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