIC ABS, MAX, MIN, SQRT
! 106: * ..
! 107: * .. Executable Statements ..
! 108: *
! 109: IF( MIN( M, N ).EQ.0 ) THEN
! 110: VALUE = ZERO
! 111: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 112: *
! 113: * Find max(abs(A(i,j))).
! 114: *
! 115: IF( LSAME( DIAG, 'U' ) ) THEN
! 116: VALUE = ONE
! 117: IF( LSAME( UPLO, 'U' ) ) THEN
! 118: DO 20 J = 1, N
! 119: DO 10 I = 1, MIN( M, J-1 )
! 120: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 121: 10 CONTINUE
! 122: 20 CONTINUE
! 123: ELSE
! 124: DO 40 J = 1, N
! 125: DO 30 I = J + 1, M
! 126: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 127: 30 CONTINUE
! 128: 40 CONTINUE
! 129: END IF
! 130: ELSE
! 131: VALUE = ZERO
! 132: IF( LSAME( UPLO, 'U' ) ) THEN
! 133: DO 60 J = 1, N
! 134: DO 50 I = 1, MIN( M, J )
! 135: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 136: 50 CONTINUE
! 137: 60 CONTINUE
! 138: ELSE
! 139: DO 80 J = 1, N
! 140: DO 70 I = J, M
! 141: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 142: 70 CONTINUE
! 143: 80 CONTINUE
! 144: END IF
! 145: END IF
! 146: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
! 147: *
! 148: * Find norm1(A).
! 149: *
! 150: VALUE = ZERO
! 151: UDIAG = LSAME( DIAG, 'U' )
! 152: IF( LSAME( UPLO, 'U' ) ) THEN
! 153: DO 110 J = 1, N
! 154: IF( ( UDIAG ) .AND. ( J.LE.M ) ) THEN
! 155: SUM = ONE
! 156: DO 90 I = 1, J - 1
! 157: SUM = SUM + ABS( A( I, J ) )
! 158: 90 CONTINUE
! 159: ELSE
! 160: SUM = ZERO
! 161: DO 100 I = 1, MIN( M, J )
! 162: SUM = SUM + ABS( A( I, J ) )
! 163: 100 CONTINUE
! 164: END IF
! 165: VALUE = MAX( VALUE, SUM )
! 166: 110 CONTINUE
! 167: ELSE
! 168: DO 140 J = 1, N
! 169: IF( UDIAG ) THEN
! 170: SUM = ONE
! 171: DO 120 I = J + 1, M
! 172: SUM = SUM + ABS( A( I, J ) )
! 173: 120 CONTINUE
! 174: ELSE
! 175: SUM = ZERO
! 176: DO 130 I = J, M
! 177: SUM = SUM + ABS( A( I, J ) )
! 178: 130 CONTINUE
! 179: END IF
! 180: VALUE = MAX( VALUE, SUM )
! 181: 140 CONTINUE
! 182: END IF
! 183: ELSE IF( LSAME( NORM, 'I' ) ) THEN
! 184: *
! 185: * Find normI(A).
! 186: *
! 187: IF( LSAME( UPLO, 'U' ) ) THEN
! 188: IF( LSAME( DIAG, 'U' ) ) THEN
! 189: DO 150 I = 1, M
! 190: WORK( I ) = ONE
! 191: 150 CONTINUE
! 192: DO 170 J = 1, N
! 193: DO 160 I = 1, MIN( M, J-1 )
! 194: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
! 195: 160 CONTINUE
! 196: 170 CONTINUE
! 197: ELSE
! 198: DO 180 I = 1, M
! 199: WORK( I ) = ZERO
! 200: 180 CONTINUE
! 201: DO 200 J = 1, N
! 202: DO 190 I = 1, MIN( M, J )
! 203: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
! 204: 190 CONTINUE
! 205: 200 CONTINUE
! 206: END IF
! 207: ELSE
! 208: IF( LSAME( DIAG, 'U' ) ) THEN
! 209: DO 210 I = 1, N
! 210: WORK( I ) = ONE
! 211: 210 CONTINUE
! 212: DO 220 I = N + 1, M
! 213: WORK( I ) = ZERO
! 214: 220 CONTINUE
! 215: DO 240 J = 1, N
! 216: DO 230 I = J + 1, M
! 217: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
! 218: 230 CONTINUE
! 219: 240 CONTINUE
! 220: ELSE
! 221: DO 250 I = 1, M
! 222: WORK( I ) = ZERO
! 223: 250 CONTINUE
! 224: DO 270 J = 1, N
! 225: DO 260 I = J, M
! 226: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
! 227: 260 CONTINUE
! 228: 270 CONTINUE
! 229: END IF
! 230: END IF
! 231: VALUE = ZERO
! 232: DO 280 I = 1, M
! 233: VALUE = MAX( VALUE, WORK( I ) )
! 234: 280 CONTINUE
! 235: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 236: *
! 237: * Find normF(A).
! 238: *
! 239: IF( LSAME( UPLO, 'U' ) ) THEN
! 240: IF( LSAME( DIAG, 'U' ) ) THEN
! 241: SCALE = ONE
! 242: SUM = MIN( M, N )
! 243: DO 290 J = 2, N
! 244: CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
! 245: 290 CONTINUE
! 246: ELSE
! 247: SCALE = ZERO
! 248: SUM = ONE
! 249: DO 300 J = 1, N
! 250: CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
! 251: 300 CONTINUE
! 252: END IF
! 253: ELSE
! 254: IF( LSAME( DIAG, 'U' ) ) THEN
! 255: SCALE = ONE
! 256: SUM = MIN( M, N )
! 257: DO 310 J = 1, N
! 258: CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
! 259: $ SUM )
! 260: 310 CONTINUE
! 261: ELSE
! 262: SCALE = ZERO
! 263: SUM = ONE
! 264: DO 320 J = 1, N
! 265: CALL DLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
! 266: 320 CONTINUE
! 267: END IF
! 268: END IF
! 269: VALUE = SCALE*SQRT( SUM )
! 270: END IF
! 271: *
! 272: DLANTR = VALUE
! 273: RETURN
! 274: *
! 275: * End of DLANTR
! 276: *
! 277: END
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